Update Content - 2025-07-18

PhDthesis were categorized as articles.
Add "fron matter" to specify zettels category

.gitignore

@@ -1,3 +1,4 @@
 nohup.out
 resources/
 public/
+static/ltximg/

config.toml

@@ -26,11 +26,11 @@ changefreq = "weekly"
 priority = 0.5
 filename = "sitemap.xml"
 
-[[menu.main]]
+# [[menu.main]]
-name = "Home"
+# name = "Home"
-weight = 10
+# weight = 10
-identifier = "home"
+# identifier = "home"
-url = "/"
+# url = "/"
 
 [[menu.main]]
 name = "Zettels"
@@ -121,9 +121,9 @@ enable = false
 hint = 30
 warn = 180
 
-[params.utterances]       # https://utteranc.es/
+# [params.utterances]       # https://utteranc.es/
-repo = "tdehaeze/brain-dump-comments"
+# repo = "tdehaeze/brain-dump-comments"
-theme = "boxy-light"
+# theme = "boxy-light"
 
 [params.valine]
 enable = false

content/article/alkhatib03_activ_struc_vibrat_contr.md

@@ -1,6 +1,6 @@
 +++
 title = "Active structural vibration control: a review"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
@@ -9,10 +9,10 @@ Tags
 
 
 Reference
-: ([Alkhatib and Golnaraghi 2003](#orgdec9959))
+: (<a href="#citeproc_bib_item_1">Alkhatib and Golnaraghi 2003</a>)
 
 Author(s)
-: Alkhatib, R., & Golnaraghi, M. F.
+: Alkhatib, R., &amp; Golnaraghi, M. F.
 
 Year
 : 2003
@@ -75,7 +75,7 @@ The major restriction to the application of feedforward adaptive filtering is th
 
 <a id="table--table:comparison-constrol-strat"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--table:comparison-constrol-strat">Table 1</a></span>:
+  <span class="table-number"><a href="#table--table:comparison-constrol-strat">Table 1</a>:</span>
   Comparison of control strategies
 </div>
 
@@ -123,14 +123,14 @@ Uncertainty can be divided into four types:
 -   neglected nonlinearities
 
 The \\(\mathcal{H}\_\infty\\)  controller is developed to address uncertainty by systematic means.
-A general block diagram of the control system is shown figure [1](#orgd2fc896).
+A general block diagram of the control system is shown [Figure 1](#figure--fig:alkhatib03-hinf-control).
 
 A **frequency shaped filter** \\(W(s)\\) coupled to selected inputs and outputs of the plant is included.
 The outputs of this frequency shaped filter define the error ouputs used to evaluate the system performance and generate the **cost** that will be used in the design process.
 
-<a id="orgd2fc896"></a>
+<a id="figure--fig:alkhatib03-hinf-control"></a>
 
-{{< figure src="/ox-hugo/alkhatib03_hinf_control.png" caption="Figure 1: Block diagram for robust control" >}}
+{{< figure src="/ox-hugo/alkhatib03_hinf_control.png" caption="<span class=\"figure-number\">Figure 1: </span>Block diagram for robust control" >}}
 
 The generalized plan \\(G\\) can be partitionned according to the input-output variables. And we have that the transfer function matrix from \\(d\\) to \\(z\\) is:
 \\[ H\_{z/d} = G\_{z/d} + G\_{z/u} K (I - G\_{y/u} K)^{-1} G\_{y/d} \\]
@@ -144,7 +144,7 @@ The objective of \\(\mathcal{H}\_\infty\\) control is to design an admissible co
 The control \\(u(t)\\) is designed to minimize a cost function \\(J\\), given the initial conditions \\(z(t\_0)\\) and \\(\dot{z}(t\_0)\\) subject to the constraint that:
 
 \begin{align\*}
-\dot{z} &= Az + Bu\\\\\\
+\dot{z} &= Az + Bu\\\\
 y &= Cz
 \end{align\*}
 
@@ -200,11 +200,11 @@ Two different methods
 
 ## Active Control Effects on the System {#active-control-effects-on-the-system}
 
-<a id="org4678494"></a>
+<a id="figure--fig:alkhatib03-1dof-control"></a>
 
-{{< figure src="/ox-hugo/alkhatib03_1dof_control.png" caption="Figure 2: 1 DoF control of a spring-mass-damping system" >}}
+{{< figure src="/ox-hugo/alkhatib03_1dof_control.png" caption="<span class=\"figure-number\">Figure 2: </span>1 DoF control of a spring-mass-damping system" >}}
 
-Consider the control system figure [2](#org4678494), the equation of motion of the system is:
+Consider the control system [Figure 2](#figure--fig:alkhatib03-1dof-control), the equation of motion of the system is:
 \\[ m\ddot{x} + c\dot{x} + kx = f\_a + f \\]
 
 The controller force can be expressed as: \\(f\_a = -g\_a \ddot{x} + g\_v \dot{x} + g\_d x\\). The equation of motion becomes:
@@ -225,7 +225,8 @@ The problem of optimizing the locations of the actuators can be more significant
 If the actuator is placed at the wrong location, the system will require a greater force control. In that case, the system is said to have a **low degree of controllability**.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgdec9959"></a>Alkhatib, Rabih, and M. F. Golnaraghi. 2003. “Active Structural Vibration Control: A Review.” _The Shock and Vibration Digest_ 35 (5):367–83. <https://doi.org/10.1177/05831024030355002>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Alkhatib, Rabih, and M. F. Golnaraghi. 2003. “Active Structural Vibration Control: A Review.” <i>The Shock and Vibration Digest</i> 35 (5): 367–83. doi:<a href="https://doi.org/10.1177/05831024030355002">10.1177/05831024030355002</a>.</div>
+</div>

content/article/bibel92_guidel_h.md

@@ -1,17 +1,17 @@
 +++
 title = "Guidelines for the selection of weighting functions for h-infinity control"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [H Infinity Control]({{< relref "h_infinity_control" >}})
+: [H Infinity Control]({{< relref "h_infinity_control.md" >}})
 
 Reference
-: ([Bibel and Malyevac 1992](#org395ccd3))
+: (<a href="#citeproc_bib_item_1">Bibel and Malyevac 1992</a>)
 
 Author(s)
-: Bibel, J. E., & Malyevac, D. S.
+: Bibel, J. E., &amp; Malyevac, D. S.
 
 Year
 : 1992
@@ -19,15 +19,15 @@ Year
 
 ## Properties of feedback control {#properties-of-feedback-control}
 
-<a id="orgd464a3c"></a>
+<a id="figure--fig:bibel92-control-diag"></a>
 
-{{< figure src="/ox-hugo/bibel92_control_diag.png" caption="Figure 1: Control System Diagram" >}}
+{{< figure src="/ox-hugo/bibel92_control_diag.png" caption="<span class=\"figure-number\">Figure 1: </span>Control System Diagram" >}}
 
-From the figure [1](#orgd464a3c), we have:
+From the [Figure 1](#figure--fig:bibel92-control-diag), we have:
 
 \begin{align\*}
-y(s) &= T(s) r(s) + S(s) d(s) - T(s) n(s)\\\\\\
+y(s) &= T(s) r(s) + S(s) d(s) - T(s) n(s)\\\\
-e(s) &= S(s) r(s) - S(s) d(s) - S(s) n(s)\\\\\\
+e(s) &= S(s) r(s) - S(s) d(s) - S(s) n(s)\\\\
 u(s) &= S(s)K(s) r(s) - S(s)K(s) d(s) - S(s)K(s) n(s)
 \end{align\*}
 
@@ -38,17 +38,15 @@ With the following definitions
 -   \\(T(s) = [I+G(s)K(s)]^{-1}G(s)K(s)\\) is the **Transmissibility** function matrix
 
 <div class="cbox">
-  <div></div>
 
 \\[ S(s) + T(s) = 1 \\]
 
 </div>
 
 <div class="cbox">
-  <div></div>
 
--   **Command following**: \\(S=0\\) and \\(T=1\\) => large gains
+-   **Command following**: \\(S=0\\) and \\(T=1\\) =&gt; large gains
--   **Disturbance rejection**: \\(S=0\\) => large gains
+-   **Disturbance rejection**: \\(S=0\\) =&gt; large gains
 -   **Sensor noise attenuation**: \\(T\\) small where the noise is concentrated
 -   **Control Sensitivity minimization**: \\(K S\\) small
 -   **Robustness to modeling errors**: \\(T\\) small in the frequency range of the expected model undertainties
@@ -68,20 +66,19 @@ We must determine some **tradeoff** between the sensitivity and the complementar
 Usually, reference signals and disturbances occur at low frequencies, while noise and modeling errors are concentrated at high frequencies. The tradeoff, in a SISO sense, is to make \\(|S(j\omega)|\\) small as low frequencies and \\(|T(j\omega)|\\) small at high frequencies.
 
 
-## \\(H\_\infty\\) and weighting functions {#h-infty--and-weighting-functions}
+## \\(H\_\infty\\) and weighting functions {#h-infty-and-weighting-functions}
 
 <div class="cbox">
-  <div></div>
 
 \\(\mathcal{H}\_\infty\\) control is a design technique with a state-space computation solution that utilizes frequency-dependent weighting functions to tune the controller's performance and robustness characteristics.
 
 </div>
 
-<a id="orgf088f75"></a>
+<a id="figure--fig:bibel92-general-plant"></a>
 
-{{< figure src="/ox-hugo/bibel92_general_plant.png" caption="Figure 2: \\(\mathcal{H}\_\infty\\) control framework" >}}
+{{< figure src="/ox-hugo/bibel92_general_plant.png" caption="<span class=\"figure-number\">Figure 2: </span>\\(\mathcal{H}\_\infty\\) control framework" >}}
 
-New design framework (figure [2](#orgf088f75)): \\(P(s)\\) is the **generalized plant** transfer function matrix:
+New design framework ([Figure 2](#figure--fig:bibel92-general-plant)): \\(P(s)\\) is the **generalized plant** transfer function matrix:
 
 -   \\(w\\): exogenous inputs
 -   \\(z\\): regulated performance output
@@ -89,7 +86,7 @@ New design framework (figure [2](#orgf088f75)): \\(P(s)\\) is the **generalized
 -   \\(y\\): measured output variables
 
 The plant \\(P\\) has two inputs and two outputs, it can be decomposed into four sub-transfer function matrices:
-\\[P = \begin{bmatrix}P\_{11} & P\_{12} \\ P\_{21} & P\_{22} \end{bmatrix}\\]
+\\[P = \begin{bmatrix}P\_{11} & P\_{12} \\\ P\_{21} & P\_{22} \end{bmatrix}\\]
 
 
 ## Lower Linear Fractional Transformation {#lower-linear-fractional-transformation}
@@ -97,7 +94,6 @@ The plant \\(P\\) has two inputs and two outputs, it can be decomposed into four
 The transformation from the input \\(w\\) to the output \\(z\\), \\(T\_{zw}\\) is called the **Lower Linear Fractional Transformation** \\(F\_l (P, K)\\).
 
 <div class="cbox">
-  <div></div>
 
 \\[T\_{zw} = F\_l (P, K) = P\_{11} + P\_{12}K (I-P\_{22})^{-1} P\_{21}\\]
 
@@ -108,25 +104,24 @@ The \\(H\_\infty\\) control problem is to find a controller that minimizes \\(\\
 
 ## Weights for inputs/outputs signals {#weights-for-inputs-outputs-signals}
 
-Since \\(S\\) and \\(T\\) cannot be minimized together at all frequency, **weights are introduced to shape the solutions**. Not only can \\(S\\) and \\(T\\) be weighted, but other regulated performance variables and inputs (figure [3](#orgff0b295)).
+Since \\(S\\) and \\(T\\) cannot be minimized together at all frequency, **weights are introduced to shape the solutions**. Not only can \\(S\\) and \\(T\\) be weighted, but other regulated performance variables and inputs ([Figure 3](#figure--fig:bibel92-hinf-weights)).
 
-<a id="orgff0b295"></a>
+<a id="figure--fig:bibel92-hinf-weights"></a>
 
-{{< figure src="/ox-hugo/bibel92_hinf_weights.png" caption="Figure 3: Input and Output weights in \\(\mathcal{H}\_\infty\\) framework" >}}
+{{< figure src="/ox-hugo/bibel92_hinf_weights.png" caption="<span class=\"figure-number\">Figure 3: </span>Input and Output weights in \\(\mathcal{H}\_\infty\\) framework" >}}
 
 The weights on the input and output variables are selected to reflect the spatial and **frequency dependence** of the respective signals and performance specifications.
 
 These inputs and output weighting functions are defined as rational, stable and **minimum-phase transfer function** (no poles or zero in the right half plane).
 
 
-## General Guidelines for Weight Selection: \\(W\_S\\) {#general-guidelines-for-weight-selection--w-s}
+## General Guidelines for Weight Selection: \\(W\_S\\) {#general-guidelines-for-weight-selection-w-s}
 
 \\(W\_S\\) is selected to reflect the desired **performance characteristics**.
 The sensitivity function \\(S\\) should have low gain at low frequency for good tracking performance and high gain at high frequencies to limit overshoot.
 We have to select \\(W\_S\\) such that \\({W\_S}^-1\\) reflects the desired shape of \\(S\\).
 
 <div class="cbox">
-  <div></div>
 
 -   **Low frequency gain**: set to the inverse of the desired steady state tracking error
 -   **High frequency gain**: set to limit overshoot (\\(0.1\\) to \\(0.5\\) is a good compromise between overshoot and response speed)
@@ -135,12 +130,11 @@ We have to select \\(W\_S\\) such that \\({W\_S}^-1\\) reflects the desired shap
 </div>
 
 
-## General Guidelines for Weight Selection: \\(W\_T\\) {#general-guidelines-for-weight-selection--w-t}
+## General Guidelines for Weight Selection: \\(W\_T\\) {#general-guidelines-for-weight-selection-w-t}
 
 We want \\(T\\) near unity for good tracking of reference and near zero for noise suppresion.
 
 <div class="cbox">
-  <div></div>
 
 A high pass weight is usualy used on \\(T\\) because the noise energy is mostly concentrated at high frequencies. It should have the following characteristics:
 
@@ -154,17 +148,17 @@ When using both \\(W\_S\\) and \\(W\_T\\), it is important to make sure that the
 
 ## Unmodeled dynamics weighting function {#unmodeled-dynamics-weighting-function}
 
-Another method of limiting the controller bandwidth and providing high frequency gain attenuation is to use a high pass weight on an **unmodeled dynamics uncertainty block** that may be added from the plant input to the plant output (figure [4](#orgc150230)).
+Another method of limiting the controller bandwidth and providing high frequency gain attenuation is to use a high pass weight on an **unmodeled dynamics uncertainty block** that may be added from the plant input to the plant output ([Figure 4](#figure--fig:bibel92-unmodeled-dynamics)).
 
-<a id="orgc150230"></a>
+<a id="figure--fig:bibel92-unmodeled-dynamics"></a>
 
-{{< figure src="/ox-hugo/bibel92_unmodeled_dynamics.png" caption="Figure 4: Unmodeled dynamics model" >}}
+{{< figure src="/ox-hugo/bibel92_unmodeled_dynamics.png" caption="<span class=\"figure-number\">Figure 4: </span>Unmodeled dynamics model" >}}
 
-The weight is chosen to cover the expected worst case magnitude of the unmodeled dynamics. A typical unmodeled dynamics weighting function is shown figure [5](#org42e3b7d).
+The weight is chosen to cover the expected worst case magnitude of the unmodeled dynamics. A typical unmodeled dynamics weighting function is shown [Figure 5](#figure--fig:bibel92-weight-dynamics).
 
-<a id="org42e3b7d"></a>
+<a id="figure--fig:bibel92-weight-dynamics"></a>
 
-{{< figure src="/ox-hugo/bibel92_weight_dynamics.png" caption="Figure 5: Example of unmodeled dynamics weight" >}}
+{{< figure src="/ox-hugo/bibel92_weight_dynamics.png" caption="<span class=\"figure-number\">Figure 5: </span>Example of unmodeled dynamics weight" >}}
 
 
 ## Inputs and Output weighting function {#inputs-and-output-weighting-function}
@@ -182,7 +176,8 @@ Typically actuator input weights are constant over frequency and set at the inve
 **The order of the weights should be kept reasonably low** to reduce the order of th resulting optimal compensator and avoid potential convergence problems in the DK interactions.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org395ccd3"></a>Bibel, John E, and D Stephen Malyevac. 1992. “Guidelines for the Selection of Weighting Functions for H-Infinity Control.” NAVAL SURFACE WARFARE CENTER DAHLGREN DIV VA.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Bibel, John E, and D Stephen Malyevac. 1992. “Guidelines for the Selection of Weighting Functions for H-Infinity Control.” NAVAL SURFACE WARFARE CENTER DAHLGREN DIV VA.</div>
+</div>

content/article/bryson93_contr_spacec_aircr.md

@@ -1,6 +1,6 @@
 +++
 title = "Control of spacecraft and aircraft"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
@@ -9,7 +9,7 @@ Tags
 
 
 Reference
-: ([Bryson 1993](#org14ecce3))
+: (<a href="#citeproc_bib_item_1">Bryson 1993</a>)
 
 Author(s)
 : Bryson, A. E.
@@ -20,7 +20,7 @@ Year
 
 ## 9.2.3 Roll-Off Filters {#9-dot-2-dot-3-roll-off-filters}
 
-[Spillover Effect]({{< relref "spillover_effect" >}})
+[Spillover Effect]({{< relref "spillover_effect.md" >}})
 
 > Synthesizing control logic using only one vibration mode means we are consciously **neglecting the higher-order vibration modes**.
 > When doing this, it is a good idea to insert "roll-off" into the control logic, so that the loop-transfer gain decreases rapidly with frequency beyond the control bandwidth.
@@ -38,20 +38,21 @@ Year
 > If a rate sensor is not co-located with an actuator on a flexible body, ans its signal is fed back to the actuator, some vibration modes are stabilized and others are destabilized, depending on the location of the sensor relative to the actuator.
 
 
-## 9.5.2 Low-Authority Control/High-Authority Control [HAC-HAC]({{< relref "hac_hac" >}}) {#9-dot-5-dot-2-low-authority-control-high-authority-control-hac-hac--hac-hac-dot-md}
+## 9.5.2 Low-Authority Control/High-Authority Control [HAC-HAC]({{< relref "hac_hac.md" >}}) {#9-dot-5-dot-2-low-authority-control-high-authority-control-hac-hac--hac-hac-dot-md}
 
-> Figure [fig:bryson93_hac_lac](#fig:bryson93_hac_lac) shows the concept of Low-Authority Control/High-Authority Control (LAC/HAC) is the s-plane.
+> [Figure 1](#figure--fig:bryson93-hac-lac) shows the concept of Low-Authority Control/High-Authority Control (LAC/HAC) is the s-plane.
 > LAC uses a co-located rate sensor to add damping to all the vibratory modes (but not the rigid-body mode).
 > HAC uses a separated displacement sensor to stabilize the rigid body mode, which slightly decreases the damping of the vibratory modes but not enough to produce instability (called "spillover")
 
-<a id="orgc9c1915"></a>
+<a id="figure--fig:bryson93-hac-lac"></a>
 
-{{< figure src="/ox-hugo/bryson93_hac_lac.png" caption="Figure 1: HAC-LAC control concept" >}}
+{{< figure src="/ox-hugo/bryson93_hac_lac.png" caption="<span class=\"figure-number\">Figure 1: </span>HAC-LAC control concept" >}}
 
 > LAC/HAC is usually insensitive to small deviation of the plant dynamics away from the design values, that is, it is **robust** to plant parameter changes.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org14ecce3"></a>Bryson, Arthur Earl. 1993. _Control of Spacecraft and Aircraft_. Princeton university press Princeton, New Jersey.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Bryson, Arthur Earl. 1993. <i>Control of Spacecraft and Aircraft</i>. Princeton university press Princeton, New Jersey.</div>
+</div>

content/article/butler11_posit_contr_lithog_equip.md

@@ -1,14 +1,14 @@
 +++
 title = "Position control in lithographic equipment"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
-: [Multivariable Control]({{< relref "multivariable_control" >}}), [Positioning Stations]({{< relref "positioning_stations" >}})
+: [Multivariable Control]({{< relref "multivariable_control.md" >}}), [Positioning Stations]({{< relref "positioning_stations.md" >}})
 
 Reference
-: ([Butler 2011](#org338ffef))
+: (<a href="#citeproc_bib_item_1">Butler 2011</a>)
 
 Author(s)
 : Butler, H.
@@ -17,7 +17,8 @@ Year
 : 2011
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org338ffef"></a>Butler, Hans. 2011. “Position Control in Lithographic Equipment.” _IEEE Control Systems_ 31 (5):28–47. <https://doi.org/10.1109/mcs.2011.941882>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Butler, Hans. 2011. “Position Control in Lithographic Equipment.” <i>IEEE Control Systems</i> 31 (5): 28–47. doi:<a href="https://doi.org/10.1109/mcs.2011.941882">10.1109/mcs.2011.941882</a>.</div>
+</div>

content/article/chen00_ident_decoup_contr_flexur_joint_hexap.md

@@ -1,17 +1,17 @@
 +++
 title = "Identification and decoupling control of flexure jointed hexapods"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}})
 
 Reference
-: ([Chen and McInroy 2000](#org1c74a9c))
+: (<a href="#citeproc_bib_item_1">Chen and McInroy 2000</a>)
 
 Author(s)
-: Chen, Y., & McInroy, J.
+: Chen, Y., &amp; McInroy, J.
 
 Year
 : 2000
@@ -31,7 +31,7 @@ Year
 
 ## Introduction {#introduction}
 
-Typical decoupling algorithm ([Decoupled Control]({{< relref "decoupled_control" >}})) impose two constraints:
+Typical decoupling algorithm ([Decoupled Control]({{< relref "decoupled_control.md" >}})) impose two constraints:
 
 -   the payload mass/inertia matrix is diagonal
 -   the geometry of the platform and attachment of the payload must be carefully chosen
@@ -43,11 +43,11 @@ The algorithm derived herein removes these constraints, thus greatly expanding t
 
 ## Dynamic Model of Flexure Jointed Hexapods {#dynamic-model-of-flexure-jointed-hexapods}
 
-The derivation of the dynamic model is done in ([McInroy 1999](#orgebf33dd)) ([Notes]({{< relref "mcinroy99_dynam" >}})).
+The derivation of the dynamic model is done in (<a href="#citeproc_bib_item_2">McInroy 1999</a>) ([Notes]({{< relref "mcinroy99_dynam.md" >}})).
 
-<a id="orga594879"></a>
+<a id="figure--fig:chen00-flexure-hexapod"></a>
 
-{{< figure src="/ox-hugo/chen00_flexure_hexapod.png" caption="Figure 1: A flexured joint Hexapod. {P} is a cartesian coordiante frame located at (and rigidly connected to) the payload's center of mass. {B} is a frame attached to the (possibly moving) base, and {U} is a universal inertial frame of reference" >}}
+{{< figure src="/ox-hugo/chen00_flexure_hexapod.png" caption="<span class=\"figure-number\">Figure 1: </span>A flexured joint Hexapod. {P} is a cartesian coordiante frame located at (and rigidly connected to) the payload's center of mass. {B} is a frame attached to the (possibly moving) base, and {U} is a universal inertial frame of reference" >}}
 
 In the joint space, the dynamics of a flexure jointed hexapod are written as:
 
@@ -56,9 +56,9 @@ In the joint space, the dynamics of a flexure jointed hexapod are written as:
 \end{equation}
 
 \begin{aligned}
-  & \left( {}^U\_P\bm{R} {}^P\bm{M}\_x {}^B\_P\bm{R}^T \bm{J}^{-1} \right) \ddot{\vec{l}} + \\\\\\
+  & \left( {}^U\_P\bm{R} {}^P\bm{M}\_x {}^B\_P\bm{R}^T \bm{J}^{-1} \right) \ddot{\vec{l}} + \\\\
-  & {}^U\_B\bm{R} \bm{J}^T \bm{B} \dot{\vec{l}} + {}^U\_B\bm{R}\bm{J}^T \bm{K}(\vec{l} - \vec{l}\_r) = \\\\\\
+  & {}^U\_B\bm{R} \bm{J}^T \bm{B} \dot{\vec{l}} + {}^U\_B\bm{R}\bm{J}^T \bm{K}(\vec{l} - \vec{l}\_r) = \\\\
-  & {}^U\_B\bm{R} \bm{J}^T \vec{f}\_m + \vec{\mathcal{F}}\_e + \vec{\mathcal{F}} + \vec{\mathcal{C}} - \\\\\\
+  & {}^U\_B\bm{R} \bm{J}^T \vec{f}\_m + \vec{\mathcal{F}}\_e + \vec{\mathcal{F}} + \vec{\mathcal{C}} - \\\\
   & \left( {}^U\_B\bm{R} \bm{J}^T \bm{M}\_s + {}^U\_P\bm{R} {}^P\bm{M}\_x {}^U\_P\bm{R}^T \bm{J}\_c \bm{J}\_B^{-1} \right) \ddot{\vec{q}}\_s
 \end{aligned}
 
@@ -79,7 +79,7 @@ where:
 -   \\(\vec{\mathcal{G}}\\) is a vector containing all gravity terms
 
 \begin{aligned}
-  \bm{M}\_p & \ddot{\vec{p}}\_s + \bm{B} \dot{\vec{p}}\_s + \bm{K} \vec{p}\_s = \vec{f}\_m + \\\\\\
+  \bm{M}\_p & \ddot{\vec{p}}\_s + \bm{B} \dot{\vec{p}}\_s + \bm{K} \vec{p}\_s = \vec{f}\_m + \\\\
   & \bm{M}\_q \ddot{\vec{q}}\_s + \bm{B} \dot{\vec{q}}\_s + \bm{J}^{-T} {}^U\_B\bm{R}^T \vec{\mathcal{F}}\_e
 \end{aligned}
 
@@ -100,9 +100,9 @@ where
 ## Experimental Results {#experimental-results}
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org1c74a9c"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In _Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)_, nil. <https://doi.org/10.1109/robot.2000.844878>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
-
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Chen, Yixin, and J.E. McInroy. 2000. “Identification and Decoupling Control of Flexure Jointed Hexapods.” In <i>Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065)</i>. doi:<a href="https://doi.org/10.1109/robot.2000.844878">10.1109/robot.2000.844878</a>.</div>
-<a id="orgebf33dd"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In <i>Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)</i>. doi:<a href="https://doi.org/10.1109/cca.1999.806694">10.1109/cca.1999.806694</a>.</div>
+</div>

content/article/chen04_decoup_contr_flexur_joint_hexap.md

@@ -1,14 +1,14 @@
 +++
 title = "Decoupled control of flexure-jointed hexapods using estimated joint-space mass-inertia matrix"
 author = ["Thomas Dehaeze"]
-draft = false
+draft = true
 +++
 
 Tags
 : [Decoupled Control]({{<relref "decoupled_control.md#" >}})
 
 Reference
-: ([Chen and McInroy 2004](#orgbe5d3d7))
+: ([Chen and McInroy 2004](#org1a36c5c))
 
 Author(s)
 : Chen, Y., & McInroy, J.
@@ -20,4 +20,4 @@ Year
 
 ## Bibliography {#bibliography}
 
-<a id="orgbe5d3d7"></a>Chen, Y., and J.E. McInroy. 2004. “Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix.” _IEEE Transactions on Control Systems Technology_ 12 (3):413–21. <https://doi.org/10.1109/tcst.2004.824339>.
+<a id="org1a36c5c"></a>Chen, Y., and J.E. McInroy. 2004. “Decoupled Control of Flexure-Jointed Hexapods Using Estimated Joint-Space Mass-Inertia Matrix.” _IEEE Transactions on Control Systems Technology_ 12 (3):413–21. <https://doi.org/10.1109/tcst.2004.824339>.

content/article/claeyssen07_amplif_piezoel_actuat.md

@@ -1,17 +1,17 @@
 +++
 title = "Amplified piezoelectric actuators: static & dynamic applications"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
+: [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}})
 
 Reference
-: ([Claeyssen et al. 2007](#org66395f6))
+: (<a href="#citeproc_bib_item_1">Claeyssen et al. 2007</a>)
 
 Author(s)
-: Claeyssen, F., Letty, R. L., Barillot, F., & Sosnicki, O.
+: Claeyssen, F., Letty, R. L., Barillot, F., &amp; Sosnicki, O.
 
 Year
 : 2007
@@ -34,7 +34,8 @@ The maximum dynamic force achievable by the actuator is determined by the prestr
 The prestress design allows a peak force equal to half the blocked force.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org66395f6"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static &#38; Dynamic Applications.” <i>Ferroelectrics</i> 351 (1): 3–14. doi:<a href="https://doi.org/10.1080/00150190701351865">10.1080/00150190701351865</a>.</div>
+</div>

content/article/collette11_review_activ_vibrat_isolat_strat.md

@@ -1,17 +1,17 @@
 +++
 title = "Review of active vibration isolation strategies"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Collette, Janssens, and Artoos 2011](#orgc3712d7))
+: (<a href="#citeproc_bib_item_1">Collette, Janssens, and Artoos 2011</a>)
 
 Author(s)
-: Collette, C., Janssens, S., & Artoos, K.
+: Collette, C., Janssens, S., &amp; Artoos, K.
 
 Year
 : 2011
@@ -51,7 +51,7 @@ The general expression of the force delivered by the actuator is \\(f = g\_a \dd
 
 <a id="table--table:active-isolation"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--table:active-isolation">Table 1</a></span>:
+  <span class="table-number"><a href="#table--table:active-isolation">Table 1</a>:</span>
   Active isolation techniques
 </div>
 
@@ -70,12 +70,13 @@ The general expression of the force delivered by the actuator is \\(f = g\_a \dd
 
 ## Conclusions {#conclusions}
 
-<a id="orgdceedb5"></a>
+<a id="figure--fig:collette11-comp-isolation-strategies"></a>
-
-{{< figure src="/ox-hugo/collette11_comp_isolation_strategies.png" caption="Figure 1: Comparison of Active Vibration Isolation Strategies" >}}
 
+{{< figure src="/ox-hugo/collette11_comp_isolation_strategies.png" caption="<span class=\"figure-number\">Figure 1: </span>Comparison of Active Vibration Isolation Strategies" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="orgc3712d7"></a>Collette, Christophe, Stef Janssens, and Kurt Artoos. 2011. “Review of Active Vibration Isolation Strategies.” _Recent Patents on Mechanical Engineeringe_ 4 (3):212–19. <https://doi.org/10.2174/2212797611104030212>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Collette, Christophe, Stef Janssens, and Kurt Artoos. 2011. “Review of Active Vibration Isolation Strategies.” <i>Recent Patents on Mechanical Engineeringe</i> 4 (3): 212–19. doi:<a href="https://doi.org/10.2174/2212797611104030212">10.2174/2212797611104030212</a>.</div>
+</div>

content/article/collette14_vibrat.md

@@ -1,17 +1,17 @@
 +++
 title = "Vibration control of flexible structures using fusion of inertial sensors and hyper-stable actuator-sensor pairs"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Sensor Fusion]({{< relref "sensor_fusion" >}})
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Sensor Fusion]({{< relref "sensor_fusion.md" >}})
 
 Reference
-: ([Collette and Matichard 2014](#org6b92a7c))
+: (<a href="#citeproc_bib_item_1">Collette and Matichard 2014</a>)
 
 Author(s)
-: Collette, C., & Matichard, F.
+: Collette, C., &amp; Matichard, F.
 
 Year
 : 2014
@@ -19,7 +19,7 @@ Year
 
 ## Introduction {#introduction}
 
-[Sensor Fusion]({{< relref "sensor_fusion" >}}) is used  to combine the benefits of different types of sensors:
+[Sensor Fusion]({{< relref "sensor_fusion.md" >}}) is used  to combine the benefits of different types of sensors:
 
 -   Relative sensor for DC positioning capability at low frequency
 -   Inertial sensors for isolation at high frequency
@@ -28,7 +28,7 @@ Year
 
 ## Different types of sensors {#different-types-of-sensors}
 
-In this paper, three types of sensors are used. Their advantages and disadvantages are summarized table [1](#table--tab:sensors).
+In this paper, three types of sensors are used. Their advantages and disadvantages are summarized [Table 1](#table--tab:sensors).
 
 > Several types of sensors can be used for the feedback control of vibration isolation systems:
 >
@@ -38,7 +38,7 @@ In this paper, three types of sensors are used. Their advantages and disadvantag
 
 <a id="table--tab:sensors"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:sensors">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:sensors">Table 1</a>:</span>
   Types of sensors
 </div>
 
@@ -51,11 +51,11 @@ In this paper, three types of sensors are used. Their advantages and disadvantag
 
 ## Inertial Control and sensor fusion configurations {#inertial-control-and-sensor-fusion-configurations}
 
-For a simple 1DoF model, two fusion-sensor configuration are studied. The results are summarized Table [2](#table--tab:fusion-trade-off).
+For a simple 1DoF model, two fusion-sensor configuration are studied. The results are summarized [Table 2](#table--tab:fusion-trade-off).
 
 <a id="table--tab:fusion-trade-off"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:fusion-trade-off">Table 2</a></span>:
+  <span class="table-number"><a href="#table--tab:fusion-trade-off">Table 2</a>:</span>
   Sensor fusion configurations
 </div>
 
@@ -100,7 +100,8 @@ Three types of sensors have been considered for the high frequency part of the f
 -   The fusion with a **force sensor** can be used to increase the loop gain with little effect on the compliance and passive isolation, provided that the blend is possible and that no active damping of flexible modes is required.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org6b92a7c"></a>Collette, C., and F Matichard. 2014. “Vibration Control of Flexible Structures Using Fusion of Inertial Sensors and Hyper-Stable Actuator-Sensor Pairs.” In _International Conference on Noise and Vibration Engineering (ISMA2014)_.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Collette, C., and F Matichard. 2014. “Vibration Control of Flexible Structures Using Fusion of Inertial Sensors and Hyper-Stable Actuator-Sensor Pairs.” In <i>International Conference on Noise and Vibration Engineering (ISMA2014)</i>.</div>
+</div>

content/article/collette15_sensor_fusion_method_high_perfor.md

@@ -1,17 +1,17 @@
 +++
 title = "Sensor fusion methods for high performance active vibration isolation systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Sensor Fusion]({{< relref "sensor_fusion.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Collette and Matichard 2015](#orgdf378e9))
+: (<a href="#citeproc_bib_item_1">Collette and Matichard 2015</a>)
 
 Author(s)
-: Collette, C., & Matichard, F.
+: Collette, C., &amp; Matichard, F.
 
 Year
 : 2015
@@ -25,7 +25,8 @@ The stability margins of the controller can be significantly increased with no o
 -   there exists a bandwidth where we can superimpose the open loop transfer functions obtained with the two sensors.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgdf378e9"></a>Collette, C., and F. Matichard. 2015. “Sensor Fusion Methods for High Performance Active Vibration Isolation Systems.” _Journal of Sound and Vibration_ 342 (nil):1–21. <https://doi.org/10.1016/j.jsv.2015.01.006>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Collette, C., and F. Matichard. 2015. “Sensor Fusion Methods for High Performance Active Vibration Isolation Systems.” <i>Journal of Sound and Vibration</i> 342: 1–21. doi:<a href="https://doi.org/10.1016/j.jsv.2015.01.006">10.1016/j.jsv.2015.01.006</a>.</div>
+</div>

content/article/csencsics20_explor_paret_front_actuat_techn.md

@@ -0,0 +1,123 @@
++++
+title = "Exploring the pareto fronts of actuation technologies for high performance mechatronic systems"
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (<a href="#citeproc_bib_item_1">Csencsics and Schitter 2020</a>)
+
+Author(s)
+: Csencsics, E., &amp; Schitter, G.
+
+Year
+: 2020
+
+
+## Abstract {#abstract}
+
+> This paper proposes a novel method for estimating the limitations of individual actuation technologies for a desired system class based on analytically obtained relations, which can be used to systematically trade off desired range and speed specifications in the design phase.
+> The method is presented along the example of **fast steering mirrors** with the tradeoff limit curves estimated for the established **piezoelectric**, **lorentz force** and **hybrid reluctance** actuation technologies.
+
+<a id="figure--fig:csencsics20-fsm-schematic"></a>
+
+{{< figure src="/ox-hugo/csencsics20_fsm_schematic.png" caption="<span class=\"figure-number\">Figure 1: </span>Fast Steering Mirror system. The main components are: mirror, actuators, position sensors and suspension system." >}}
+
+
+## Fast Steering Mirrors {#fast-steering-mirrors}
+
+
+### Application area and performance specification {#application-area-and-performance-specification}
+
+<a id="table--tab:fsm-requirements"></a>
+<div class="table-caption">
+  <span class="table-number"><a href="#table--tab:fsm-requirements">Table 1</a>:</span>
+  FSM performance requirements for two application
+</div>
+
+| Application       | Pointing        | Scanning |
+|-------------------|-----------------|----------|
+| System Range      | large           | large    |
+| System Dimensions | arbitrary       | compact  |
+| Main objective    | dist. rejection | tracking |
+| Bandwidth         | high            | high     |
+| Motion amplitude  | small           | large    |
+| Mover inertia     | arbitrary       | small    |
+| Precision         | high            | high     |
+
+
+### Safe operating area {#safe-operating-area}
+
+The concept of the Safe Operating Area (SOA) relates the frequency of a sinusoidal reference to the maximum admissible scan amplitude that still stays within the limits of the system.
+
+From figure [2](#figure--fig:csencsics20-soa) we can already see that piezo are typically used for system with high bandwidth and small range.
+
+<a id="figure--fig:csencsics20-soa"></a>
+
+{{< figure src="/ox-hugo/csencsics20_soa.png" caption="<span class=\"figure-number\">Figure 1: </span>Measured safe operating area of closed-loop FSM systems with sinusoidal reference signals. Piezo actuated in blue, lorentz force actuated in red and hybrid reluctance actuated in green." >}}
+
+
+## Limitations of actuator technology {#limitations-of-actuator-technology}
+
+
+### Piezo actuation {#piezo-actuation}
+
+Piezo actuated FMS are in general **high stiffness** system, for which the **bandwidth limitation** for feedback control is typically given by the **first mechanical resonance**.
+
+<a id="figure--fig:csencsics20-typical-piezo-fsm"></a>
+
+{{< figure src="/ox-hugo/csencsics20_typical_piezo_fsm.png" caption="<span class=\"figure-number\">Figure 1: </span>Piezo actuated FSM cross section" >}}
+
+The angular range of the FSM is:
+
+\begin{equation}
+\phi = \frac{L/1000}{2 d}
+\end{equation}
+
+with \\(L\\) the length of the stack, and d the distance between the stacks and the center of rotation (the factor 1000 is linked to the fact that typical piezo stack have a store equal to 0.1% of their length).
+
+The first resonance frequency is:
+
+\begin{equation}
+f\_{PZA} = \frac{1}{2\pi L}\sqrt{\frac{3E}{\rho\_\text{piezo}}}
+\end{equation}
+
+with \\(E\\) the elastic modulus and \\(\rho\_\text{piezo}\\) the density of the piezo material.
+
+As the resonance limits the achievable bandwidth, we therefore have that \\(f\_{\text{max,PZA}} \propto 1/\phi\\).
+
+
+### Lorentz force actuation {#lorentz-force-actuation}
+
+Lorentz force actuated FSM are in general **low stiffness** systems, which typically have a control bandwidth beyond the suspension mode that is usually limited by the **internal modes of the moving part**.
+
+The mover's mass is dominating the dynamics of low stiffness systems beyond the suspension mode.
+
+<a id="figure--fig:csencsics20-typical-lorentz-fsm"></a>
+
+{{< figure src="/ox-hugo/csencsics20_typical_lorentz_fsm.png" caption="<span class=\"figure-number\">Figure 1: </span>Lorentz force actuator designs." >}}
+
+\begin{equation}
+f\_\text{max,LFA} = \frac{1}{2\pi} k\_\text{LFA} \sqrt{\frac{1}{\phi J\_\text{init} + \Delta\_J + 2 d \phi^2}}
+\end{equation}
+
+
+### Hybrid reluctance force actuation {#hybrid-reluctance-force-actuation}
+
+<a id="figure--fig:csencsics20-typical-hybrid-reluctance-fsm"></a>
+
+{{< figure src="/ox-hugo/csencsics20_typical_hybrid_reluctance_fsm.png" caption="<span class=\"figure-number\">Figure 1: </span>Hybrid reluctance actuator designs" >}}
+
+
+## Pareto front estimates for FSM systems {#pareto-front-estimates-for-fsm-systems}
+
+<a id="figure--fig:csencsics20-pareto-estimate"></a>
+
+{{< figure src="/ox-hugo/csencsics20_pareto_estimate.png" caption="<span class=\"figure-number\">Figure 1: </span>Two dimensional performance space for FSM systems showing the tradeoff between range and bandwidth. Commercially available (symbols) as well as academically reported systems (dots) actuated by piezo (blue), Lorentz force (red) and reluctance actuators (green) are depicted." >}}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Csencsics, Ernst, and Georg Schitter. 2020. “Exploring the Pareto Fronts of Actuation Technologies for High Performance Mechatronic Systems.” <i>IEEE/ASME Transactions on Mechatronics</i>. IEEE.</div>
+</div>

content/article/dasgupta00_stewar_platf_manip.md

@@ -1,24 +1,24 @@
 +++
 title = "The stewart platform manipulator: a review"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}})
 
 Reference
-: ([Dasgupta and Mruthyunjaya 2000](#org9c198f3))
+: (<a href="#citeproc_bib_item_1">Dasgupta and Mruthyunjaya 2000</a>)
 
 Author(s)
-: Dasgupta, B., & Mruthyunjaya, T.
+: Dasgupta, B., &amp; Mruthyunjaya, T.
 
 Year
 : 2000
 
 <a id="table--tab:parallel-vs-serial-manipulators"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:parallel-vs-serial-manipulators">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:parallel-vs-serial-manipulators">Table 1</a>:</span>
   Parallel VS serial manipulators
 </div>
 
@@ -34,7 +34,8 @@ Year
 The generalized Stewart platforms consists of two rigid bodies (referred to as the base and the platform) connected through six extensible legs, each with spherical joints at both ends.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org9c198f3"></a>Dasgupta, Bhaskar, and T.S. Mruthyunjaya. 2000. “The Stewart Platform Manipulator: A Review.” _Mechanism and Machine Theory_ 35 (1):15–40. <https://doi.org/10.1016/s0094-114x(99)>00006-3.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Dasgupta, Bhaskar, and T.S. Mruthyunjaya. 2000. “The Stewart Platform Manipulator: A Review.” <i>Mechanism and Machine Theory</i> 35 (1): 15–40. doi:<a href="https://doi.org/10.1016/s0094-114x(99)00006-3">10.1016/s0094-114x(99)00006-3</a>.</div>
+</div>

content/article/devasia07_survey_contr_issues_nanop.md

@@ -1,6 +1,6 @@
 +++
 title = "A survey of control issues in nanopositioning"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
@@ -9,25 +9,26 @@ Tags
 
 
 Reference
-: ([Devasia, Eleftheriou, and Moheimani 2007](#orgfa66307))
+: (<a href="#citeproc_bib_item_1">Devasia, Eleftheriou, and Moheimani 2007</a>)
 
 Author(s)
-: Devasia, S., Eleftheriou, E., & Moheimani, S. R.
+: Devasia, S., Eleftheriou, E., &amp; Moheimani, S. R.
 
 Year
 : 2007
 
 -   Talks about Scanning Tunneling Microscope (STM) and Scanning Probe Microscope (SPM)
--   [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}}): Creep, Hysteresis, Vibrations, Modeling errors
+-   [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}}): Creep, Hysteresis, Vibrations, Modeling errors
 -   Interesting analysis about Bandwidth-Precision-Range tradeoffs
 -   Control approaches for piezoelectric actuators: feedforward, Feedback, Iterative, Sensorless controls
 
-<a id="orgd34b44a"></a>
+<a id="figure--fig:devasia07-piezoelectric-tradeoff"></a>
-
-{{< figure src="/ox-hugo/devasia07_piezoelectric_tradeoff.png" caption="Figure 1: Tradeoffs between bandwidth, precision and range" >}}
 
+{{< figure src="/ox-hugo/devasia07_piezoelectric_tradeoff.png" caption="<span class=\"figure-number\">Figure 1: </span>Tradeoffs between bandwidth, precision and range" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="orgfa66307"></a>Devasia, Santosh, Evangelos Eleftheriou, and SO Reza Moheimani. 2007. “A Survey of Control Issues in Nanopositioning.” _IEEE Transactions on Control Systems Technology_ 15 (5). IEEE:802–23.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Devasia, Santosh, Evangelos Eleftheriou, and SO Reza Moheimani. 2007. “A Survey of Control Issues in Nanopositioning.” <i>IEEE Transactions on Control Systems Technology</i> 15 (5). IEEE: 802–23.</div>
+</div>

content/article/fleming10_nanop_system_with_force_feedb.md

@@ -1,14 +1,14 @@
 +++
 title = "Nanopositioning system with force feedback for high-performance tracking and vibration control"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Force Sensors]({{< relref "force_sensors" >}})
+: [Sensor Fusion]({{< relref "sensor_fusion.md" >}}), [Force Sensors]({{< relref "force_sensors.md" >}})
 
 Reference
-: ([Fleming 2010](#org21788cf))
+: (<a href="#citeproc_bib_item_1">Fleming 2010</a>)
 
 Author(s)
 : Fleming, A.
@@ -31,9 +31,9 @@ Year
 
 ## Model of a multi-layer monolithic piezoelectric stack actuator {#model-of-a-multi-layer-monolithic-piezoelectric-stack-actuator}
 
-<a id="org699947b"></a>
+<a id="figure--fig:fleming10-piezo-model"></a>
 
-{{< figure src="/ox-hugo/fleming10_piezo_model.png" caption="Figure 1: Schematic of a multi-layer monolithic piezoelectric stack actuator model" >}}
+{{< figure src="/ox-hugo/fleming10_piezo_model.png" caption="<span class=\"figure-number\">Figure 1: </span>Schematic of a multi-layer monolithic piezoelectric stack actuator model" >}}
 
 The actuator experiences an internal stress in response to an applied voltage.
 This stress is represented by the voltage dependent force \\(F\_a\\) and is related to free displacement by
@@ -78,7 +78,7 @@ If an **n-layer** piezoelectric transducer is used as a force sensor, the genera
 
 We can use a **charge amplifier** to measure the force \\(F\_s\\).
 
-{{< figure src="/ox-hugo/fleming10_charge_ampl_piezo.png" caption="Figure 2: Electrical model of a piezoelectric force sensor is shown in gray. Developed charge \\(q\\) is proportional to the strain and hence the force experienced by the sensor. Op-amp charge amplifier produces an output voltage \\(V\_s\\) equal to \\(-q/C\_s\\)" >}}
+{{< figure src="/ox-hugo/fleming10_charge_ampl_piezo.png" caption="<span class=\"figure-number\">Figure 2: </span>Electrical model of a piezoelectric force sensor is shown in gray. Developed charge \\(q\\) is proportional to the strain and hence the force experienced by the sensor. Op-amp charge amplifier produces an output voltage \\(V\_s\\) equal to \\(-q/C\_s\\)" >}}
 
 The output voltage \\(V\_s\\) is equal to
 \\[ V\_s = -\frac{q}{C\_s} = -\frac{n d\_{33}F\_s}{C\_s} \\]
@@ -116,12 +116,13 @@ The capacitance of a piezoelectric stack is typically between \\(1 \mu F\\) and
 
 ## Tested feedback control strategies {#tested-feedback-control-strategies}
 
-<a id="orgc6b14a0"></a>
+<a id="figure--fig:fleming10-fb-control-strats"></a>
-
-{{< figure src="/ox-hugo/fleming10_fb_control_strats.png" caption="Figure 3: Comparison of: (a) basic integral control. (b) direct tracking control. (c) dual-sensor feedback. (d) low frequency bypass" >}}
 
+{{< figure src="/ox-hugo/fleming10_fb_control_strats.png" caption="<span class=\"figure-number\">Figure 3: </span>Comparison of: (a) basic integral control. (b) direct tracking control. (c) dual-sensor feedback. (d) low frequency bypass" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="org21788cf"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>IEEE/ASME Transactions on Mechatronics</i> 15 (3): 433–47. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
+</div>

content/article/fleming12_estim.md

@@ -1,7 +1,7 @@
 +++
 title = "Estimating the resolution of nanopositioning systems from frequency domain data"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
@@ -9,7 +9,7 @@ Tags
 
 
 Reference
-: ([Fleming 2012](#orgc7d7404))
+: (<a href="#citeproc_bib_item_1">Fleming 2012</a>)
 
 Author(s)
 : Fleming, A. J.
@@ -18,7 +18,8 @@ Year
 : 2012
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgc7d7404"></a>Fleming, Andrew J. 2012. “Estimating the Resolution of Nanopositioning Systems from Frequency Domain Data.” In _2012 IEEE International Conference on Robotics and Automation_, nil. <https://doi.org/10.1109/icra.2012.6224850>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Fleming, Andrew J. 2012. “Estimating the Resolution of Nanopositioning Systems from Frequency Domain Data.” In <i>2012 IEEE International Conference on Robotics and Automation</i>. doi:<a href="https://doi.org/10.1109/icra.2012.6224850">10.1109/icra.2012.6224850</a>.</div>
+</div>

content/article/fleming13_review_nanom_resol_posit_sensor.md

@@ -1,14 +1,14 @@
 +++
 title = "A review of nanometer resolution position sensors: operation and performance"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Position Sensors]({{< relref "position_sensors" >}})
+: [Position Sensors]({{< relref "position_sensors.md" >}})
 
 Reference
-: ([Fleming 2013](#org687716f))
+: (<a href="#citeproc_bib_item_1">Fleming 2013</a>)
 
 Author(s)
 : Fleming, A. J.
@@ -28,28 +28,28 @@ Year
 Usually quoted as a percentage of the fill-scale range (FSR):
 
 \begin{equation}
-  \text{mapping error (\%)} = \pm 100 \frac{\max{}|e\_m(v)|}{\text{FSR}}
+  \text{mapping error (\\%)} = \pm 100 \frac{\max{}|e\_m(v)|}{\text{FSR}}
 \end{equation}
 
 With \\(e\_m(v)\\) is the mapping error.
 
-<a id="org0a1d321"></a>
+<a id="figure--fig:mapping-error"></a>
 
-{{< figure src="/ox-hugo/fleming13_mapping_error.png" caption="Figure 1: The actual position versus the output voltage of a position sensor. The calibration function \\(f\_{cal}(v)\\) is an approximation of the sensor mapping function \\(f\_a(v)\\) where \\(v\\) is the voltage resulting from a displacement \\(x\\). \\(e\_m(v)\\) is the residual error." >}}
+{{< figure src="/ox-hugo/fleming13_mapping_error.png" caption="<span class=\"figure-number\">Figure 1: </span>The actual position versus the output voltage of a position sensor. The calibration function \\(f\_{cal}(v)\\) is an approximation of the sensor mapping function \\(f\_a(v)\\) where \\(v\\) is the voltage resulting from a displacement \\(x\\). \\(e\_m(v)\\) is the residual error." >}}
 
 
 ### Drift and Stability {#drift-and-stability}
 
 If the shape of the mapping function actually varies with time, the maximum error due to drift must be evaluated by finding the worst-case mapping error.
 
-<a id="orgc781e90"></a>
+<a id="figure--fig:drift-stability"></a>
 
-{{< figure src="/ox-hugo/fleming13_drift_stability.png" caption="Figure 2: The worst case range of a linear mapping function \\(f\_a(v)\\) for a given error in sensitivity and offset." >}}
+{{< figure src="/ox-hugo/fleming13_drift_stability.png" caption="<span class=\"figure-number\">Figure 2: </span>The worst case range of a linear mapping function \\(f\_a(v)\\) for a given error in sensitivity and offset." >}}
 
 
 ### Bandwidth {#bandwidth}
 
-The bandwidth of a position sensor is the frequency at which the magnitude of the transfer function \\(P(s) = v(s)/x(s)\\) drops by \\(3\,dB\\).
+The bandwidth of a position sensor is the frequency at which the magnitude of the transfer function \\(P(s) = v(s)/x(s)\\) drops by \\(3\\,dB\\).
 
 Although the bandwidth specification is useful for predicting the resolution of sensor, it reveals very little about the measurement errors caused by sensor dynamics.
 
@@ -57,7 +57,7 @@ The frequency domain position error is
 
 \begin{equation}
   \begin{aligned}
-    e\_{bw}(s) &= x(s) - v(s) \\\\\\
+    e\_{bw}(s) &= x(s) - v(s) \\\\
               &= x(s) (1 - P(s))
   \end{aligned}
 \end{equation}
@@ -66,7 +66,7 @@ If the actual position is a sinewave of peak amplitude \\(A = \text{FSR}/2\\):
 
 \begin{equation}
   \begin{aligned}
-    e\_{bw} &= \pm \frac{\text{FSR}}{2} |1 - P(s)| \\\\\\
+    e\_{bw} &= \pm \frac{\text{FSR}}{2} |1 - P(s)| \\\\
            &\approx \pm A n \frac{f}{f\_c}
   \end{aligned}
 \end{equation}
@@ -143,15 +143,15 @@ To characterize the resolution, we use the probability that the measured value i
 
 If the measurement noise is approximately Gaussian, the resolution can be quantified by the standard deviation \\(\sigma\\) (RMS value).
 
-The empirical rule states that there is a \\(99.7\%\\) probability that a sample of a Gaussian random process lie within \\(\pm 3 \sigma\\).
+The empirical rule states that there is a \\(99.7\\%\\) probability that a sample of a Gaussian random process lie within \\(\pm 3 \sigma\\).
 This if we define the resolution as \\(\delta = 6 \sigma\\), we will referred to as the \\(6\sigma\text{-resolution}\\).
 
 Another important parameter that must be specified when quoting resolution is the sensor bandwidth.
-There is usually a trade-off between bandwidth and resolution (figure [3](#org86a5909)).
+There is usually a trade-off between bandwidth and resolution ([Figure 3](#figure--fig:tradeoff-res-bandwidth)).
 
-<a id="org86a5909"></a>
+<a id="figure--fig:tradeoff-res-bandwidth"></a>
 
-{{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="Figure 3: The resolution versus banwidth of a position sensor." >}}
+{{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="<span class=\"figure-number\">Figure 3: </span>The resolution versus banwidth of a position sensor." >}}
 
 Many type of sensor have a limited full-scale-range (FSR) and tend to have an approximated proportional relationship between the resolution and range.
 As a result, it is convenient to consider the ratio of resolution to the FSR, or equivalently, the dynamic range (DNR).
@@ -166,23 +166,24 @@ A convenient method for reporting this ratio is in parts-per-million (ppm):
 
 <a id="table--tab:summary-position-sensors"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:summary-position-sensors">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:summary-position-sensors">Table 1</a>:</span>
   Summary of position sensor characteristics. The dynamic range (DNR) and resolution are approximations based on a full-scale range of \(100\,\mu m\) and a first order bandwidth of \(1\,kHz\)
 </div>
 
 | Sensor Type    | Range                              | DNR     | Resolution | Max. BW     | Accuracy  |
-|----------------|----------------------------------|---------|------------|----------|-----------|
+|----------------|------------------------------------|---------|------------|-------------|-----------|
-| Metal foil     | \\(10-500\,\mu m\\)              | 230 ppm | 23 nm      | 1-10 kHz | 1% FSR    |
+| Metal foil     | \\(10-500\\,\mu m\\)               | 230 ppm | 23 nm      | 1-10 kHz    | 1% FSR    |
-| Piezoresistive | \\(1-500\,\mu m\\)               | 5 ppm   | 0.5 nm     | >100 kHz | 1% FSR    |
+| Piezoresistive | \\(1-500\\,\mu m\\)                | 5 ppm   | 0.5 nm     | &gt;100 kHz | 1% FSR    |
-| Capacitive     | \\(10\,\mu m\\) to \\(10\,mm\\)  | 24 ppm  | 2.4 nm     | 100 kHz  | 0.1% FSR  |
+| Capacitive     | \\(10\\,\mu m\\) to \\(10\\,mm\\)  | 24 ppm  | 2.4 nm     | 100 kHz     | 0.1% FSR  |
-| Electrothermal | \\(10\,\mu m\\) to \\(1\,mm\\)   | 100 ppm | 10 nm      | 10 kHz   | 1% FSR    |
+| Electrothermal | \\(10\\,\mu m\\) to \\(1\\,mm\\)   | 100 ppm | 10 nm      | 10 kHz      | 1% FSR    |
-| Eddy current   | \\(100\,\mu m\\) to \\(80\,mm\\) | 10 ppm  | 1 nm       | 40 kHz   | 0.1% FSR  |
+| Eddy current   | \\(100\\,\mu m\\) to \\(80\\,mm\\) | 10 ppm  | 1 nm       | 40 kHz      | 0.1% FSR  |
-| LVDT           | \\(0.5-500\,mm\\)                | 10 ppm  | 5 nm       | 1 kHz    | 0.25% FSR |
+| LVDT           | \\(0.5-500\\,mm\\)                 | 10 ppm  | 5 nm       | 1 kHz       | 0.25% FSR |
-| Interferometer | Meters                           |         | 0.5 nm     | >100kHz  | 1 ppm FSR |
+| Interferometer | Meters                             |         | 0.5 nm     | &gt;100kHz  | 1 ppm FSR |
-| Encoder        | Meters                           |         | 6 nm       | >100kHz  | 5 ppm FSR |
+| Encoder        | Meters                             |         | 6 nm       | &gt;100kHz  | 5 ppm FSR |
-
 
 
 ## Bibliography {#bibliography}
 
-<a id="org687716f"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” _Sensors and Actuators a: Physical_ 190 (nil):106–26. <https://doi.org/10.1016/j.sna.2012.10.016>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Fleming, Andrew J. 2013. “A Review of Nanometer Resolution Position Sensors: Operation and Performance.” <i>Sensors and Actuators a: Physical</i> 190: 106–26. doi:<a href="https://doi.org/10.1016/j.sna.2012.10.016">10.1016/j.sna.2012.10.016</a>.</div>
+</div>

content/article/fleming15_low_order_dampin_track_contr.md

@@ -1,7 +1,7 @@
 +++
 title = "Low-order damping and tracking control for scanning probe systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
@@ -9,16 +9,17 @@ Tags
 
 
 Reference
-: ([Fleming, Teo, and Leang 2015](#org0b5cc88))
+: (<a href="#citeproc_bib_item_1">Fleming, Teo, and Leang 2015</a>)
 
 Author(s)
-: Fleming, A. J., Teo, Y. R., & Leang, K. K.
+: Fleming, A. J., Teo, Y. R., &amp; Leang, K. K.
 
 Year
 : 2015
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org0b5cc88"></a>Fleming, Andrew J., Yik Ren Teo, and Kam K. Leang. 2015. “Low-Order Damping and Tracking Control for Scanning Probe Systems.” _Frontiers in Mechanical Engineering_ 1 (nil):nil. <https://doi.org/10.3389/fmech.2015.00014>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Fleming, Andrew J., Yik Ren Teo, and Kam K. Leang. 2015. “Low-Order Damping and Tracking Control for Scanning Probe Systems.” <i>Frontiers in Mechanical Engineering</i> 1. doi:<a href="https://doi.org/10.3389/fmech.2015.00014">10.3389/fmech.2015.00014</a>.</div>
+</div>

content/article/furqan17_studies_stewar_platf_manip.md

@@ -1,25 +0,0 @@
-+++
-title = "Studies on stewart platform manipulator: a review"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}})
-
-Reference
-: ([Furqan, Suhaib, and Ahmad 2017](#org1144495))
-
-Author(s)
-: Furqan, M., Suhaib, M., & Ahmad, N.
-
-Year
-: 2017
-
-Lots of references.
-
-
-
-## Bibliography {#bibliography}
-
-<a id="org1144495"></a>Furqan, Mohd, Mohd Suhaib, and Nazeer Ahmad. 2017. “Studies on Stewart Platform Manipulator: A Review.” _Journal of Mechanical Science and Technology_ 31 (9):4459–70. <https://doi.org/10.1007/s12206-017-0846-1>.

content/article/furutani04_nanom_cuttin_machin_using_stewar.md

@@ -1,17 +1,17 @@
 +++
 title = "Nanometre-cutting machine using a stewart-platform parallel mechanism"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}})
 
 Reference
-: ([Furutani, Suzuki, and Kudoh 2004](#org9d14335))
+: (<a href="#citeproc_bib_item_1">Furutani, Suzuki, and Kudoh 2004</a>)
 
 Author(s)
-: Furutani, K., Suzuki, M., & Kudoh, R.
+: Furutani, K., Suzuki, M., &amp; Kudoh, R.
 
 Year
 : 2004
@@ -26,7 +26,7 @@ Year
 
 Possible sources of error:
 
--   position error of the link ends in assembly => simulation of position error and it is not significant
+-   position error of the link ends in assembly =&gt; simulation of position error and it is not significant
 -   Inaccurate modelling of the links
 -   insufficient generative force
 -   unwanted deformation of the links
@@ -35,7 +35,8 @@ To minimize the errors, a calibration is done between the required leg length an
 Then, it is fitted with 4th order polynomial and included in the control architecture.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org9d14335"></a>Furutani, Katsushi, Michio Suzuki, and Ryusei Kudoh. 2004. “Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism.” _Measurement Science and Technology_ 15 (2):467–74. <https://doi.org/10.1088/0957-0233/15/2/022>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Furutani, Katsushi, Michio Suzuki, and Ryusei Kudoh. 2004. “Nanometre-Cutting Machine Using a Stewart-Platform Parallel Mechanism.” <i>Measurement Science and Technology</i> 15 (2): 467–74. doi:<a href="https://doi.org/10.1088/0957-0233/15/2/022">10.1088/0957-0233/15/2/022</a>.</div>
+</div>

content/article/gao15_measur_techn_precis_posit.md

@@ -1,14 +1,14 @@
 +++
 title = "Measurement technologies for precision positioning"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
-: [Position Sensors]({{< relref "position_sensors" >}})
+: [Position Sensors]({{< relref "position_sensors.md" >}})
 
 Reference
-: ([Gao et al. 2015](#org07ae1a8))
+: (<a href="#citeproc_bib_item_1">Gao et al. 2015</a>)
 
 Author(s)
 : Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …
@@ -17,7 +17,8 @@ Year
 : 2015
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org07ae1a8"></a>Gao, W., S.W. Kim, H. Bosse, H. Haitjema, Y.L. Chen, X.D. Lu, W. Knapp, A. Weckenmann, W.T. Estler, and H. Kunzmann. 2015. “Measurement Technologies for Precision Positioning.” _CIRP Annals_ 64 (2):773–96. <https://doi.org/10.1016/j.cirp.2015.05.009>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Gao, W., S.W. Kim, H. Bosse, H. Haitjema, Y.L. Chen, X.D. Lu, W. Knapp, A. Weckenmann, W.T. Estler, and H. Kunzmann. 2015. “Measurement Technologies for Precision Positioning.” <i>CIRP Annals</i> 64 (2): 773–96. doi:<a href="https://doi.org/10.1016/j.cirp.2015.05.009">10.1016/j.cirp.2015.05.009</a>.</div>
+</div>

content/article/garg07_implem_chall_multiv_contr.md

@@ -1,14 +1,14 @@
 +++
 title = "Implementation challenges for multivariable control: what you did not learn in school!"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Multivariable Control]({{< relref "multivariable_control" >}})
+: [Multivariable Control]({{< relref "multivariable_control.md" >}})
 
 Reference
-: ([Garg 2007](#org18482cb))
+: (<a href="#citeproc_bib_item_1">Garg 2007</a>)
 
 Author(s)
 : Garg, S.
@@ -35,7 +35,8 @@ The control rate should be weighted appropriately in order to not saturate the s
 -   importance of scaling the plant prior to synthesis and also replacing pure integrators with slow poles
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org18482cb"></a>Garg, Sanjay. 2007. “Implementation Challenges for Multivariable Control: What You Did Not Learn in School!” In _AIAA Guidance, Navigation and Control Conference and Exhibit_, nil. <https://doi.org/10.2514/6.2007-6334>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Garg, Sanjay. 2007. “Implementation Challenges for Multivariable Control: What You Did Not Learn in School!” In <i>AIAA Guidance, Navigation and Control Conference and Exhibit</i>. doi:<a href="https://doi.org/10.2514/6.2007-6334">10.2514/6.2007-6334</a>.</div>
+</div>

content/article/geng95_intel_contr_system_multip_degree.md

@@ -1,27 +1,28 @@
 +++
 title = "An intelligent control system for multiple degree-of-freedom vibration isolation"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Geng et al. 1995](#orgb245b96))
+: (<a href="#citeproc_bib_item_1">Geng et al. 1995</a>)
 
 Author(s)
-: Geng, Z. J., Pan, G. G., Haynes, L. S., Wada, B. K., & Garba, J. A.
+: Geng, Z. J., Pan, G. G., Haynes, L. S., Wada, B. K., &amp; Garba, J. A.
 
 Year
 : 1995
 
-<a id="orgec71c1f"></a>
+<a id="figure--fig:geng95-control-structure"></a>
-
-{{< figure src="/ox-hugo/geng95_control_structure.png" caption="Figure 1: Local force feedback and adaptive acceleration feedback for active isolation" >}}
 
+{{< figure src="/ox-hugo/geng95_control_structure.png" caption="<span class=\"figure-number\">Figure 1: </span>Local force feedback and adaptive acceleration feedback for active isolation" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="orgb245b96"></a>Geng, Z. Jason, George G. Pan, Leonard S. Haynes, Ben K. Wada, and John A. Garba. 1995. “An Intelligent Control System for Multiple Degree-of-Freedom Vibration Isolation.” _Journal of Intelligent Material Systems and Structures_ 6 (6):787–800. <https://doi.org/10.1177/1045389x9500600607>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Geng, Z. Jason, George G. Pan, Leonard S. Haynes, Ben K. Wada, and John A. Garba. 1995. “An Intelligent Control System for Multiple Degree-of-Freedom Vibration Isolation.” <i>Journal of Intelligent Material Systems and Structures</i> 6 (6): 787–800. doi:<a href="https://doi.org/10.1177/1045389x9500600607">10.1177/1045389x9500600607</a>.</div>
+</div>

content/article/geraldes23_fly_scan_orien_motion_analy.md

@@ -0,0 +1,84 @@
++++
+title = "Fly-scan-oriented motion analyses and upgraded beamline integration architecture for the high-dynamic double-crystal monochromator at sirius/lnls"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (<a href="#citeproc_bib_item_1">Geraldes et al. 2023</a>)
+
+Author(s)
+: Geraldes, R. R., Luiz, S. A. L., Neto, J. L. d. B., Telles Ren\\'e Silva Soares, Reis, R. D. d., Calligaris, G. A., Witvoet, G., …
+
+Year
+: 2023
+
+
+## Effect of different d spacing {#effect-of-different-d-spacing}
+
+> Thus, if different d-spacings are found in the two crystals, an ideal energy matching for maximum flux would be related to slightly different \\(\theta\_B\\) in the crystals, such that the monochromatic beam would no longer be exactly parallel to the incoming beam, and **the magnitude of the deviation would be variable over the operational energy range**.
+
+
+## Effect of pitch error on source motion {#effect-of-pitch-error-on-source-motion}
+
+> Then, considering that variations of the virtual source are often proportionally related to shifts of the beam at the sample through the beamline optics, **a common requirement is having them small compared with the source size**.
+> With **X-ray source sizes of about 5 um** and **L commonly of the order of 30m** for modern beamlines, a typical budget of 10% pushes **pitch errors to the range of 10 nrad** only.
+
+
+## Correct pitch errors with gap adjustments {#correct-pitch-errors-with-gap-adjustments}
+
+> It can be seen that displacements in the virtual source related to pitch errors may be at least partly compensated by energy-dependent beam offset corrections via gap adjustments.
+
+
+## Allow some flux loss in order to have a more stable beam {#allow-some-flux-loss-in-order-to-have-a-more-stable-beam}
+
+> The angular boundaries for pitch around an ideal energy tuning, which might be already out or perfect parallelism due to d-spacing variations, can be derived as a fraction of the angular bandwidth of the Darwin width of the crystals.
+> This can be used, for example, to **evaluate acceptable flux losses in trying to keep the incoming and outgoing beam parallel despite thermal effects**.
+
+The pitch bandwidth for typical Si111 and Si311 can vary from 100urad at low energy to &lt;1urad at high energy.
+
+
+## Analytical effect of miss-cut on the change of beam height {#analytical-effect-of-miss-cut-on-the-change-of-beam-height}
+
+> This indicates that in reality the **gap motion range may need to be larger by a few percent than nominally expected**, that sensitivities at low angles may vary by more than one order of magnitude, that **calibrations for fixed exit may require more than the simpler trigonometric relation** of (2), and that the required velocities and accelerations related to the fly scan are in practice different from nominal ones.
+
+
+### Estimate the effect of the miss-cut on the beam error for our values of angles and miss-cut {#estimate-the-effect-of-the-miss-cut-on-the-beam-error-for-our-values-of-angles-and-miss-cut}
+
+
+## High dynamic range: low energy and high energy issues {#high-dynamic-range-low-energy-and-high-energy-issues}
+
+> Hence, **differences of three to four orders of magnitude occur for the gap velocity for a given energy variation rate** within the operational range of the HD-DCM.
+>
+> For a control-based instrument like the HD-DCM, these aspects place demanding specifications on metrology and acquisition hardware, since very high resolution and low noise are required for the lower angular (higher energy) range, whereas high rates are necessary at the opposite limit.
+>
+> For example, while the angular resolution in the Bragg angle quadrature encoder is 50nrad for high angular resolution and small control errors, for an energy scan of 1keV/s, the crystal angular speed requirements would be around 0.1deg/s at the high energy range and as much as 40deg/s at the low energy limit.
+> In the latter case, the counting rates would have to be higher than the current electronics capacity of 10 MHz.
+>
+> Similarly for the gap, with a resolution of 0.1 nm from the quadrature laser interferometers for the nanometre-level control performance, an equivalent energy rate scan speed with Si(111) crystals without a miscut would translate to about 0.8 mm/s and 20 mm/s at the high and low energy limits, respectively.
+> In the latter case, counting rates would need to reach 200 MHz.
+
+
+## Bragg control has a bandwidth of 20Hz {#bragg-control-has-a-bandwidth-of-20hz}
+
+
+## Crystal control has a bandwidth between 150Hz and 250Hz {#crystal-control-has-a-bandwidth-between-150hz-and-250hz}
+
+
+## They are using the Bragg angle reference signal to measure the wanted crystal distance {#they-are-using-the-bragg-angle-reference-signal-to-measure-the-wanted-crystal-distance}
+
+They are not using the encoder signal as we are doing.
+
+
+## Modes of operation {#modes-of-operation}
+
+1.  Standalone (similar as what we are using).
+2.  Follower: follows an encoder signal from the ID
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Geraldes, Renan Ramalho, Sergio Augusto Lordano Luiz, João Leandro de Brito Neto, Telles René Silva Soares, Ricardo Donizeth dos Reis, Guilherme A. Calligaris, Gert Witvoet, and J. P. M. B. Vermeulen. 2023. “Fly-Scan-Oriented Motion Analyses and Upgraded Beamline Integration Architecture for the High-Dynamic Double-Crystal Monochromator at Sirius/Lnls.” <i>Journal of Synchrotron Radiation</i> 30 (1): 90–110. doi:<a href="https://doi.org/10.1107/s1600577522010724">10.1107/s1600577522010724</a>.</div>
+</div>

content/article/hanieh03_activ_stewar.md

@@ -1,23 +0,0 @@
-+++
-title = "Active isolation and damping of vibrations via stewart platform"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Active Damping]({{< relref "active_damping" >}})
-
-Reference
-: ([Hanieh 2003](#org2d21f87))
-
-Author(s)
-: Hanieh, A. A.
-
-Year
-: 2003
-
-
-
-## Bibliography {#bibliography}
-
-<a id="org2d21f87"></a>Hanieh, Ahmed Abu. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Université Libre de Bruxelles, Brussels, Belgium.

content/article/hauge04_sensor_contr_space_based_six.md

@@ -1,17 +1,17 @@
 +++
 title = "Sensors and control of a space-based six-axis vibration isolation system"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Cubic Architecture]({{< relref "cubic_architecture" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Cubic Architecture]({{< relref "cubic_architecture.md" >}})
 
 Reference
-: ([Hauge and Campbell 2004](#org186272b))
+: (<a href="#citeproc_bib_item_1">Hauge and Campbell 2004</a>)
 
 Author(s)
-: Hauge, G., & Campbell, M.
+: Hauge, G., &amp; Campbell, M.
 
 Year
 : 2004
@@ -24,22 +24,22 @@ Year
 -   Vibration isolation using a Stewart platform
 -   Experimental comparison of Force sensor and Inertial Sensor and associated control architecture for vibration isolation
 
-<a id="org37bf22a"></a>
+<a id="figure--fig:hauge04-stewart-platform"></a>
 
-{{< figure src="/ox-hugo/hauge04_stewart_platform.png" caption="Figure 1: Hexapod for active vibration isolation" >}}
+{{< figure src="/ox-hugo/hauge04_stewart_platform.png" caption="<span class=\"figure-number\">Figure 1: </span>Hexapod for active vibration isolation" >}}
 
-**Stewart platform** (Figure [1](#org37bf22a)):
+**Stewart platform** ([Figure 1](#figure--fig:hauge04-stewart-platform)):
 
 -   Low corner frequency
 -   Large actuator stroke (\\(\pm5mm\\))
--   Sensors in each strut (Figure [2](#org8b97871)):
+-   Sensors in each strut ([Figure 2](#figure--fig:hauge05-struts)):
     -   three-axis load cell
     -   base and payload geophone in parallel with the struts
     -   LVDT
 
-<a id="org8b97871"></a>
+<a id="figure--fig:hauge05-struts"></a>
 
-{{< figure src="/ox-hugo/hauge05_struts.png" caption="Figure 2: Strut" >}}
+{{< figure src="/ox-hugo/hauge05_struts.png" caption="<span class=\"figure-number\">Figure 2: </span>Strut" >}}
 
 > Force sensors typically work well because they are not as sensitive to payload and base dynamics, but are limited in performance by a low-frequency zero pair resulting from the cross-axial stiffness.
 
@@ -64,9 +64,9 @@ With \\(|T(\omega)|\\) is the Frobenius norm of the transmissibility matrix and
 
 -   single strut axis as the cubic Stewart platform can be decomposed into 6 single-axis systems
 
-<a id="org1bec2a6"></a>
+<a id="figure--fig:hauge05-strut-model"></a>
 
-{{< figure src="/ox-hugo/hauge04_strut_model.png" caption="Figure 3: Strut model" >}}
+{{< figure src="/ox-hugo/hauge04_strut_model.png" caption="<span class=\"figure-number\">Figure 3: </span>Strut model" >}}
 
 **Zero Pair when using a Force Sensor**:
 
@@ -76,8 +76,8 @@ With \\(|T(\omega)|\\) is the Frobenius norm of the transmissibility matrix and
 
 **Control**:
 
--   Single-axis controllers => combine them into a full six-axis controller => evaluate the full controller in terms of stability and robustness
+-   Single-axis controllers =&gt; combine them into a full six-axis controller =&gt; evaluate the full controller in terms of stability and robustness
--   Sensitivity weighted LQG controller (SWLQG) => address robustness in flexible dynamic systems
+-   Sensitivity weighted LQG controller (SWLQG) =&gt; address robustness in flexible dynamic systems
 -   Three type of controller:
     -   Force feedback (cell-based)
     -   Inertial feedback (geophone-based)
@@ -87,7 +87,7 @@ With \\(|T(\omega)|\\) is the Frobenius norm of the transmissibility matrix and
 
 <a id="table--tab:hauge05-comp-load-cell-geophone"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:hauge05-comp-load-cell-geophone">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:hauge05-comp-load-cell-geophone">Table 1</a>:</span>
   Typical characteristics of sensors used for isolation in hexapod systems
 </div>
 
@@ -126,7 +126,7 @@ And we find that for \\(u\\) and \\(y\\) to be an acceptable pair for high gain
 
 **Inertial feedback**:
 
--   Non-Collocated => multiple phase drops that limit the bandwidth of the controller
+-   Non-Collocated =&gt; multiple phase drops that limit the bandwidth of the controller
 -   Good performance, but the transmissibility "pops" due to low phase margin and thus this indicates robustness problems
 
 **Combined force/velocity feedback**:
@@ -136,12 +136,13 @@ And we find that for \\(u\\) and \\(y\\) to be an acceptable pair for high gain
 -   The performance requirements are met
 -   Good robustness
 
-<a id="org0a496f7"></a>
+<a id="figure--fig:hauge04-obtained-transmissibility"></a>
-
-{{< figure src="/ox-hugo/hauge04_obtained_transmissibility.png" caption="Figure 4: Experimental open loop (solid) and closed loop six-axis transmissibility using the geophone only controller (dotted), and combined geophone/load cell controller (dashed)" >}}
 
+{{< figure src="/ox-hugo/hauge04_obtained_transmissibility.png" caption="<span class=\"figure-number\">Figure 4: </span>Experimental open loop (solid) and closed loop six-axis transmissibility using the geophone only controller (dotted), and combined geophone/load cell controller (dashed)" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="org186272b"></a>Hauge, G.S., and M.E. Campbell. 2004. “Sensors and Control of a Space-Based Six-Axis Vibration Isolation System.” _Journal of Sound and Vibration_ 269 (3-5):913–31. <https://doi.org/10.1016/s0022-460x(03)>00206-2.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Hauge, G.S., and M.E. Campbell. 2004. “Sensors and Control of a Space-Based Six-Axis Vibration Isolation System.” <i>Journal of Sound and Vibration</i> 269 (3-5): 913–31. doi:<a href="https://doi.org/10.1016/s0022-460x(03)00206-2">10.1016/s0022-460x(03)00206-2</a>.</div>
+</div>

content/article/holler12_instr_x_ray_nano_imagin.md

@@ -1,17 +1,17 @@
 +++
 title = "An instrument for 3d x-ray nano-imaging"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}}), [Positioning Stations]({{< relref "positioning_stations" >}})
+: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system.md" >}}), [Positioning Stations]({{< relref "positioning_stations.md" >}})
 
 Reference
-: ([Holler et al. 2012](#orgacde90c))
+: (<a href="#citeproc_bib_item_1">Holler et al. 2012</a>)
 
 Author(s)
-: Holler, M., Raabe, J., Diaz, A., Guizar-Sicairos, M., Quitmann, C., Menzel, A., & Bunk, O.
+: Holler, M., Raabe, J., Diaz, A., Guizar-Sicairos, M., Quitmann, C., Menzel, A., &amp; Bunk, O.
 
 Year
 : 2012
@@ -19,9 +19,9 @@ Year
 Instrument similar to the NASS.
 Obtain position stability of 10nm (standard deviation).
 
-<a id="org03c494c"></a>
+<a id="figure--fig:holler12-station"></a>
 
-{{< figure src="/ox-hugo/holler12_station.png" caption="Figure 1: Schematic of the tomography setup" >}}
+{{< figure src="/ox-hugo/holler12_station.png" caption="<span class=\"figure-number\">Figure 1: </span>Schematic of the tomography setup" >}}
 
 -   **Limited resolution due to instrumentation**:
     The resolution of ptychographic tomography remains above 100nm due to instabilities and drifts of the scanning systems.
@@ -39,7 +39,8 @@ Obtain position stability of 10nm (standard deviation).
 -   **Feedback Loop**: Using the signals from the 2 interferometers, the loop is closed to compensate low frequency vibrations and thermal drifts.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgacde90c"></a>Holler, M., J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk. 2012. “An Instrument for 3d X-Ray Nano-Imaging.” _Review of Scientific Instruments_ 83 (7):073703. <https://doi.org/10.1063/1.4737624>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Holler, M., J. Raabe, A. Diaz, M. Guizar-Sicairos, C. Quitmann, A. Menzel, and O. Bunk. 2012. “An Instrument for 3d X-Ray Nano-Imaging.” <i>Review of Scientific Instruments</i> 83 (7): 073703. doi:<a href="https://doi.org/10.1063/1.4737624">10.1063/1.4737624</a>.</div>
+</div>

content/article/holterman05_activ_dampin_based_decoup_colloc_contr.md

@@ -1,23 +1,24 @@
 +++
 title = "Active damping based on decoupled collocated control"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = true
 +++
 
 Tags
-: [Active Damping](active_damping.md)
+: [Active Damping]({{< relref "active_damping.md" >}})
 
 Reference
-: ([Holterman and deVries 2005](#org5d6fef0))
+: (<a href="#citeproc_bib_item_1">Holterman and deVries 2005</a>)
 
 Author(s)
-: Holterman, J., & deVries, T.
+: Holterman, J., &amp; deVries, T.
 
 Year
 : 2005
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org5d6fef0"></a>Holterman, J., and T.J.A. deVries. 2005. “Active Damping Based on Decoupled Collocated Control.” _IEEE/ASME Transactions on Mechatronics_ 10 (2):135–45. <https://doi.org/10.1109/tmech.2005.844702>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Holterman, J., and T.J.A. deVries. 2005. “Active Damping Based on Decoupled Collocated Control.” <i>IEEE/ASME Transactions on Mechatronics</i> 10 (2): 135–45. doi:<a href="https://doi.org/10.1109/tmech.2005.844702">10.1109/tmech.2005.844702</a>.</div>
+</div>

content/article/ito16_compar_class_high_precis_actuat.md

@@ -1,17 +1,17 @@
 +++
 title = "Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Actuators]({{< relref "actuators" >}})
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Actuators]({{< relref "actuators.md" >}})
 
 Reference
-: ([Ito and Schitter 2016](#org3484be8))
+: (<a href="#citeproc_bib_item_1">Ito and Schitter 2016</a>)
 
 Author(s)
-: Ito, S., & Schitter, G.
+: Ito, S., &amp; Schitter, G.
 
 Year
 : 2016
@@ -20,7 +20,7 @@ Year
 ## Classification of high-precision actuators {#classification-of-high-precision-actuators}
 
 <div class="table-caption">
-  <span class="table-number">Table 1</span>:
+  <span class="table-number">Table 1:</span>
   Zero/Low and High stiffness actuators
 </div>
 
@@ -41,9 +41,9 @@ In this paper, the piezoelectric actuator/electronics adds a time delay which is
 -   **Low Stiffness** actuator is defined as the ones where the transmissibility stays below 0dB at all frequency
 -   **High Stiffness** actuator is defined as the ones where the transmissibility goes above 0dB at some frequency
 
-<a id="org7e94abb"></a>
+<a id="figure--fig:ito16-low-high-stiffness-actuators"></a>
 
-{{< figure src="/ox-hugo/ito16_low_high_stiffness_actuators.png" caption="Figure 1: Definition of low-stiffness and high-stiffness actuator" >}}
+{{< figure src="/ox-hugo/ito16_low_high_stiffness_actuators.png" caption="<span class=\"figure-number\">Figure 1: </span>Definition of low-stiffness and high-stiffness actuator" >}}
 
 
 ## Low-Stiffness / High-Stiffness characteristics {#low-stiffness-high-stiffness-characteristics}
@@ -54,9 +54,9 @@ In this paper, the piezoelectric actuator/electronics adds a time delay which is
 
 ## Controller Design {#controller-design}
 
-<a id="org02696ae"></a>
+<a id="figure--fig:ito16-transmissibility"></a>
 
-{{< figure src="/ox-hugo/ito16_transmissibility.png" caption="Figure 2: Obtained transmissibility" >}}
+{{< figure src="/ox-hugo/ito16_transmissibility.png" caption="<span class=\"figure-number\">Figure 2: </span>Obtained transmissibility" >}}
 
 
 ## Discussion {#discussion}
@@ -67,7 +67,8 @@ In practice, this is difficult to achieve with piezoelectric actuators as their
 In contrast, the frequency band between the first and the other resonances of Lorentz actuators can be broad by design making them more suitable to construct a low-stiffness actuators.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org3484be8"></a>Ito, Shingo, and Georg Schitter. 2016. “Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation.” _IEEE/ASME Transactions on Mechatronics_ 21 (2):1169–78. <https://doi.org/10.1109/tmech.2015.2478658>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Ito, Shingo, and Georg Schitter. 2016. “Comparison and Classification of High-Precision Actuators Based on Stiffness Influencing Vibration Isolation.” <i>IEEE/ASME Transactions on Mechatronics</i> 21 (2): 1169–78. doi:<a href="https://doi.org/10.1109/tmech.2015.2478658">10.1109/tmech.2015.2478658</a>.</div>
+</div>

content/article/jiao18_dynam_model_exper_analy_stewar.md

@@ -1,23 +1,24 @@
 +++
 title = "Dynamic modeling and experimental analyses of stewart platform with flexible hinges"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}})
 
 Reference
-: ([Jiao et al. 2018](#org9f472e3))
+: (<a href="#citeproc_bib_item_1">Jiao et al. 2018</a>)
 
 Author(s)
-: Jiao, J., Wu, Y., Yu, K., & Zhao, R.
+: Jiao, J., Wu, Y., Yu, K., &amp; Zhao, R.
 
 Year
 : 2018
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org9f472e3"></a>Jiao, Jian, Ying Wu, Kaiping Yu, and Rui Zhao. 2018. “Dynamic Modeling and Experimental Analyses of Stewart Platform with Flexible Hinges.” _Journal of Vibration and Control_ 25 (1):151–71. <https://doi.org/10.1177/1077546318772474>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Jiao, Jian, Ying Wu, Kaiping Yu, and Rui Zhao. 2018. “Dynamic Modeling and Experimental Analyses of Stewart Platform with Flexible Hinges.” <i>Journal of Vibration and Control</i> 25 (1): 151–71. doi:<a href="https://doi.org/10.1177/1077546318772474">10.1177/1077546318772474</a>.</div>
+</div>

content/article/kwakernaak93_robus_contr_h_tutor_paper.md

@@ -1,14 +1,14 @@
 +++
 title = "Robust control and H-Infinity optimization - Tutorial paper"
 author = ["Thomas Dehaeze"]
-draft = false
+draft = true
 +++
 
 Tags
-: [H Infinity Control]({{< relref "h_infinity_control" >}}), [Weighting Functions]({{< relref "weighting_functions" >}})
+: [H Infinity Control]({{<relref "h_infinity_control.md#" >}}), [Weighting Functions]({{<relref "weighting_functions.md#" >}})
 
 Reference
-: ([Kwakernaak 1993](#orge60c373))
+: ([Kwakernaak 1993](#orgb190420))
 
 Author(s)
 : Kwakernaak, H.
@@ -19,4 +19,4 @@ Year
 
 ## Bibliography {#bibliography}
 
-<a id="orge60c373"></a>Kwakernaak, Huibert. 1993. “Robust Control and H$infty$-Optimization - Tutorial Paper.” _Automatica_ 29 (2):255–73. <https://doi.org/10.1016/0005-1098(93)>90122-a.
+<a id="orgb190420"></a>Kwakernaak, Huibert. 1993. “Robust Control and H$\Infty$-Optimization - Tutorial Paper.” _Automatica_ 29 (2):255–73. <https://doi.org/10.1016/0005-1098(93)90122-a>.

content/article/lee03_posit_contr_stewar_platf_using.md

@@ -1,5 +0,0 @@
-+++
-title = "Position control of a stewart platform using inverse dynamics control with approximate dynamics"
-author = ["Thomas Dehaeze"]
-draft = false
-+++

content/article/legnani12_new_isotr_decoup_paral_manip.md

@@ -1,17 +1,17 @@
 +++
 title = "A new isotropic and decoupled 6-dof parallel manipulator"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}})
 
 Reference
-: ([Legnani et al. 2012](#orga1e3bf2))
+: (<a href="#citeproc_bib_item_1">Legnani et al. 2012</a>)
 
 Author(s)
-: Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D.
+: Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., &amp; Tosi, D.
 
 Year
 : 2012
@@ -22,16 +22,17 @@ Year
 
 Example of generated isotropic manipulator (not decoupled).
 
-<a id="org0cc8ba8"></a>
+<a id="figure--fig:legnani12-isotropy-gen"></a>
 
-{{< figure src="/ox-hugo/legnani12_isotropy_gen.png" caption="Figure 1: Location of the leg axes using an isotropy generator" >}}
+{{< figure src="/ox-hugo/legnani12_isotropy_gen.png" caption="<span class=\"figure-number\">Figure 1: </span>Location of the leg axes using an isotropy generator" >}}
 
-<a id="org0474665"></a>
+<a id="figure--fig:legnani12-generated-isotropy"></a>
-
-{{< figure src="/ox-hugo/legnani12_generated_isotropy.png" caption="Figure 2: Isotropic configuration" >}}
 
+{{< figure src="/ox-hugo/legnani12_generated_isotropy.png" caption="<span class=\"figure-number\">Figure 2: </span>Isotropic configuration" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="orga1e3bf2"></a>Legnani, G., I. Fassi, H. Giberti, S. Cinquemani, and D. Tosi. 2012. “A New Isotropic and Decoupled 6-Dof Parallel Manipulator.” _Mechanism and Machine Theory_ 58 (nil):64–81. <https://doi.org/10.1016/j.mechmachtheory.2012.07.008>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Legnani, G., I. Fassi, H. Giberti, S. Cinquemani, and D. Tosi. 2012. “A New Isotropic and Decoupled 6-Dof Parallel Manipulator.” <i>Mechanism and Machine Theory</i> 58: 64–81. doi:<a href="https://doi.org/10.1016/j.mechmachtheory.2012.07.008">10.1016/j.mechmachtheory.2012.07.008</a>.</div>
+</div>

content/article/li01_simul_vibrat_isolat_point_contr.md

@@ -0,0 +1,26 @@
++++
+title = "Simultaneous vibration isolation and pointing control of flexure jointed hexapods"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Li, Hamann, and McInroy 2001</a>)
+
+Author(s)
+: Li, X., Hamann, J. C., &amp; McInroy, J. E.
+
+Year
+: 2001
+
+-   if the hexapod is designed such that the payload mass/inertia matrix (\\(M\_x\\)) and \\(J^T J\\) are diagonal, the dynamics from \\(u\\) to \\(y\\) are decoupled.
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Li, Xiaochun, Jerry C. Hamann, and John E. McInroy. 2001. “Simultaneous Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” In <i>Smart Structures and Materials 2001: Smart Structures and Integrated Systems</i>. doi:<a href="https://doi.org/10.1117/12.436521">10.1117/12.436521</a>.</div>
+</div>

content/article/lin06_distur_atten_precis_hexap_point.md

@@ -1,7 +1,7 @@
 +++
 title = "Disturbance attenuation in precise hexapod pointing using positive force feedback"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
@@ -9,16 +9,17 @@ Tags
 
 
 Reference
-: ([Lin and McInroy 2006](#org0bfd86d))
+: (<a href="#citeproc_bib_item_1">Lin and McInroy 2006</a>)
 
 Author(s)
-: Lin, H., & McInroy, J. E.
+: Lin, H., &amp; McInroy, J. E.
 
 Year
 : 2006
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org0bfd86d"></a>Lin, Haomin, and John E. McInroy. 2006. “Disturbance Attenuation in Precise Hexapod Pointing Using Positive Force Feedback.” _Control Engineering Practice_ 14 (11):1377–86. <https://doi.org/10.1016/j.conengprac.2005.10.002>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Lin, Haomin, and John E. McInroy. 2006. “Disturbance Attenuation in Precise Hexapod Pointing Using Positive Force Feedback.” <i>Control Engineering Practice</i> 14 (11): 1377–86. doi:<a href="https://doi.org/10.1016/j.conengprac.2005.10.002">10.1016/j.conengprac.2005.10.002</a>.</div>
+</div>

content/article/liu19_review_indus_mimo_decoup_contr.md

@@ -1,25 +0,0 @@
-+++
-title = "A review of industrial mimo decoupling control"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-:
-
-
-Reference
-: ([Liu et al. 2019](#org9f65386))
-
-Author(s)
-: Liu, L., Tian, S., Xue, D., Zhang, T., Chen, Y., & Zhang, S.
-
-Year
-: 2019
-
--\* Liu, L. et al. (2019): A review of industrial mimo decoupling control :article:ignore:
-
-
-## Bibliography {#bibliography}
-
-<a id="org9f65386"></a>Liu, Lu, Siyuan Tian, Dingyu Xue, Tao Zhang, YangQuan Chen, and Shuo Zhang. 2019. “A Review of Industrial Mimo Decoupling Control.” _International Journal of Control, Automation and Systems_ 17 (5):1246–54. <https://doi.org/10.1007/s12555-018-0367-4>.

content/article/mcinroy00_desig_contr_flexur_joint_hexap.md

@@ -1,7 +1,7 @@
 +++
 title = "Design and control of flexure jointed hexapods"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
@@ -9,16 +9,17 @@ Tags
 
 
 Reference
-: ([McInroy and Hamann 2000](#org04a7c92))
+: (<a href="#citeproc_bib_item_1">McInroy and Hamann 2000</a>)
 
 Author(s)
-: McInroy, J., & Hamann, J.
+: McInroy, J., &amp; Hamann, J.
 
 Year
 : 2000
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org04a7c92"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” _IEEE Transactions on Robotics and Automation_ 16 (4):372–81. <https://doi.org/10.1109/70.864229>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>McInroy, J.E., and J.C. Hamann. 2000. “Design and Control of Flexure Jointed Hexapods.” <i>IEEE Transactions on Robotics and Automation</i> 16 (4): 372–81. doi:<a href="https://doi.org/10.1109/70.864229">10.1109/70.864229</a>.</div>
+</div>

content/article/mcinroy02_model_desig_flexur_joint_stewar.md

@@ -1,6 +1,6 @@
 +++
 title = "Modeling and design of flexure jointed stewart platforms for control purposes"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
@@ -9,7 +9,7 @@ Tags
 
 
 Reference
-: ([McInroy 2002](#org2871bf9))
+: (<a href="#citeproc_bib_item_2">McInroy 2002</a>)
 
 Author(s)
 : McInroy, J.
@@ -17,7 +17,7 @@ Author(s)
 Year
 : 2002
 
-This short paper is very similar to ([McInroy 1999](#org1d169f9)).
+This short paper is very similar to (<a href="#citeproc_bib_item_1">McInroy 1999</a>).
 
 > This paper develops guidelines for designing the flexure joints to facilitate closed-loop control.
 
@@ -36,15 +36,15 @@ This short paper is very similar to ([McInroy 1999](#org1d169f9)).
 
 ## Flexure Jointed Hexapod Dynamics {#flexure-jointed-hexapod-dynamics}
 
-<a id="org4ea1e8b"></a>
+<a id="figure--fig:mcinroy02-leg-model"></a>
 
-{{< figure src="/ox-hugo/mcinroy02_leg_model.png" caption="Figure 1: The dynamics of the ith strut. A parallel spring, damper, and actautor drives the moving mass of the strut and a payload" >}}
+{{< figure src="/ox-hugo/mcinroy02_leg_model.png" caption="<span class=\"figure-number\">Figure 1: </span>The dynamics of the ith strut. A parallel spring, damper, and actautor drives the moving mass of the strut and a payload" >}}
 
-The strut can be modeled as consisting of a parallel arrangement of an actuator force, a spring and some damping driving a mass (Figure [1](#org4ea1e8b)).
+The strut can be modeled as consisting of a parallel arrangement of an actuator force, a spring and some damping driving a mass ([Figure 1](#figure--fig:mcinroy02-leg-model)).
 
 Thus, **the strut does not output force directly, but rather outputs a mechanically filtered force**.
 
-The model of the strut are shown in Figure [1](#org4ea1e8b) with:
+The model of the strut are shown in [Figure 1](#figure--fig:mcinroy02-leg-model) with:
 
 -   \\(m\_{s\_i}\\) moving strut mass
 -   \\(k\_i\\) spring constant
@@ -78,10 +78,10 @@ The payload is modeled as a rigid body:
 
 \begin{equation}
 \underbrace{\begin{bmatrix}
-m I\_3 & 0\_{3\times 3} \\\\\\
+m I\_3 & 0\_{3\times 3} \\\\
 0\_{3\times 3}   & {}^cI
 \end{bmatrix}}\_{M\_x} \ddot{\mathcal{X}} + \underbrace{\begin{bmatrix}
-  0\_{3 \times 1} \\ \omega \times {}^cI\omega
+  0\_{3 \times 1} \\\ \omega \times {}^cI\omega
 \end{bmatrix}}\_{c(\omega)} = \mathcal{F} \label{eq:payload\_dynamics}
 \end{equation}
 
@@ -107,7 +107,7 @@ where \\(J\\) is the manipulator Jacobian and \\({}^U\_BR\\) is the rotation mat
 The total generalized force acting on the payload is the sum of the strut, exogenous, and gravity forces:
 
 \begin{equation}
-  \mathcal{F} = {}^UJ^T f\_p + \mathcal{F}\_e - \begin{bmatrix} mg \\ 0\_{3\times 1} \end{bmatrix} \label{eq:generalized\_force}
+  \mathcal{F} = {}^UJ^T f\_p + \mathcal{F}\_e - \begin{bmatrix} mg \\\ 0\_{3\times 1} \end{bmatrix} \label{eq:generalized\_force}
 \end{equation}
 
 where:
@@ -115,10 +115,10 @@ where:
 -   \\(\mathcal{F}\_e\\) represents a vector of exogenous generalized forces applied at the center of mass
 -   \\(g\\) is the gravity vector
 
-By combining \eqref{eq:strut_dynamics_vec}, \eqref{eq:payload_dynamics} and \eqref{eq:generalized_force}, a single equation describing the dynamics of a flexure jointed hexapod can be found:
+By combining \eqref{eq:strut\_dynamics\_vec}, \eqref{eq:payload\_dynamics} and \eqref{eq:generalized\_force}, a single equation describing the dynamics of a flexure jointed hexapod can be found:
 
 \begin{equation}
-  {}^UJ^T [ f\_m - M\_s \ddot{l} - B \dot{l} - K(l - l\_r) - M\_s \ddot{q}\_u - M\_s g\_u + M\_s v\_2] + \mathcal{F}\_e - \begin{bmatrix} mg \\ 0\_{3\times 1} \end{bmatrix} = M\_x \ddot{\mathcal{X}} + c(\omega) \label{eq:eom\_fjh}
+  {}^UJ^T [ f\_m - M\_s \ddot{l} - B \dot{l} - K(l - l\_r) - M\_s \ddot{q}\_u - M\_s g\_u + M\_s v\_2] + \mathcal{F}\_e - \begin{bmatrix} mg \\\ 0\_{3\times 1} \end{bmatrix} = M\_x \ddot{\mathcal{X}} + c(\omega) \label{eq:eom\_fjh}
 \end{equation}
 
 Joint (\\(l\\)) and Cartesian (\\(\mathcal{X}\\)) terms are still mixed.
@@ -132,21 +132,21 @@ Many prior hexapod dynamic formulations assume that the strut exerts force only
 The flexure joints Hexapods transmit forces (or torques) proportional to the deflection of the joints.
 This section establishes design guidelines for the spherical flexure joint to guarantee that the dynamics remain tractable for control.
 
-<a id="org5bc5fa8"></a>
+<a id="figure--fig:mcinroy02-model-strut-joint"></a>
 
-{{< figure src="/ox-hugo/mcinroy02_model_strut_joint.png" caption="Figure 2: A simplified dynamic model of a strut and its joint" >}}
+{{< figure src="/ox-hugo/mcinroy02_model_strut_joint.png" caption="<span class=\"figure-number\">Figure 2: </span>A simplified dynamic model of a strut and its joint" >}}
 
-Figure [2](#org5bc5fa8) depicts a strut, along with the corresponding force diagram.
+[Figure 2](#figure--fig:mcinroy02-model-strut-joint) depicts a strut, along with the corresponding force diagram.
 The force diagram is obtained using standard finite element assumptions (\\(\sin \theta \approx \theta\\)).
 Damping terms are neglected.
 \\(k\_r\\) denotes the rotational stiffness of the spherical joint.
 
-From Figure [2](#org5bc5fa8) (b), Newton's second law yields:
+From [Figure 2](#figure--fig:mcinroy02-model-strut-joint) (b), Newton's second law yields:
 
 \begin{equation}
   f\_p = \begin{bmatrix}
-  -f\_m + m\_s \Delta \ddot{x} + k\Delta x \\\\\\
+  -f\_m + m\_s \Delta \ddot{x} + k\Delta x \\\\
-  m\_s \Delta \ddot{y} + \frac{k\_r}{l^2} \Delta y \\\\\\
+  m\_s \Delta \ddot{y} + \frac{k\_r}{l^2} \Delta y \\\\
   m\_s \Delta \ddot{z} + \frac{k\_r}{l^2} \Delta z
 \end{bmatrix}
 \end{equation}
@@ -157,16 +157,16 @@ The force is aligned perfectly with the strut only if \\(m\_s = 0\\) and \\(k\_r
 To examine the passive behavior, let \\(f\_m = 0\\) and consider a sinusoidal motion:
 
 \begin{equation}
-  \begin{bmatrix} \Delta x \\ \Delta y \\ \Delta z \end{bmatrix} =
+  \begin{bmatrix} \Delta x \\\ \Delta y \\\ \Delta z \end{bmatrix} =
-  \begin{bmatrix} A\_x \cos \omega t \\ A\_y \cos \omega t \\  A\_z \cos \omega t \end{bmatrix}
+  \begin{bmatrix} A\_x \cos \omega t \\\ A\_y \cos \omega t \\\  A\_z \cos \omega t \end{bmatrix}
 \end{equation}
 
 This yields:
 
 \begin{equation}
   f\_p = \begin{bmatrix}
-    \Big( -m\_s \omega^2 + k \Big) A\_x \cos \omega t \\\\\\
+    \Big( -m\_s \omega^2 + k \Big) A\_x \cos \omega t \\\\
-    \Big( -m\_s \omega^2 + \frac{k\_r}{l^2} \Big) A\_y \cos \omega t \\\\\\
+    \Big( -m\_s \omega^2 + \frac{k\_r}{l^2} \Big) A\_y \cos \omega t \\\\
     \Big( -m\_s \omega^2 + \frac{k\_r}{l^2} \Big) A\_z \cos \omega t
   \end{bmatrix}
 \end{equation}
@@ -189,7 +189,6 @@ The first part depends on the mechanical terms and the frequency of the movement
 \end{equation}
 
 <div class="important">
-  <div></div>
 
 In order to get dominance at low frequencies, the hexapod must be designed so that:
 
@@ -201,13 +200,12 @@ In order to get dominance at low frequencies, the hexapod must be designed so th
 
 This puts a limit on the rotational stiffness of the flexure joint and shows that as the strut is made softer (by decreasing \\(k\\)), the spherical flexure joint must be made proportionately softer.
 
-By satisfying \eqref{eq:cond_stiff}, \\(f\_p\\) can be aligned with the strut for frequencies much below the spherical joint's resonance mode:
+By satisfying \eqref{eq:cond\_stiff}, \\(f\_p\\) can be aligned with the strut for frequencies much below the spherical joint's resonance mode:
 \\[ \omega \ll \sqrt{\frac{k\_r}{m\_s l^2}} \rightarrow x\_{\text{gain}\_\omega} \approx \frac{k}{k\_r/l^2} \gg 1 \\]
 At frequencies much above the strut's resonance mode, \\(f\_p\\) is not dominated by its \\(x\\) component:
 \\[ \omega \gg \sqrt{\frac{k}{m\_s}} \rightarrow x\_{\text{gain}\_\omega} \approx 1 \\]
 
 <div class="important">
-  <div></div>
 
 To ensure that the control system acts only in the band of frequencies where dominance is retained, the control bandwidth can be selected so that:
 
@@ -226,16 +224,15 @@ In this case, it is reasonable to use:
 \end{equation}
 
 <div class="important">
-  <div></div>
 
-By designing the flexure jointed hexapod and its controller so that both \eqref{eq:cond_stiff} and \eqref{eq:cond_bandwidth} are met, the dynamics of the hexapod can be greatly reduced in complexity.
+By designing the flexure jointed hexapod and its controller so that both \eqref{eq:cond\_stiff} and \eqref{eq:cond\_bandwidth} are met, the dynamics of the hexapod can be greatly reduced in complexity.
 
 </div>
 
 
 ## Relationships between joint and cartesian space {#relationships-between-joint-and-cartesian-space}
 
-Equation \eqref{eq:eom_fjh} is not suitable for control analysis and design because \\(\ddot{\mathcal{X}}\\) is implicitly a function of \\(\ddot{q}\_u\\).
+Equation \eqref{eq:eom\_fjh} is not suitable for control analysis and design because \\(\ddot{\mathcal{X}}\\) is implicitly a function of \\(\ddot{q}\_u\\).
 
 This section will derive this implicit relationship.
 Let denote:
@@ -269,9 +266,9 @@ By using the vector triple identity \\(a \cdot (b \times c) = b \cdot (c \times
 \end{equation}
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org1d169f9"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
-
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In <i>Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)</i>. doi:<a href="https://doi.org/10.1109/cca.1999.806694">10.1109/cca.1999.806694</a>.</div>
-<a id="org2871bf9"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” <i>IEEE/ASME Transactions on Mechatronics</i> 7 (1): 95–99. doi:<a href="https://doi.org/10.1109/3516.990892">10.1109/3516.990892</a>.</div>
+</div>

content/article/mcinroy99_dynam.md

@@ -1,14 +1,14 @@
 +++
 title = "Dynamic modeling of flexure jointed hexapods for control purposes"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}})
 
 Reference
-: ([McInroy 1999](#orgc5d256d))
+: (<a href="#citeproc_bib_item_1">McInroy 1999</a>)
 
 Author(s)
 : McInroy, J.
@@ -16,7 +16,7 @@ Author(s)
 Year
 : 1999
 
-This conference paper has been further published in a journal as a short note ([McInroy 2002](#orge25929e)).
+This conference paper has been further published in a journal as a short note (<a href="#citeproc_bib_item_2">McInroy 2002</a>).
 
 
 ## Abstract {#abstract}
@@ -38,22 +38,22 @@ The actuators for FJHs can be divided into two categories:
 1.  soft (voice coil), which employs a spring flexure mount
 2.  hard (piezoceramic or magnetostrictive), which employs a compressive load spring.
 
-<a id="org89aa8b3"></a>
+<a id="figure--fig:mcinroy99-general-hexapod"></a>
 
-{{< figure src="/ox-hugo/mcinroy99_general_hexapod.png" caption="Figure 1: A general Stewart Platform" >}}
+{{< figure src="/ox-hugo/mcinroy99_general_hexapod.png" caption="<span class=\"figure-number\">Figure 1: </span>A general Stewart Platform" >}}
 
-Since both actuator types employ force production in parallel with a spring, they can both be modeled as shown in Figure [2](#org0b2b1e5).
+Since both actuator types employ force production in parallel with a spring, they can both be modeled as shown in [Figure 2](#figure--fig:mcinroy99-strut-model).
 
 In order to provide low frequency passive vibration isolation, the hard actuators are sometimes placed in series with additional passive springs.
 
-<a id="org0b2b1e5"></a>
+<a id="figure--fig:mcinroy99-strut-model"></a>
 
-{{< figure src="/ox-hugo/mcinroy99_strut_model.png" caption="Figure 2: The dynamics of the i'th strut. A parallel spring, damper and actuator drives the moving mass of the strut and a payload" >}}
+{{< figure src="/ox-hugo/mcinroy99_strut_model.png" caption="<span class=\"figure-number\">Figure 2: </span>The dynamics of the i'th strut. A parallel spring, damper and actuator drives the moving mass of the strut and a payload" >}}
 
 <a id="table--tab:mcinroy99-strut-model"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:mcinroy99-strut-model">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:mcinroy99-strut-model">Table 1</a>:</span>
-  Definition of quantities on Figure <a href="#org0b2b1e5">2</a>
+  Definition of quantities on <a href="#org1f8da5d">2</a>
 </div>
 
 | **Symbol**                   | **Meaning**                                |
@@ -70,11 +70,11 @@ In order to provide low frequency passive vibration isolation, the hard actuator
 | \\(v\_i = p\_i - q\_i\\)     | vector pointing from the bottom to the top |
 | \\(\hat{u}\_i = v\_i/l\_i\\) | unit direction of the strut                |
 
-It is here supposed that \\(f\_{p\_i}\\) is predominantly in the strut direction (explained in ([McInroy 2002](#orge25929e))).
+It is here supposed that \\(f\_{p\_i}\\) is predominantly in the strut direction (explained in (<a href="#citeproc_bib_item_2">McInroy 2002</a>)).
 This is a good approximation unless the spherical joints and extremely stiff or massive, of high inertia struts are used.
 This allows to reduce considerably the complexity of the model.
 
-From Figure [2](#org0b2b1e5) (b), forces along the strut direction are summed to yield (projected along the strut direction, hence the \\(\hat{u}\_i^T\\) term):
+From [Figure 2](#figure--fig:mcinroy99-strut-model) (b), forces along the strut direction are summed to yield (projected along the strut direction, hence the \\(\hat{u}\_i^T\\) term):
 
 \begin{equation}
   m\_i \hat{u}\_i^T \ddot{p}\_i = f\_{m\_i} - f\_{p\_i} - m\_i \hat{u}\_i^Tg - k\_i(l\_i - l\_{r\_i}) - b\_i \dot{l}\_i
@@ -105,10 +105,10 @@ The payload is modeled as a rigid body:
 
 \begin{equation}
 \underbrace{\begin{bmatrix}
-m I\_3 & 0\_{3\times 3} \\\\\\
+m I\_3 & 0\_{3\times 3} \\\\
 0\_{3\times 3}   & {}^cI
 \end{bmatrix}}\_{M\_x} \ddot{\mathcal{X}} + \underbrace{\begin{bmatrix}
-  0\_{3 \times 1} \\ \omega \times {}^cI\omega
+  0\_{3 \times 1} \\\ \omega \times {}^cI\omega
 \end{bmatrix}}\_{c(\omega)} = \mathcal{F} \label{eq:payload\_dynamics}
 \end{equation}
 
@@ -134,7 +134,7 @@ where \\(J\\) is the manipulator Jacobian and \\({}^U\_BR\\) is the rotation mat
 The total generalized force acting on the payload is the sum of the strut, exogenous, and gravity forces:
 
 \begin{equation}
-  \mathcal{F} = {}^UJ^T f\_p + \mathcal{F}\_e - \begin{bmatrix} mg \\ 0\_{3\times 1} \end{bmatrix} \label{eq:generalized\_force}
+  \mathcal{F} = {}^UJ^T f\_p + \mathcal{F}\_e - \begin{bmatrix} mg \\\ 0\_{3\times 1} \end{bmatrix} \label{eq:generalized\_force}
 \end{equation}
 
 where:
@@ -142,11 +142,11 @@ where:
 -   \\(\mathcal{F}\_e\\) represents a vector of exogenous generalized forces applied at the center of mass
 -   \\(g\\) is the gravity vector
 
-By combining \eqref{eq:strut_dynamics_vec}, \eqref{eq:payload_dynamics} and \eqref{eq:generalized_force}, a single equation describing the dynamics of a flexure jointed hexapod can be found:
+By combining \eqref{eq:strut\_dynamics\_vec}, \eqref{eq:payload\_dynamics} and \eqref{eq:generalized\_force}, a single equation describing the dynamics of a flexure jointed hexapod can be found:
 
 \begin{aligned}
-  & {}^UJ^T [ f\_m - M\_s \ddot{l} - B \dot{l} - K(l - l\_r) - M\_s \ddot{q}\_u\\\\\\
+  & {}^UJ^T [ f\_m - M\_s \ddot{l} - B \dot{l} - K(l - l\_r) - M\_s \ddot{q}\_u\\\\
-  & - M\_s g\_u + M\_s v\_2] + \mathcal{F}\_e - \begin{bmatrix} mg \\ 0\_{3\times 1} \end{bmatrix} = M\_x \ddot{\mathcal{X}} + c(\omega)
+  & - M\_s g\_u + M\_s v\_2] + \mathcal{F}\_e - \begin{bmatrix} mg \\\ 0\_{3\times 1} \end{bmatrix} = M\_x \ddot{\mathcal{X}} + c(\omega)
 \end{aligned}
 
 Joint (\\(l\\)) and Cartesian (\\(\mathcal{X}\\)) terms are still mixed.
@@ -162,9 +162,9 @@ In the next section, a connection between the two will be found to complete the
 ## Control Example {#control-example}
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgc5d256d"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In _Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)_, nil. <https://doi.org/10.1109/cca.1999.806694>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
-
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>McInroy, J.E. 1999. “Dynamic Modeling of Flexure Jointed Hexapods for Control Purposes.” In <i>Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328)</i>. doi:<a href="https://doi.org/10.1109/cca.1999.806694">10.1109/cca.1999.806694</a>.</div>
-<a id="orge25929e"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” _IEEE/ASME Transactions on Mechatronics_ 7 (1):95–99. <https://doi.org/10.1109/3516.990892>.
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>———. 2002. “Modeling and Design of Flexure Jointed Stewart Platforms for Control Purposes.” <i>IEEE/ASME Transactions on Mechatronics</i> 7 (1): 95–99. doi:<a href="https://doi.org/10.1109/3516.990892">10.1109/3516.990892</a>.</div>
+</div>

content/article/oomen18_advan_motion_contr_precis_mechat.md

@@ -1,14 +1,14 @@
 +++
 title = "Advanced motion control for precision mechatronics: control, identification, and learning of complex systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Motion Control](motion_control.md)
+: [Motion Control]({{< relref "motion_control.md" >}})
 
 Reference
-: ([Oomen 2018](#orge2156f8))
+: (<a href="#citeproc_bib_item_1">Oomen 2018</a>)
 
 Author(s)
 : Oomen, T.
@@ -16,12 +16,170 @@ Author(s)
 Year
 : 2018
 
-<a id="org6d729fe"></a>
 
-{{< figure src="/ox-hugo/oomen18_next_gen_loop_gain.png" caption="Figure 1: Envisaged developments in motion systems. In traditional motion systems, the control bandwidth takes place in the rigid-body region. In the next generation systemes, flexible dynamics are foreseen to occur within the control bandwidth." >}}
+## Introduction {#introduction}
+
+Control of positioning systems is traditionally simplified by an excellent mechanical design.
+In particular, the mechanical design is such that the system is stiff and highly reproducible.
+In conjunction with moderate performance requirements, the control bandwidth is well-below the resonance frequency of the flexible mechanics as is shown in [Figure 1](#figure--fig:oomen18-next-gen-loop-gain) (a).
+As a result, the system can often be completely **decoupled** in the frequency range relevant for control.
+Consequently, the control design is divided into well-manageable SISO control loops.
+
+Although motion control design is well developed, presently available techniques mainly apply to positioning systems that behave as a rigid body in the relevant frequency range.
+On one hand, increasing performance requirements hamper the validity of this assumption, since the bandwidth has to increase, leading to flexible dynamics in the cross-over region, see [Figure 1](#figure--fig:oomen18-next-gen-loop-gain) (b).
+
+<a id="figure--fig:oomen18-next-gen-loop-gain"></a>
+
+{{< figure src="/ox-hugo/oomen18_next_gen_loop_gain.png" caption="<span class=\"figure-number\">Figure 1: </span>Envisaged developments in motion systems. In traditional motion systems, the control bandwidth takes place in the rigid-body region. In the next generation systemes, flexible dynamics are foreseen to occur within the control bandwidth." >}}
 
 
+## Traditional motion control {#traditional-motion-control}
 
-## Bibliography {#bibliography}
+In the frequency range that is relevant for control, the dynamical behavior is mainly determined by the mechanics.
+In particular, the mechanics can typically be described as:
 
-<a id="orge2156f8"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” _IEEJ Journal of Industry Applications_ 7 (2):127–40. <https://doi.org/10.1541/ieejjia.7.127>.
+\begin{equation}
+G\_m = \sum\_{i=1}^{n\_{RB}} \frac{c\_i b\_i^T}{s^2} + \sum\_{n\_{RB} + 1}^{n\_s} \frac{c\_i b\_i^T}{s^2 + 2\xi \omega\_i s + \omega\_i^2}
+\end{equation}
+
+where the first term refers to rigid body modes and the second term to flexible modes.
+
+-   \\(n\_{RB}\\) is the number of rigid body modes
+-   \\(c\_i \in \mathbb{R}^{n\_y}\\) and \\(b\_i \in \mathbb{R}^{n\_u}\\) are associated with the mode shapes
+-   \\(\xi\_i, \omega\_i \in \mathbb{R}\_+\\)
+
+In traditional positioning systems, the number of actuators \\(n\_u\\) and sensors \\(n\_y\\) equals the number of rigid body modes \\(n\_{RB}\\) and are positioned such that the matrix \\(\sum\_{i=1}^{n\_{RB}} c\_i b\_i^T\\) is invertible.
+In this case, matrices \\(T\_u\\) and \\(T\_y\\) can be selected such that:
+
+\begin{equation}
+G = T\_y G\_m T\_u = \frac{1}{s^2} I\_{n\_{RB}} + G\_{\text{flex}}
+\end{equation}
+
+A tradition motion control architecture is shown in [Figure 2](#figure--fig:oomen18-control-architecture).
+
+<a id="figure--fig:oomen18-control-architecture"></a>
+
+{{< figure src="/ox-hugo/oomen18_control_architecture.png" caption="<span class=\"figure-number\">Figure 2: </span>Traditional motion control architecture" >}}
+
+
+### Traditional feedforward design {#traditional-feedforward-design}
+
+[Feedforward Control]({{< relref "feedforward_control.md" >}}) can effectively compensate for reference induced error signals.
+In particular, \\(f\\) should be selected such that \\(r - G f\\) is minimized.
+In the low frequency range, the system is decoupled and \\(G\_{\text{flex}}\\) can be ignored, in which case \\(f = G^{-1} r\\).
+In practice, the feedforward signal is selected as \\(f = ms^2 r\\).
+
+
+### Traditional feedback design {#traditional-feedback-design}
+
+The [Feedback Controller]({{< relref "feedback_control.md" >}}) has to minimize \\((1 + GK)^{-1}(\delta - v)\\).
+The main idea is that rigid body decoupling of \\(G\\) enables the shaping of the diagonal elements of \\(K\\) through a decentralized feedback controller.
+As a result, each diagonal element of \\(K\\) may be tuned independently.
+Typically, a PID controller is tuned through manual loop-shaping, followed by notch filters to account the the flexible modes that hamper stability and/or performance.
+
+
+### Traditional design procedure {#traditional-design-procedure}
+
+Traditional motion control design divides the multi-variable control design problems into sub-problems that are manageable by manual control design.
+The traditional procedure consists of the following steps:
+
+-   identify an FRF of \\(G\_m\\)
+-   decouple the plant to obtain an FRF of \\(G\\)
+-   design \\(K\\) using manual loop-shaping, consisting of PID with notches
+-   tune a feedforward controller, e.g. \\(f = m s^2 r\\)
+
+
+## Precision motion control developments {#precision-motion-control-developments}
+
+
+### Challenges {#challenges}
+
+High performance mechatronic systems are becoming lighter and lighter.
+Such lightweight systems exhibit predominant flexible dynamical behavior, as well as an increased susceptibility to disturbances.
+
+This leads to several challenges for motion control design:
+
+-   **Unmeasured performance variables** due to spatio-temporal deformations.
+    In particular, the location where the performance is desired may not be directly measured.
+-   **Many additional inputs and outputs** can be exploited to actively control the flexible dynamical behavior.
+    Spatially distributed actuators can actively provide stiffness and damping to the mechanical deformations.
+-   **Position dependent behavior** is almost unavoidable.
+    For instance in gantry stage designs, mass distribution change due to motion, leading to additional position-dependent behavior.
+    A key challenge lies in handling the position dependence of future systems
+-   A **system-of-systems perspective** on motion control design provides a strong potential for performance enhancement of the overall system.
+    In particular, typical manufacturing machines and scientific instruments involves multiple controlled subsystems where the two subsystems have to move relative to each other.
+    Performance limitations in each subsystem will negatively impact the overall performance.
+    A joint design enables that individual subsystems will be able to compensate each other's limitations.
+    A main challenge lies in an increase of the complexity of the control problem.
+-   **Thermal dynamics**, in addition to mechanical deformations are expected to become substantially more important due to increasing performance specifications.
+-   **Vibrations**, such as flow induced vibrations of cooling liquids and floor vibrations, have to be attenuated.
+
+
+### Generalized plant approach {#generalized-plant-approach}
+
+A generalized plant framework allows for a systematic way to address the future challenges in advanced motion control.
+
+The generalized plant is depicted in [Figure 3](#figure--fig:oomen18-generalized-plant):
+
+-   \\(z\\) are the performance variables
+-   \\(y\\) and \\(u\\) are the measured variables and measured variables, respectively
+-   \\(w\\) contains the exogenous inputs, typically including both reference signals and disturbances.
+
+<a id="figure--fig:oomen18-generalized-plant"></a>
+
+{{< figure src="/ox-hugo/oomen18_generalized_plant.png" caption="<span class=\"figure-number\">Figure 3: </span>Generalized plant setup" >}}
+
+
+## Feedback and Identification for Control {#feedback-and-identification-for-control}
+
+Feedback control is essential to deal with uncertainty in the system dynamics \\(G\\) and disturbances \\(v\\).
+Indeed, the main goal of feedback si to render the system insensitive to such uncertainties.
+
+
+### Norm-based control {#norm-based-control}
+
+A model-based design is foreseen to be able to systematically address the above mentioned challenges.
+
+To specify the control goal, the criterion:
+
+\begin{equation}
+J(G, K) = \\| \mathcal{F}\_l(P(G), K) \\|
+\end{equation}
+
+is posed, where the goal is to compute:
+
+\begin{equation}
+K\_{\text{opt}} = \text{arg} \text{min}\_{K} J(G\_0, K)
+\end{equation}
+
+Where \\(\\| \cdot \\|\\) denotes a suitable norm, e.g. \\(\mathcal{H}\_2\\) or \\(\mathcal{H}\_\infty\\), and \\(\mathcal{F}\_l\\) denotes a lower linear fractional transformation.
+
+\\(G\_0\\) denotes the true system, which is generally unknown and represented by a model \\(\hat{G}\\).
+
+
+### Nominal modeling for control {#nominal-modeling-for-control}
+
+To arrive at a mathematically tractable optimization problem, knowledge of the true system is represented through a model \\(\hat{G}\\).
+The central question is how to obtain such a model that is suitable for controller design.
+[System Identification]({{< relref "system_identification.md" >}}) as opposed to first principles modeling, is an inexpensive, fast and accurate approach to obtain such a model.
+Indeed, the machine is often already built, enabling direct experimentation.
+
+The model \\(\hat{G}\\) that results from system identification is an approximation of the true system \\(G\_0\\) for several reasons:
+
+-   motion systems often contains an infinite number of modes \\(n\_s\\), while a model of limited complexity may be desirable from a control perspective
+-   parasitic non-linearities are present, including nonlinear damping
+-   identification experiments are based on finite time disturbed observations, leading to uncertainties on estimated parameters
+
+
+### Toward robust motion control {#toward-robust-motion-control}
+
+Doing a model based control design using an identified model may not work well due to a lack of robustness.
+Indeed, if \\(K(\hat{G})\\) is designed solely based on \\(\hat{G}\\), there is no reason to assume that it achieves a suitable level of performance on \\(G\_0\\).
+This motivates a robust control design, where the **model quality is explicitly addressed during controller synthesis**.
+
+
+## Feedforward and learning {#feedforward-and-learning}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” <i>IEEJ Journal of Industry Applications</i> 7 (2): 127–40. doi:<a href="https://doi.org/10.1541/ieejjia.7.127">10.1541/ieejjia.7.127</a>.</div>
+</div>

content/article/preumont02_force_feedb_versus_accel_feedb.md

@@ -1,17 +1,17 @@
 +++
 title = "Force feedback versus acceleration feedback in active vibration isolation"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Preumont et al. 2002](#orgbec44eb))
+: (<a href="#citeproc_bib_item_1">Preumont et al. 2002</a>)
 
 Author(s)
-: Preumont, A., A. Francois, Bossens, F., & Abu-Hanieh, A.
+: Preumont, A., A. Francois, Bossens, F., &amp; Abu-Hanieh, A.
 
 Year
 : 2002
@@ -26,16 +26,16 @@ The force applied to a **rigid body** is proportional to its acceleration, thus
 Thus force feedback and acceleration feedback are equivalent for solid bodies.
 When there is a flexible payload, the two sensing options are not longer equivalent.
 
--   For light payload (Figure [1](#orga040a9a)), the acceleration feedback gives larger damping on the higher mode.
+-   For light payload ([Figure 1](#figure--fig:preumont02-force-acc-fb-light)), the acceleration feedback gives larger damping on the higher mode.
--   For heavy payload (Figure [2](#org1916ab2)), the acceleration feedback do not give alternating poles and zeros and thus for high control gains, the system becomes unstable
+-   For heavy payload ([Figure 2](#figure--fig:preumont02-force-acc-fb-heavy)), the acceleration feedback do not give alternating poles and zeros and thus for high control gains, the system becomes unstable
 
-<a id="orga040a9a"></a>
+<a id="figure--fig:preumont02-force-acc-fb-light"></a>
 
-{{< figure src="/ox-hugo/preumont02_force_acc_fb_light.png" caption="Figure 1: Root locus for **light** flexible payload, (a) Force feedback, (b) acceleration feedback" >}}
+{{< figure src="/ox-hugo/preumont02_force_acc_fb_light.png" caption="<span class=\"figure-number\">Figure 1: </span>Root locus for **light** flexible payload, (a) Force feedback, (b) acceleration feedback" >}}
 
-<a id="org1916ab2"></a>
+<a id="figure--fig:preumont02-force-acc-fb-heavy"></a>
 
-{{< figure src="/ox-hugo/preumont02_force_acc_fb_heavy.png" caption="Figure 2: Root locus for **heavy** flexible payload, (a) Force feedback, (b) acceleration feedback" >}}
+{{< figure src="/ox-hugo/preumont02_force_acc_fb_heavy.png" caption="<span class=\"figure-number\">Figure 2: </span>Root locus for **heavy** flexible payload, (a) Force feedback, (b) acceleration feedback" >}}
 
 Guaranteed stability of the force feedback:
 
@@ -46,7 +46,8 @@ The same is true for the transfer function from the force actuator to the relati
 > According to physical interpretation of the zeros, they represent the resonances of the subsystem  constrained by the sensor and the actuator.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgbec44eb"></a>Preumont, A., A. François, F. Bossens, and A. Abu-Hanieh. 2002. “Force Feedback Versus Acceleration Feedback in Active Vibration Isolation.” _Journal of Sound and Vibration_ 257 (4):605–13. <https://doi.org/10.1006/jsvi.2002.5047>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Preumont, A., A. François, F. Bossens, and A. Abu-Hanieh. 2002. “Force Feedback versus Acceleration Feedback in Active Vibration Isolation.” <i>Journal of Sound and Vibration</i> 257 (4): 605–13. doi:<a href="https://doi.org/10.1006/jsvi.2002.5047">10.1006/jsvi.2002.5047</a>.</div>
+</div>

content/article/preumont07_six_axis_singl_stage_activ.md

@@ -1,14 +1,14 @@
 +++
 title = "A six-axis single-stage active vibration isolator based on stewart platform"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}})
 
 Reference
-: ([Preumont et al. 2007](#org003735a))
+: (<a href="#citeproc_bib_item_1">Preumont et al. 2007</a>)
 
 Author(s)
 : Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., …
@@ -18,35 +18,36 @@ Year
 
 Summary:
 
--   **Cubic** Stewart platform (Figure [3](#org144c76e))
+-   **Cubic** Stewart platform ([Figure 3](#figure--fig:preumont07-stewart-platform))
     -   Provides uniform control capability
     -   Uniform stiffness in all directions
     -   minimizes the cross-coupling among actuators and sensors of different legs
--   Flexible joints (Figure [2](#org04bd941))
+-   Flexible joints ([Figure 2](#figure--fig:preumont07-flexible-joints))
 -   Piezoelectric force sensors
 -   Voice coil actuators
 -   Decentralized feedback control approach for vibration isolation
--   Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure [1](#org06a63d6))
+-   Effect of parasitic stiffness of the flexible joints on the IFF performance ([Figure 1](#figure--fig:preumont07-iff-effect-stiffness))
 -   The Stewart platform has 6 suspension modes at different frequencies.
     Thus the gain of the IFF controller cannot be optimal for all the modes.
     It is better if all the modes of the platform are near to each other.
 -   Discusses the design of the legs in order to maximize the natural frequency of the local modes.
 -   To estimate the isolation performance of the Stewart platform, a scalar indicator is defined as the Frobenius norm of the transmissibility matrix
 
-<a id="org06a63d6"></a>
+<a id="figure--fig:preumont07-iff-effect-stiffness"></a>
 
-{{< figure src="/ox-hugo/preumont07_iff_effect_stiffness.png" caption="Figure 1: Root locus with IFF with no parasitic stiffness and with parasitic stiffness" >}}
+{{< figure src="/ox-hugo/preumont07_iff_effect_stiffness.png" caption="<span class=\"figure-number\">Figure 1: </span>Root locus with IFF with no parasitic stiffness and with parasitic stiffness" >}}
 
-<a id="org04bd941"></a>
+<a id="figure--fig:preumont07-flexible-joints"></a>
 
-{{< figure src="/ox-hugo/preumont07_flexible_joints.png" caption="Figure 2: Flexible joints used for the Stewart platform" >}}
+{{< figure src="/ox-hugo/preumont07_flexible_joints.png" caption="<span class=\"figure-number\">Figure 2: </span>Flexible joints used for the Stewart platform" >}}
 
-<a id="org144c76e"></a>
+<a id="figure--fig:preumont07-stewart-platform"></a>
-
-{{< figure src="/ox-hugo/preumont07_stewart_platform.png" caption="Figure 3: Stewart platform" >}}
 
+{{< figure src="/ox-hugo/preumont07_stewart_platform.png" caption="<span class=\"figure-number\">Figure 3: </span>Stewart platform" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="org003735a"></a>Preumont, A., M. Horodinca, I. Romanescu, B. de Marneffe, M. Avraam, A. Deraemaeker, F. Bossens, and A. Abu Hanieh. 2007. “A Six-Axis Single-Stage Active Vibration Isolator Based on Stewart Platform.” _Journal of Sound and Vibration_ 300 (3-5):644–61. <https://doi.org/10.1016/j.jsv.2006.07.050>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Preumont, A., M. Horodinca, I. Romanescu, B. de Marneffe, M. Avraam, A. Deraemaeker, F. Bossens, and A. Abu Hanieh. 2007. “A Six-Axis Single-Stage Active Vibration Isolator Based on Stewart Platform.” <i>Journal of Sound and Vibration</i> 300 (3-5): 644–61. doi:<a href="https://doi.org/10.1016/j.jsv.2006.07.050">10.1016/j.jsv.2006.07.050</a>.</div>
+</div>

content/article/saxena12_advan_inter_model_contr_techn.md

@@ -1,26 +1,26 @@
 +++
 title = "Advances in internal model control technique: a review and future prospects"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Complementary Filters]({{< relref "complementary_filters" >}}), [Virtual Sensor Fusion]({{< relref "virtual_sensor_fusion" >}})
+: [Complementary Filters]({{< relref "complementary_filters.md" >}}), [Virtual Sensor Fusion]({{< relref "virtual_sensor_fusion.md" >}})
 
 Reference
-: ([Saxena and Hote 2012](#org13b6614))
+: (<a href="#citeproc_bib_item_1">Saxena and Hote 2012</a>)
 
 Author(s)
-: Saxena, S., & Hote, Y.
+: Saxena, S., &amp; Hote, Y.
 
 Year
 : 2012
 
 
-## Proposed Filter \\(F(s)\\) {#proposed-filter--fs}
+## Proposed Filter \\(F(s)\\) {#proposed-filter-f--s}
 
 \begin{align\*}
-  F(s) &= \frac{1}{(\lambda s + 1)^n} \\\\\\
+  F(s) &= \frac{1}{(\lambda s + 1)^n} \\\\
   F(s) &= \frac{n \lambda + 1}{(\lambda s + 1)^n}
 \end{align\*}
 
@@ -41,7 +41,7 @@ The structure can then be modified and we obtain a new controller \\(Q(s)\\).
 IMC is related to the classical controller through:
 
 \begin{align\*}
-Q(s) = \frac{C(s)}{1+G\_M(s)C(s)} \\\\\\
+Q(s) = \frac{C(s)}{1+G\_M(s)C(s)} \\\\
 C(s) = \frac{Q(s)}{1-G\_M(s)Q(s)}
 \end{align\*}
 
@@ -85,7 +85,8 @@ Issues:
 The interesting feature regarding IMC is that the design scheme is identical to the open-loop control design procedure and the implementation of IMC results in a feedback system, thereby copying the disturbances and parameter uncertainties, while open-loop control is not.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org13b6614"></a>Saxena, Sahaj, and YogeshV Hote. 2012. “Advances in Internal Model Control Technique: A Review and Future Prospects.” _IETE Technical Review_ 29 (6):461. <https://doi.org/10.4103/0256-4602.105001>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Saxena, Sahaj, and YogeshV Hote. 2012. “Advances in Internal Model Control Technique: A Review and Future Prospects.” <i>IETE Technical Review</i> 29 (6): 461. doi:<a href="https://doi.org/10.4103/0256-4602.105001">10.4103/0256-4602.105001</a>.</div>
+</div>

content/article/schellekens98_desig_precis.md

@@ -1,23 +1,24 @@
 +++
 title = "Design for precision: current status and trends"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
-: [Precision Engineering]({{< relref "precision_engineering" >}})
+: [Precision Engineering]({{< relref "precision_engineering.md" >}})
 
 Reference
-: ([Schellekens et al. 1998](#org035ecc6))
+: (<a href="#citeproc_bib_item_1">Schellekens et al. 1998</a>)
 
 Author(s)
-: Schellekens, P., Rosielle, N., Vermeulen, H., Vermeulen, M., Wetzels, S., & Pril, W.
+: Schellekens, P., Rosielle, N., Vermeulen, H., Vermeulen, M., Wetzels, S., &amp; Pril, W.
 
 Year
 : 1998
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org035ecc6"></a>Schellekens, P., N. Rosielle, H. Vermeulen, M. Vermeulen, S. Wetzels, and W. Pril. 1998. “Design for Precision: Current Status and Trends.” _Cirp Annals_, no. 2:557–86. <https://doi.org/10.1016/s0007-8506(07)>63243-0.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Schellekens, P., N. Rosielle, H. Vermeulen, M. Vermeulen, S. Wetzels, and W. Pril. 1998. “Design for Precision: Current Status and Trends.” <i>Cirp Annals</i>, no. 2: 557–86. doi:<a href="https://doi.org/10.1016/s0007-8506(07)63243-0">10.1016/s0007-8506(07)63243-0</a>.</div>
+</div>

content/article/schroeck01_compen_desig_linear_time_invar.md

@@ -1,7 +1,7 @@
 +++
 title = "On compensator design for linear time-invariant dual-input single-output systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
@@ -9,16 +9,17 @@ Tags
 
 
 Reference
-: ([Schroeck, Messner, and McNab 2001](#orga580bdc))
+: (<a href="#citeproc_bib_item_1">Schroeck, Messner, and McNab 2001</a>)
 
 Author(s)
-: Schroeck, S., Messner, W., & McNab, R.
+: Schroeck, S., Messner, W., &amp; McNab, R.
 
 Year
 : 2001
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orga580bdc"></a>Schroeck, S.J., W.C. Messner, and R.J. McNab. 2001. “On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems.” _IEEE/ASME Transactions on Mechatronics_ 6 (1):50–57. <https://doi.org/10.1109/3516.914391>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Schroeck, S.J., W.C. Messner, and R.J. McNab. 2001. “On Compensator Design for Linear Time-Invariant Dual-Input Single-Output Systems.” <i>IEEE/ASME Transactions on Mechatronics</i> 6 (1): 50–57. doi:<a href="https://doi.org/10.1109/3516.914391">10.1109/3516.914391</a>.</div>
+</div>

content/article/sebastian12_nanop_with_multip_sensor.md

@@ -1,23 +1,24 @@
 +++
 title = "Nanopositioning with multiple sensors: a case study in data storage"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
-: [Sensor Fusion]({{< relref "sensor_fusion" >}})
+: [Sensor Fusion]({{< relref "sensor_fusion.md" >}})
 
 Reference
-: ([Sebastian and Pantazi 2012](#orge399d74))
+: (<a href="#citeproc_bib_item_1">Sebastian and Pantazi 2012</a>)
 
 Author(s)
-: Sebastian, A., & Pantazi, A.
+: Sebastian, A., &amp; Pantazi, A.
 
 Year
 : 2012
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orge399d74"></a>Sebastian, Abu, and Angeliki Pantazi. 2012. “Nanopositioning with Multiple Sensors: A Case Study in Data Storage.” _IEEE Transactions on Control Systems Technology_ 20 (2):382–94. <https://doi.org/10.1109/tcst.2011.2177982>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Sebastian, Abu, and Angeliki Pantazi. 2012. “Nanopositioning with Multiple Sensors: A Case Study in Data Storage.” <i>IEEE Transactions on Control Systems Technology</i> 20 (2): 382–94. doi:<a href="https://doi.org/10.1109/tcst.2011.2177982">10.1109/tcst.2011.2177982</a>.</div>
+</div>

content/article/souleille18_concep_activ_mount_space_applic.md

@@ -1,17 +1,17 @@
 +++
 title = "A concept of active mount for space applications"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Active Damping](active_damping.md)
+: [Active Damping]({{< relref "active_damping.md" >}})
 
 Reference
-: ([Souleille et al. 2018](#orgdd47abc))
+: (<a href="#citeproc_bib_item_1">Souleille et al. 2018</a>)
 
 Author(s)
-: Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, & Collette, C.
+: Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gonccalo, &amp; Collette, C.
 
 Year
 : 2018
@@ -23,25 +23,25 @@ This article discusses the use of Integral Force Feedback with amplified piezoel
 
 ## Single degree-of-freedom isolator {#single-degree-of-freedom-isolator}
 
-Figure [1](#org4d65c6e) shows a picture of the amplified piezoelectric stack.
+[Figure 1](#figure--fig:souleille18-model-piezo) shows a picture of the amplified piezoelectric stack.
 The piezoelectric actuator is divided into two parts: one is used as an actuator, and the other one is used as a force sensor.
 
-<a id="org4d65c6e"></a>
+<a id="figure--fig:souleille18-model-piezo"></a>
 
-{{< figure src="/ox-hugo/souleille18_model_piezo.png" caption="Figure 1: Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator" >}}
+{{< figure src="/ox-hugo/souleille18_model_piezo.png" caption="<span class=\"figure-number\">Figure 1: </span>Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator" >}}
 
 <div class="table-caption">
-  <span class="table-number">Table 1</span>:
+  <span class="table-number">Table 1:</span>
   Parameters used for the model of the APA 100M
 </div>
 
 |            | Value                  | Meaning                                                        |
-|------------|-----------------------|----------------------------------------------------------------|
+|------------|------------------------|----------------------------------------------------------------|
-| \\(m\\)    | \\(1\,[kg]\\)         | Payload mass                                                   |
+| \\(m\\)    | \\(1\\,[kg]\\)         | Payload mass                                                   |
-| \\(k\_e\\) | \\(4.8\,[N/\mu m]\\)  | Stiffness used to adjust the pole of the isolator              |
+| \\(k\_e\\) | \\(4.8\\,[N/\mu m]\\)  | Stiffness used to adjust the pole of the isolator              |
-| \\(k\_1\\) | \\(0.96\,[N/\mu m]\\) | Stiffness of the metallic suspension when the stack is removed |
+| \\(k\_1\\) | \\(0.96\\,[N/\mu m]\\) | Stiffness of the metallic suspension when the stack is removed |
-| \\(k\_a\\) | \\(65\,[N/\mu m]\\)   | Stiffness of the actuator                                      |
+| \\(k\_a\\) | \\(65\\,[N/\mu m]\\)   | Stiffness of the actuator                                      |
-| \\(c\_1\\) | \\(10\,[N/(m/s)]\\)   | Added viscous damping                                          |
+| \\(c\_1\\) | \\(10\\,[N/(m/s)]\\)   | Added viscous damping                                          |
 
 The dynamic equation of the system is:
 
@@ -61,39 +61,40 @@ and the control force is given by:
   f = F\_s G(s) = F\_s \frac{g}{s}
 \end{equation}
 
-The effect of the controller are shown in Figure [2](#org3336e8f):
+The effect of the controller are shown in [Figure 2](#figure--fig:souleille18-tf-iff-result):
 
 -   the resonance peak is almost critically damped
 -   the passive isolation \\(\frac{x\_1}{w}\\) is not degraded at high frequencies
 -   the degradation of the compliance \\(\frac{x\_1}{F}\\) induced by feedback is limited at \\(\frac{1}{k\_1}\\)
 -   the fraction of the force transmitted to the payload that is measured by the force sensor is reduced at low frequencies
 
-<a id="org3336e8f"></a>
+<a id="figure--fig:souleille18-tf-iff-result"></a>
 
-{{< figure src="/ox-hugo/souleille18_tf_iff_result.png" caption="Figure 2: Matrix of transfer functions from input (w, f, F) to output (Fs, x1) in open loop (blue curves) and closed loop (dashed red curves)" >}}
+{{< figure src="/ox-hugo/souleille18_tf_iff_result.png" caption="<span class=\"figure-number\">Figure 2: </span>Matrix of transfer functions from input (w, f, F) to output (Fs, x1) in open loop (blue curves) and closed loop (dashed red curves)" >}}
 
-<a id="org20a69be"></a>
+<a id="figure--fig:souleille18-root-locus"></a>
 
-{{< figure src="/ox-hugo/souleille18_root_locus.png" caption="Figure 3: Single DoF system. Comparison between the theoretical (solid curve) and the experimental (crosses) root-locus" >}}
+{{< figure src="/ox-hugo/souleille18_root_locus.png" caption="<span class=\"figure-number\">Figure 3: </span>Single DoF system. Comparison between the theoretical (solid curve) and the experimental (crosses) root-locus" >}}
 
 
 ## Flexible payload mounted on three isolators {#flexible-payload-mounted-on-three-isolators}
 
-A heavy payload is mounted on a set of three isolators (Figure [4](#orga310d92)).
+A heavy payload is mounted on a set of three isolators ([Figure 4](#figure--fig:souleille18-setup-flexible-payload)).
 The payload consists of two  masses, connected through flexible blades such that the flexible resonance of the payload in the vertical direction is around 65Hz.
 
-<a id="orga310d92"></a>
+<a id="figure--fig:souleille18-setup-flexible-payload"></a>
 
-{{< figure src="/ox-hugo/souleille18_setup_flexible_payload.png" caption="Figure 4: Right: picture of the experimental setup. It consists of a flexible payload mounted on a set of three isolators. Left: simplified sketch of the setup, showing only the vertical direction" >}}
+{{< figure src="/ox-hugo/souleille18_setup_flexible_payload.png" caption="<span class=\"figure-number\">Figure 4: </span>Right: picture of the experimental setup. It consists of a flexible payload mounted on a set of three isolators. Left: simplified sketch of the setup, showing only the vertical direction" >}}
 
-As shown in Figure [5](#org3c2e029), both the suspension modes and the flexible modes of the payload can be critically damped.
+As shown in [Figure 5](#figure--fig:souleille18-result-damping-transmissibility), both the suspension modes and the flexible modes of the payload can be critically damped.
 
-<a id="org3c2e029"></a>
+<a id="figure--fig:souleille18-result-damping-transmissibility"></a>
-
-{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="Figure 5: Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}}
 
+{{< figure src="/ox-hugo/souleille18_result_damping_transmissibility.png" caption="<span class=\"figure-number\">Figure 5: </span>Transmissibility between the table top \\(w\\) and \\(m\_1\\)" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="orgdd47abc"></a>Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” _CEAS Space Journal_ 10 (2). Springer:157–65.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” <i>CEAS Space Journal</i> 10 (2). Springer: 157–65.</div>
+</div>

content/article/spanos95_soft_activ_vibrat_isolat.md

@@ -1,31 +1,31 @@
 +++
 title = "A soft 6-axis active vibration isolator"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Spanos, Rahman, and Blackwood 1995](#org2800cc5))
+: (<a href="#citeproc_bib_item_1">Spanos, Rahman, and Blackwood 1995</a>)
 
 Author(s)
-: Spanos, J., Rahman, Z., & Blackwood, G.
+: Spanos, J., Rahman, Z., &amp; Blackwood, G.
 
 Year
 : 1995
 
-**Stewart Platform** (Figure [1](#orgcac471d)):
+**Stewart Platform** ([Figure 1](#figure--fig:spanos95-stewart-platform)):
 
 -   Voice Coil
 -   Flexible joints (cross-blades)
 -   Force Sensors
 -   Cubic Configuration
 
-<a id="orgcac471d"></a>
+<a id="figure--fig:spanos95-stewart-platform"></a>
 
-{{< figure src="/ox-hugo/spanos95_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
+{{< figure src="/ox-hugo/spanos95_stewart_platform.png" caption="<span class=\"figure-number\">Figure 1: </span>Stewart Platform" >}}
 
 Total mass of the paylaod: 30kg
 Center of gravity is 9cm above the geometry center of the mount (cube's center?).
@@ -41,9 +41,9 @@ After redesign of the struts:
 -   low frequency zero at 2.6Hz but non-minimum phase (not explained).
     Small viscous damping material in the cross blade flexures made the zero minimum phase again.
 
-<a id="org5cb89c4"></a>
+<a id="figure--fig:spanos95-iff-plant"></a>
 
-{{< figure src="/ox-hugo/spanos95_iff_plant.png" caption="Figure 2: Experimentally measured transfer function from voice coil drive voltage to collocated load cell output voltage" >}}
+{{< figure src="/ox-hugo/spanos95_iff_plant.png" caption="<span class=\"figure-number\">Figure 2: </span>Experimentally measured transfer function from voice coil drive voltage to collocated load cell output voltage" >}}
 
 The controller used consisted of:
 
@@ -52,14 +52,15 @@ The controller used consisted of:
 -   first order lag filter to provide adequate phase margin at the low frequency crossover
 -   a first order high pass filter to attenuate the excess gain resulting from the low frequency zero
 
-The results in terms of transmissibility are shown in Figure [3](#orgd8726b9).
+The results in terms of transmissibility are shown in [Figure 3](#figure--fig:spanos95-results).
 
-<a id="orgd8726b9"></a>
+<a id="figure--fig:spanos95-results"></a>
-
-{{< figure src="/ox-hugo/spanos95_results.png" caption="Figure 3: Experimentally measured Frobenius norm of the 6-axis transmissibility" >}}
 
+{{< figure src="/ox-hugo/spanos95_results.png" caption="<span class=\"figure-number\">Figure 3: </span>Experimentally measured Frobenius norm of the 6-axis transmissibility" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="org2800cc5"></a>Spanos, J., Z. Rahman, and G. Blackwood. 1995. “A Soft 6-Axis Active Vibration Isolator.” In _Proceedings of 1995 American Control Conference - ACC’95_, nil. <https://doi.org/10.1109/acc.1995.529280>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Spanos, J., Z. Rahman, and G. Blackwood. 1995. “A Soft 6-Axis Active Vibration Isolator.” In <i>Proceedings of 1995 American Control Conference - ACC’95</i>. doi:<a href="https://doi.org/10.1109/acc.1995.529280">10.1109/acc.1995.529280</a>.</div>
+</div>

content/article/stankevic17_inter_charac_rotat_stages_x_ray_nanot.md

@@ -1,14 +1,14 @@
 +++
 title = "Interferometric characterization of rotation stages for x-ray nanotomography"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}}), [Positioning Stations]({{< relref "positioning_stations" >}})
+: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system.md" >}}), [Positioning Stations]({{< relref "positioning_stations.md" >}})
 
 Reference
-: ([Stankevic et al. 2017](#org125690d))
+: (<a href="#citeproc_bib_item_1">Stankevic et al. 2017</a>)
 
 Author(s)
 : Stankevic, T., Engblom, C., Langlois, F., Alves, F., Lestrade, A., Jobert, N., Cauchon, G., …
@@ -19,18 +19,19 @@ Year
 -   Similar Station than the NASS
 -   Similar Metrology with fiber based interferometers and cylindrical reference mirror
 
-<a id="org5481c46"></a>
+<a id="figure--fig:stankevic17-station"></a>
 
-{{< figure src="/ox-hugo/stankevic17_station.png" caption="Figure 1: Positioning Station" >}}
+{{< figure src="/ox-hugo/stankevic17_station.png" caption="<span class=\"figure-number\">Figure 1: </span>Positioning Station" >}}
 
 -   **Thermal expansion**: Stabilized down to \\(5mK/h\\) using passive water flow through the baseplate below the sample stage and in the interferometry reference frame.
 -   **Controller**: Two Independant PID loops
--   Repeatable errors => feedforward (Look Up Table)
+-   Repeatable errors =&gt; feedforward (Look Up Table)
--   Non-repeatable errors => feedback
+-   Non-repeatable errors =&gt; feedback
 -   Result: 40nm runout error
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org125690d"></a>Stankevic, Tomas, Christer Engblom, Florent Langlois, Filipe Alves, Alain Lestrade, Nicolas Jobert, Gilles Cauchon, Ulrich Vogt, and Stefan Kubsky. 2017. “Interferometric Characterization of Rotation Stages for X-Ray Nanotomography.” _Review of Scientific Instruments_ 88 (5):053703. <https://doi.org/10.1063/1.4983405>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Stankevic, Tomas, Christer Engblom, Florent Langlois, Filipe Alves, Alain Lestrade, Nicolas Jobert, Gilles Cauchon, Ulrich Vogt, and Stefan Kubsky. 2017. “Interferometric Characterization of Rotation Stages for X-Ray Nanotomography.” <i>Review of Scientific Instruments</i> 88 (5): 053703. doi:<a href="https://doi.org/10.1063/1.4983405">10.1063/1.4983405</a>.</div>
+</div>

content/article/sun16_pract_multiv_contr_approac_based.md

@@ -1,23 +0,0 @@
-+++
-title = "A practical multivariable control approach based on inverted decoupling and decentralized active disturbance rejection control"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Decoupled Control](decoupled_control.md)
-
-Reference
-: ([Sun et al. 2016](#org2268976))
-
-Author(s)
-: Sun, L., Dong, J., Li, D., & Lee, K. Y.
-
-Year
-: 2016
-
-
-
-## Bibliography {#bibliography}
-
-<a id="org2268976"></a>Sun, Li, Junyi Dong, Donghai Li, and Kwang Y. Lee. 2016. “A Practical Multivariable Control Approach Based on Inverted Decoupling and Decentralized Active Disturbance Rejection Control.” _Industrial & Engineering Chemistry Research_ 55 (7):2008–19. <https://doi.org/10.1021/acs.iecr.5b03738>.

content/article/tang18_decen_vibrat_contr_voice_coil.md

@@ -1,23 +1,24 @@
 +++
 title = "Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}})
 
 Reference
-: ([Tang, Cao, and Yu 2018](#orgb3d3aa7))
+: (<a href="#citeproc_bib_item_1">Tang, Cao, and Yu 2018</a>)
 
 Author(s)
-: Tang, J., Cao, D., & Yu, T.
+: Tang, J., Cao, D., &amp; Yu, T.
 
 Year
 : 2018
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgb3d3aa7"></a>Tang, Jie, Dengqing Cao, and Tianhu Yu. 2018. “Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments.” _Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science_ 233 (1):132–45. <https://doi.org/10.1177/0954406218756941>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Tang, Jie, Dengqing Cao, and Tianhu Yu. 2018. “Decentralized Vibration Control of a Voice Coil Motor-Based Stewart Parallel Mechanism: Simulation and Experiments.” <i>Proceedings of the Institution of Mechanical Engineers, Part c: Journal of Mechanical Engineering Science</i> 233 (1): 132–45. doi:<a href="https://doi.org/10.1177/0954406218756941">10.1177/0954406218756941</a>.</div>
+</div>

content/article/thayer02_six_axis_vibrat_isolat_system.md

@@ -9,7 +9,7 @@ Tags
 
 
 Reference
-: ([Thayer et al. 2002](#org7584b4b))
+: ([Thayer et al. 2002](#org3291862))
 
 Author(s)
 : Thayer, D., Campbell, M., Vagners, J., & Flotow, A. v.
@@ -20,4 +20,4 @@ Year
 
 ## Bibliography {#bibliography}
 
-<a id="org7584b4b"></a>Thayer, Doug, Mark Campbell, Juris Vagners, and Andrew von Flotow. 2002. “Six-Axis Vibration Isolation System Using Soft Actuators and Multiple Sensors.” _Journal of Spacecraft and Rockets_ 39 (2):206–12. <https://doi.org/10.2514/2.3821>.
+<a id="org3291862"></a>Thayer, Doug, Mark Campbell, Juris Vagners, and Andrew von Flotow. 2002. “Six-Axis Vibration Isolation System Using Soft Actuators and Multiple Sensors.” _Journal of Spacecraft and Rockets_ 39 (2):206–12. <https://doi.org/10.2514/2.3821>.

content/article/thurner15_fiber_based_distan_sensin_inter.md

@@ -1,14 +1,14 @@
 +++
 title = "Fiber-Based Distance Sensing Interferometry"
 author = ["Thomas Dehaeze"]
-draft = false
+draft = true
 +++
 
 Tags
-: [Interferometers]({{< relref "interferometers" >}})
+: [Interferometers]({{<relref "interferometers.md#" >}})
 
 Reference
-: ([Thurner et al. 2015](#org6f5a8f6))
+: ([Thurner et al. 2015](#org7174c7b))
 
 Author(s)
 : Thurner, K., Quacquarelli, F. P., Braun, Pierre-Francois, Dal Savio, C., & Karrai, K.
@@ -17,6 +17,7 @@ Year
 : 2015
 
 
+
 ## Bibliography {#bibliography}
 
-<a id="org6f5a8f6"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.
+<a id="org7174c7b"></a>Thurner, Klaus, Francesca Paola Quacquarelli, Pierre-François Braun, Claudio Dal Savio, and Khaled Karrai. 2015. “Fiber-Based Distance Sensing Interferometry.” _Applied Optics_ 54 (10). Optical Society of America:3051–63.

content/article/tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip.md

@@ -1,17 +1,17 @@
 +++
 title = "Sensor fusion for active vibration isolation in precision equipment"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Sensor Fusion]({{< relref "sensor_fusion" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Sensor Fusion]({{< relref "sensor_fusion.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Tjepkema, Dijk, and Soemers 2012](#org06c1cb7))
+: (<a href="#citeproc_bib_item_1">Tjepkema, van Dijk, and Soemers 2012</a>)
 
 Author(s)
-: Tjepkema, D., Dijk, J. v., & Soemers, H.
+: Tjepkema, D., Dijk, J. v., &amp; Soemers, H.
 
 Year
 : 2012
@@ -43,11 +43,12 @@ Control law: \\(f = -Gx\\)
 
 ## Design constraints and control bandwidth {#design-constraints-and-control-bandwidth}
 
-Heavier sensor => lower noise but it is harder to maintain collocation with the actuator => that limits the bandwidth.
+Heavier sensor =&gt; lower noise but it is harder to maintain collocation with the actuator =&gt; that limits the bandwidth.
 There is a compromise between sensor noise and the influence of the sensor size on the system's design and on the control bandwidth.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org06c1cb7"></a>Tjepkema, D., J. van Dijk, and H.M.J.R. Soemers. 2012. “Sensor Fusion for Active Vibration Isolation in Precision Equipment.” _Journal of Sound and Vibration_ 331 (4):735–49. <https://doi.org/10.1016/j.jsv.2011.09.022>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Tjepkema, D., J. van Dijk, and H.M.J.R. Soemers. 2012. “Sensor Fusion for Active Vibration Isolation in Precision Equipment.” <i>Journal of Sound and Vibration</i> 331 (4): 735–49. doi:<a href="https://doi.org/10.1016/j.jsv.2011.09.022">10.1016/j.jsv.2011.09.022</a>.</div>
+</div>

content/article/vcech19_essen_chall_motion_contr_educat.md

@@ -0,0 +1,20 @@
++++
+title = "Essential challenges in motion control education"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: <vcech19_essen_chall_motion_contr_educat>
+
+Author(s)
+: M. \VCech, J. K\\"onigsmarkov\\'a, Goubej, M., Oomen, T., & Visioli, A.
+
+Year
+: 2019
+
+<./biblio/references.bib>

content/article/voorhoeve15_ident_high_tech_motion_system.md

@@ -1,5 +0,0 @@
-+++
-title = "Identification of high-tech motion systems: an active vibration isolation benchmark"
-author = ["Thomas Dehaeze"]
-draft = false
-+++

content/article/wang12_autom_marker_full_field_hard.md

@@ -1,17 +1,17 @@
 +++
 title = "Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system" >}})
+: [Nano Active Stabilization System]({{< relref "nano_active_stabilization_system.md" >}})
 
 Reference
-: ([Wang et al. 2012](#orgf2371c9))
+: (<a href="#citeproc_bib_item_1">Wang et al. 2012</a>)
 
 Author(s)
-: Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M.
+: Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., &amp; Feser, M.
 
 Year
 : 2012
@@ -20,13 +20,14 @@ Year
 That limits the type of samples that is studied
 
 There is a need for markerless nano-tomography
-=> the key requirement is the precision and stability of the positioning stages.
+=&gt; the key requirement is the precision and stability of the positioning stages.
 
 **Passive rotational run-out error system**:
 It uses calibrated metrology disc and capacitive sensors
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgf2371c9"></a>Wang, Jun, Yu-chen Karen Chen, Qingxi Yuan, Andrei Tkachuk, Can Erdonmez, Benjamin Hornberger, and Michael Feser. 2012. “Automated Markerless Full Field Hard X-Ray Microscopic Tomography at Sub-50 Nm 3-Dimension Spatial Resolution.” _Applied Physics Letters_ 100 (14):143107. <https://doi.org/10.1063/1.3701579>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Wang, Jun, Yu-chen Karen Chen, Qingxi Yuan, Andrei Tkachuk, Can Erdonmez, Benjamin Hornberger, and Michael Feser. 2012. “Automated Markerless Full Field Hard X-Ray Microscopic Tomography at Sub-50 Nm 3-Dimension Spatial Resolution.” <i>Applied Physics Letters</i> 100 (14): 143107. doi:<a href="https://doi.org/10.1063/1.3701579">10.1063/1.3701579</a>.</div>
+</div>

content/article/wang16_inves_activ_vibrat_isolat_stewar.md

@@ -1,17 +1,17 @@
 +++
 title = "Investigation on active vibration isolation of a stewart platform with piezoelectric actuators"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Flexible Joints]({{< relref "flexible_joints" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}})
 
 Reference
-: ([Wang et al. 2016](#org89f2008))
+: (<a href="#citeproc_bib_item_1">Wang et al. 2016</a>)
 
 Author(s)
-: Wang, C., Xie, X., Chen, Y., & Zhang, Z.
+: Wang, C., Xie, X., Chen, Y., &amp; Zhang, Z.
 
 Year
 : 2016
@@ -25,23 +25,23 @@ Year
 The model is compared with a Finite Element model and is shown to give the same results.
 The proposed model is thus effective.
 
-<a id="org0d482b7"></a>
+<a id="figure--fig:wang16-stewart-platform"></a>
 
-{{< figure src="/ox-hugo/wang16_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
+{{< figure src="/ox-hugo/wang16_stewart_platform.png" caption="<span class=\"figure-number\">Figure 1: </span>Stewart Platform" >}}
 
 **Control**:
 Combines:
 
--   the FxLMS-based adaptive inverse control => suppress transmission of periodic vibrations
+-   the FxLMS-based adaptive inverse control =&gt; suppress transmission of periodic vibrations
--   direct feedback of integrated forces => dampen vibration of inherent modes and thus reduce random vibrations
+-   direct feedback of integrated forces =&gt; dampen vibration of inherent modes and thus reduce random vibrations
 
-Force Feedback (Figure [2](#org1b645a1)).
+Force Feedback ([Figure 2](#figure--fig:wang16-force-feedback)).
 
 -   the force sensor is mounted **between the base and the strut**
 
-<a id="org1b645a1"></a>
+<a id="figure--fig:wang16-force-feedback"></a>
 
-{{< figure src="/ox-hugo/wang16_force_feedback.png" caption="Figure 2: Feedback of integrated forces in the platform" >}}
+{{< figure src="/ox-hugo/wang16_force_feedback.png" caption="<span class=\"figure-number\">Figure 2: </span>Feedback of integrated forces in the platform" >}}
 
 Sorts of HAC-LAC control:
 
@@ -54,7 +54,8 @@ Sorts of HAC-LAC control:
 -   Effectiveness of control methods are shown
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org89f2008"></a>Wang, Chaoxin, Xiling Xie, Yanhao Chen, and Zhiyi Zhang. 2016. “Investigation on Active Vibration Isolation of a Stewart Platform with Piezoelectric Actuators.” _Journal of Sound and Vibration_ 383 (November). Elsevier BV:1–19. <https://doi.org/10.1016/j.jsv.2016.07.021>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Wang, Chaoxin, Xiling Xie, Yanhao Chen, and Zhiyi Zhang. 2016. “Investigation on Active Vibration Isolation of a Stewart Platform with Piezoelectric Actuators.” <i>Journal of Sound and Vibration</i> 383 (November). Elsevier BV: 1–19. doi:<a href="https://doi.org/10.1016/j.jsv.2016.07.021">10.1016/j.jsv.2016.07.021</a>.</div>
+</div>

content/article/yang19_dynam_model_decoup_contr_flexib.md

@@ -1,17 +1,17 @@
 +++
 title = "Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}), [Cubic Architecture]({{< relref "cubic_architecture" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}}), [Cubic Architecture]({{< relref "cubic_architecture.md" >}})
 
 Reference
-: ([Yang et al. 2019](#orgb15122e))
+: (<a href="#citeproc_bib_item_1">Yang et al. 2019</a>)
 
 Author(s)
-: Yang, X., Wu, H., Chen, B., Kang, S., & Cheng, S.
+: Yang, X., Wu, H., Chen, B., Kang, S., &amp; Cheng, S.
 
 Year
 : 2019
@@ -25,27 +25,27 @@ Year
 The joint stiffness impose a limitation on the control performance using force sensors as it adds a zero at low frequency in the dynamics.
 Thus, this stiffness is taken into account in the dynamics and compensated for.
 
-**Stewart platform** (Figure [1](#org479da8d)):
+**Stewart platform** ([Figure 1](#figure--fig:yang19-stewart-platform)):
 
 -   piezoelectric actuators
--   flexible joints (Figure [2](#org83afe99))
+-   flexible joints ([Figure 2](#figure--fig:yang19-flexible-joints))
 -   force sensors (used for vibration isolation)
 -   displacement sensors (used to decouple the dynamics)
 -   cubic (even though not said explicitly)
 
-<a id="org479da8d"></a>
+<a id="figure--fig:yang19-stewart-platform"></a>
 
-{{< figure src="/ox-hugo/yang19_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
+{{< figure src="/ox-hugo/yang19_stewart_platform.png" caption="<span class=\"figure-number\">Figure 1: </span>Stewart Platform" >}}
 
-<a id="org83afe99"></a>
+<a id="figure--fig:yang19-flexible-joints"></a>
 
-{{< figure src="/ox-hugo/yang19_flexible_joints.png" caption="Figure 2: Flexible Joints" >}}
+{{< figure src="/ox-hugo/yang19_flexible_joints.png" caption="<span class=\"figure-number\">Figure 2: </span>Flexible Joints" >}}
 
-The stiffness of the flexible joints (Figure [2](#org83afe99)) are computed with an FEM model and shown in Table [1](#table--tab:yang19-stiffness-flexible-joints).
+The stiffness of the flexible joints ([Figure 2](#figure--fig:yang19-flexible-joints)) are computed with an FEM model and shown in [Table 1](#table--tab:yang19-stiffness-flexible-joints).
 
 <a id="table--tab:yang19-stiffness-flexible-joints"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:yang19-stiffness-flexible-joints">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:yang19-stiffness-flexible-joints">Table 1</a>:</span>
   Stiffness of flexible joints obtained by FEM
 </div>
 
@@ -105,11 +105,11 @@ In order to apply this control strategy:
 -   The jacobian has to be computed
 -   No information about modal matrix is needed
 
-The block diagram of the control strategy is represented in Figure [3](#orgd526d94).
+The block diagram of the control strategy is represented in [Figure 3](#figure--fig:yang19-control-arch).
 
-<a id="orgd526d94"></a>
+<a id="figure--fig:yang19-control-arch"></a>
 
-{{< figure src="/ox-hugo/yang19_control_arch.png" caption="Figure 3: Control Architecture used" >}}
+{{< figure src="/ox-hugo/yang19_control_arch.png" caption="<span class=\"figure-number\">Figure 3: </span>Control Architecture used" >}}
 
 \\(H(s)\\) is designed as a proportional plus integral compensator:
 \\[ H(s) = k\_p + k\_i/s \\]
@@ -121,12 +121,12 @@ Substituting \\(H(s)\\) in the equation of motion gives that:
 
 **Experimental Validation**:
 An external Shaker is used to excite the base and accelerometers are located on the base and mobile platforms to measure their motion.
-The results are shown in Figure [4](#orge73e046).
+The results are shown in [Figure 4](#figure--fig:yang19-results).
 In theory, the vibration performance can be improved, however in practice, increasing the gain causes saturation of the piezoelectric actuators and then the instability occurs.
 
-<a id="orge73e046"></a>
+<a id="figure--fig:yang19-results"></a>
 
-{{< figure src="/ox-hugo/yang19_results.png" caption="Figure 4: Frequency response of the acceleration ratio between the paylaod and excitation (Transmissibility)" >}}
+{{< figure src="/ox-hugo/yang19_results.png" caption="<span class=\"figure-number\">Figure 4: </span>Frequency response of the acceleration ratio between the paylaod and excitation (Transmissibility)" >}}
 
 > A model-based controller is then designed based on the leg’s force and position feedback.
 > The position feedback compensates the effect of parasitic bending and torsional stiffness of the flexible joints.
@@ -134,7 +134,8 @@ In theory, the vibration performance can be improved, however in practice, incre
 > The proportional and integral gains in the sub-controller are used to separately regulate the vibration isolation bandwidth and active damping simultaneously for the six vibration modes.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgb15122e"></a>Yang, XiaoLong, HongTao Wu, Bai Chen, ShengZheng Kang, and ShiLi Cheng. 2019. “Dynamic Modeling and Decoupled Control of a Flexible Stewart Platform for Vibration Isolation.” _Journal of Sound and Vibration_ 439 (January). Elsevier BV:398–412. <https://doi.org/10.1016/j.jsv.2018.10.007>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Yang, XiaoLong, HongTao Wu, Bai Chen, ShengZheng Kang, and ShiLi Cheng. 2019. “Dynamic Modeling and Decoupled Control of a Flexible Stewart Platform for Vibration Isolation.” <i>Journal of Sound and Vibration</i> 439 (January). Elsevier BV: 398–412. doi:<a href="https://doi.org/10.1016/j.jsv.2018.10.007">10.1016/j.jsv.2018.10.007</a>.</div>
+</div>

content/article/yong12_invit_review_artic.md

@@ -0,0 +1,22 @@
++++
+title = "Invited review article: high-speed flexure-guided nanopositioning: mechanical design and control issues"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (<a href="#citeproc_bib_item_1">Yong et al. 2012</a>)
+
+Author(s)
+: Yong, Y. K., Moheimani, S. O. R., Kenton, B. J., &amp; Leang, K. K.
+
+Year
+: 2012
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Yong, Y. K., S. O. R. Moheimani, B. J. Kenton, and K. K. Leang. 2012. “Invited Review Article: High-Speed Flexure-Guided Nanopositioning: Mechanical Design and Control Issues.” <i>Review of Scientific Instruments</i> 83 (12): 121101. doi:<a href="https://doi.org/10.1063/1.4765048">10.1063/1.4765048</a>.</div>
+</div>

content/article/yun20_inves_two_stage_vibrat_suppr.md

@@ -1,7 +1,7 @@
 +++
 title = "Investigation on two-stage vibration suppression and precision pointing for space optical payloads"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
-draft = false
+draft = true
 +++
 
 Tags
@@ -9,16 +9,17 @@ Tags
 
 
 Reference
-: ([Yun et al. 2020](#org70fb5c6))
+: (<a href="#citeproc_bib_item_1">Yun et al. 2020</a>)
 
 Author(s)
-: Yun, H., Liu, L., Li, Q., & Yang, H.
+: Yun, H., Liu, L., Li, Q., &amp; Yang, H.
 
 Year
 : 2020
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org70fb5c6"></a>Yun, Hai, Lei Liu, Qing Li, and Hongjie Yang. 2020. “Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads.” _Aerospace Science and Technology_ 96 (nil):105543. <https://doi.org/10.1016/j.ast.2019.105543>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Yun, Hai, Lei Liu, Qing Li, and Hongjie Yang. 2020. “Investigation on Two-Stage Vibration Suppression and Precision Pointing for Space Optical Payloads.” <i>Aerospace Science and Technology</i> 96: 105543. doi:<a href="https://doi.org/10.1016/j.ast.2019.105543">10.1016/j.ast.2019.105543</a>.</div>
+</div>

content/article/zhang11_six_dof.md

@@ -1,17 +1,17 @@
 +++
 title = "Six dof active vibration control using stewart platform with non-cubic configuration"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Zhang et al. 2011](#org293b885))
+: (<a href="#citeproc_bib_item_1">Zhang et al. 2011</a>)
 
 Author(s)
-: Zhang, Z., Liu, J., Mao, J., Guo, Y., & Ma, Y.
+: Zhang, Z., Liu, J., Mao, J., Guo, Y., &amp; Ma, Y.
 
 Year
 : 2011
@@ -20,17 +20,18 @@ Year
 -   **Flexible** joints
 -   Magnetostrictive actuators
 -   Strong coupled motions along different axes
--   Non-cubic architecture => permits to have larger workspace which was required
+-   Non-cubic architecture =&gt; permits to have larger workspace which was required
 -   Structure parameters (radius of plates, length of struts) are determined by optimization of the condition number of the Jacobian matrix
 -   **Accelerometers** for active isolation
 -   Adaptive FIR filters for active isolation control
 
-<a id="orgf49a13c"></a>
+<a id="figure--fig:zhang11-platform"></a>
-
-{{< figure src="/ox-hugo/zhang11_platform.png" caption="Figure 1: Prototype of the non-cubic stewart platform" >}}
 
+{{< figure src="/ox-hugo/zhang11_platform.png" caption="<span class=\"figure-number\">Figure 1: </span>Prototype of the non-cubic stewart platform" >}}
 
 
 ## Bibliography {#bibliography}
 
-<a id="org293b885"></a>Zhang, Zhen, J Liu, Jq Mao, Yx Guo, and Yh Ma. 2011. “Six DOF Active Vibration Control Using Stewart Platform with Non-Cubic Configuration.” In _2011 6th IEEE Conference on Industrial Electronics and Applications_, nil. <https://doi.org/10.1109/iciea.2011.5975679>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Zhang, Zhen, J Liu, Jq Mao, Yx Guo, and Yh Ma. 2011. “Six DOF Active Vibration Control Using Stewart Platform with Non-Cubic Configuration.” In <i>2011 6th IEEE Conference on Industrial Electronics and Applications</i>. doi:<a href="https://doi.org/10.1109/iciea.2011.5975679">10.1109/iciea.2011.5975679</a>.</div>
+</div>

content/article/zuo04_elemen_system_desig_activ_passiv_vibrat_isolat.md

@@ -1,63 +0,0 @@
-+++
-title = "Element and system design for active and passive vibration isolation"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}})
-
-Reference
-: ([Zuo 2004](#orgf5a4502))
-
-Author(s)
-: Zuo, L.
-
-Year
-: 2004
-
-<div style="display: none;">
-\(
-\newcommand{\eatLabel}[2]{}
-\newenvironment{subequations}{\eatLabel}{}
-\)
-</div>
-
-\begin{equation}
-  \begin{align}
-  \left[ H\_{xf}(\omega) \right]\_{n \times n} &= \left[ S\_{x^\prime v}(\omega) \right]\_{n \times n} \left[ S\_{f^\prime v}(\omega) \right]\_{n \times n}^{-1} \\\\\\
-  \left[ H\_{xf}(\omega) \right]\_{n \times n} &= \left[ S\_{f^\prime f^\prime}(\omega) \right]\_{n \times n}^{-1} \left[ S\_{x^\prime f^\prime}(\omega) \right]\_{n \times n}
-  \end{align}
-\end{equation}
-
-> Vibration isolation systems can have various system architectures.
-> When we configure an active isolation system, we can use compliant actuators (such as voice coils) or stiff actuators (such as PZT stacks).
-> We also need to consider how to **combine the active actuation with passive elements**: we can place the actuator in parallel or in series with the passive elements.
-> Most of the isolation systems fall into the category of soft active mounts, in which a compliant actuator is placed in parallel with a spring.
-> A second category is **hard active mounts**, in which the **payload mass is directly mounted to a stiff actuator**.
-> Soft active mounts generally have advantages for better passive performance; hard active mounts are favored for payload disturbance rejection, but combination with passive stages is required due to the lack of isolation performance out of the control bandwidth.
-> Beard, von Flotow and Schubert proposed another type of hard mount, wherein **a stiff PZT actuator is placed in series with a spring** stiffer than the top passive stage.
-> They found that coupling from flexible modes is much smaller than in soft active mounts in the load (force) feedback.
-> Note that reaction force actuators can also work with soft mounts or hard mounts.
-
-<a id="org9c33e29"></a>
-
-{{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="Figure 1: PZT actuator and spring in series" >}}
-
-<a id="org141cdb3"></a>
-
-{{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="Figure 2: Voice coil actuator and spring in parallel" >}}
-
-<a id="org2ed63ef"></a>
-
-{{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="Figure 3: Transmission from PZT voltage to geophone output" >}}
-
-<a id="orgc14af87"></a>
-
-{{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="Figure 4: Transmission from voice coil voltage to geophone output" >}}
-
-
-
-## Bibliography {#bibliography}
-
-<a id="orgf5a4502"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.

content/book/du10_model_contr_vibrat_mechan_system.md

@@ -1,17 +1,17 @@
 +++
 title = "Modeling and control of vibration in mechanical systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = true
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Du and Xie 2010](#orga475b60))
+: (<a href="#citeproc_bib_item_1">Du and Xie 2010</a>)
 
 Author(s)
-: Du, C., & Xie, L.
+: Du, C., &amp; Xie, L.
 
 Year
 : 2010
@@ -110,7 +110,7 @@ Year
 ### 2.5 Conclusion {#2-dot-5-conclusion}
 
 
-## 3. Modeling of [Stewart Platforms]({{< relref "stewart_platforms" >}}) {#3-dot-modeling-of-stewart-platforms--stewart-platforms-dot-md}
+## 3. Modeling of [Stewart Platforms]({{< relref "stewart_platforms.md" >}}) {#3-dot-modeling-of-stewart-platforms--stewart-platforms-dot-md}
 
 
 ### 3.1 Introduction {#3-dot-1-introduction}
@@ -152,7 +152,7 @@ Year
 #### 4.2.4 Suspension {#4-dot-2-dot-4-suspension}
 
 
-#### 4.2.5 An application example &#8211; Disk vibration reduction via stacked disks {#4-dot-2-dot-5-an-application-example-and-8211-disk-vibration-reduction-via-stacked-disks}
+#### 4.2.5 An application example &amp;#8211; Disk vibration reduction via stacked disks {#4-dot-2-dot-5-an-application-example-and-8211-disk-vibration-reduction-via-stacked-disks}
 
 
 ### 4.3 Self-adapting systems {#4-dot-3-self-adapting-systems}
@@ -179,13 +179,13 @@ Year
 ### 5.1 Introduction {#5-dot-1-introduction}
 
 
-### 5.2 H2 and H&#8734; norms {#5-dot-2-h2-and-h-and-8734-norms}
+### 5.2 H2 and H&amp;#8734; norms {#5-dot-2-h2-and-h-and-8734-norms}
 
 
 #### 5.2.1 H2 norm {#5-dot-2-dot-1-h2-norm}
 
 
-#### 5.2.2 H&#8734; norm {#5-dot-2-dot-2-h-and-8734-norm}
+#### 5.2.2 H&amp;#8734; norm {#5-dot-2-dot-2-h-and-8734-norm}
 
 
 ### 5.3 H2 optimal control {#5-dot-3-h2-optimal-control}
@@ -197,7 +197,7 @@ Year
 #### 5.3.2 Discrete-time case {#5-dot-3-dot-2-discrete-time-case}
 
 
-### 5.4 H&#8734; control {#5-dot-4-h-and-8734-control}
+### 5.4 H&amp;#8734; control {#5-dot-4-h-and-8734-control}
 
 
 #### 5.4.1 Continuous-time case {#5-dot-4-dot-1-continuous-time-case}
@@ -227,13 +227,13 @@ Year
 ### 5.8 Conclusion {#5-dot-8-conclusion}
 
 
-## 6. Mixed H2/H&#8734; Control Design for Vibration Rejection {#6-dot-mixed-h2-h-and-8734-control-design-for-vibration-rejection}
+## 6. Mixed H2/H&amp;#8734; Control Design for Vibration Rejection {#6-dot-mixed-h2-h-and-8734-control-design-for-vibration-rejection}
 
 
 ### 6.1 Introduction {#6-dot-1-introduction}
 
 
-### 6.2 Mixed H2/H&#8734; control problem {#6-dot-2-mixed-h2-h-and-8734-control-problem}
+### 6.2 Mixed H2/H&amp;#8734; control problem {#6-dot-2-mixed-h2-h-and-8734-control-problem}
 
 
 ### 6.3 Method 1: slack variable approach {#6-dot-3-method-1-slack-variable-approach}
@@ -266,7 +266,7 @@ Year
 ### 7.3 Design in continuous-time domain {#7-dot-3-design-in-continuous-time-domain}
 
 
-#### 7.3.1 H&#8734; loop shaping for low-hump sensitivity functions {#7-dot-3-dot-1-h-and-8734-loop-shaping-for-low-hump-sensitivity-functions}
+#### 7.3.1 H&amp;#8734; loop shaping for low-hump sensitivity functions {#7-dot-3-dot-1-h-and-8734-loop-shaping-for-low-hump-sensitivity-functions}
 
 
 #### 7.3.2 Application examples {#7-dot-3-dot-2-application-examples}
@@ -395,7 +395,7 @@ Year
 ### 10.5 Conclusion {#10-dot-5-conclusion}
 
 
-## 11. H&#8734;-Based Design for Disturbance Observer {#11-dot-h-and-8734-based-design-for-disturbance-observer}
+## 11. H&amp;#8734;-Based Design for Disturbance Observer {#11-dot-h-and-8734-based-design-for-disturbance-observer}
 
 
 ### 11.1 Introduction {#11-dot-1-introduction}
@@ -533,7 +533,8 @@ Year
 ### 15.6 Conclusion {#15-dot-6-conclusion}
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orga475b60"></a>Du, Chunling, and Lihua Xie. 2010. _Modeling and Control of Vibration in Mechanical Systems_. Automation and Control Engineering. CRC Press. <https://doi.org/10.1201/9781439817995>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Du, Chunling, and Lihua Xie. 2010. <i>Modeling and Control of Vibration in Mechanical Systems</i>. Automation and Control Engineering. CRC Press. doi:<a href="https://doi.org/10.1201/9781439817995">10.1201/9781439817995</a>.</div>
+</div>

content/book/du19_multi_actuat_system_contr.md

@@ -1,6 +1,6 @@
 +++
 title = "Multi-stage actuation systems and control"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 description = "Proposes a way to combine multiple actuators (short stroke and long stroke) for control."
 keywords = ["Control", "Mechatronics"]
 draft = false
@@ -11,10 +11,10 @@ Tags
 
 
 Reference
-: ([Du and Pang 2019](#org2403f17))
+: (<a href="#citeproc_bib_item_1">Du and Pang 2019</a>)
 
 Author(s)
-: Du, C., & Pang, C. K.
+: Du, C., &amp; Pang, C. K.
 
 Year
 : 2019
@@ -43,11 +43,11 @@ When high bandwidth, high position accuracy and long stroke are required simulta
 Popular choices for coarse actuator are:
 
 -   DC motor
--   [Voice Coil Motors]({{< relref "voice_coil_actuators" >}}) (VCM)
+-   [Voice Coil Motors]({{< relref "voice_coil_actuators.md" >}}) (VCM)
 -   Permanent magnet stepper motor
 -   Permanent magnet linear synchronous motor
 
-As fine actuators, most of the time [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}}) are used.
+As fine actuators, most of the time [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}}) are used.
 
 In order to overcome fine actuator stringent stroke limitation and increase control bandwidth, three-stage actuation systems are necessary in practical applications.
 
@@ -75,26 +75,26 @@ which includes the resonance model
 and the resonance \\(P\_{ri}(s)\\) can be represented as one of the following forms
 
 \begin{align\*}
- P\_{ri}(s) &= \frac{\omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2} \\\\\\
+ P\_{ri}(s) &= \frac{\omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2} \\\\
- P\_{ri}(s) &= \frac{b\_{1i} \omega\_i s + b\_{0i} \omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2} \\\\\\
+ P\_{ri}(s) &= \frac{b\_{1i} \omega\_i s + b\_{0i} \omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2} \\\\
  P\_{ri}(s) &= \frac{b\_{2i} s^2 + b\_{1i} \omega\_i s + b\_{0i} \omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2}
 \end{align\*}
 
 
 #### Secondary Actuators {#secondary-actuators}
 
-We here consider two types of secondary actuators: the PZT milliactuator (figure [1](#org4cc1c22)) and the microactuator.
+We here consider two types of secondary actuators: the PZT milliactuator ([Figure 1](#figure--fig:pzt-actuator)) and the microactuator.
 
-<a id="org4cc1c22"></a>
+<a id="figure--fig:pzt-actuator"></a>
 
-{{< figure src="/ox-hugo/du19_pzt_actuator.png" caption="Figure 1: A PZT-actuator suspension" >}}
+{{< figure src="/ox-hugo/du19_pzt_actuator.png" caption="<span class=\"figure-number\">Figure 1: </span>A PZT-actuator suspension" >}}
 
 There are three popular types of micro-actuators: electrostatic moving-slider microactuator, PZT slider-driven microactuator and thermal microactuator.
-There characteristics are shown on table [1](#table--tab:microactuator).
+There characteristics are shown on [Table 1](#table--tab:microactuator).
 
 <a id="table--tab:microactuator"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:microactuator">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:microactuator">Table 1</a>:</span>
   Performance comparison of microactuators
 </div>
 
@@ -107,11 +107,11 @@ There characteristics are shown on table [1](#table--tab:microactuator).
 
 ### Single-Stage Actuation Systems {#single-stage-actuation-systems}
 
-A typical closed-loop control system is shown on figure [2](#org3b2af5e), where \\(P\_v(s)\\) and \\(C(z)\\) represent the actuator system and its controller.
+A typical closed-loop control system is shown on [Figure 2](#figure--fig:single-stage-control), where \\(P\_v(s)\\) and \\(C(z)\\) represent the actuator system and its controller.
 
-<a id="org3b2af5e"></a>
+<a id="figure--fig:single-stage-control"></a>
 
-{{< figure src="/ox-hugo/du19_single_stage_control.png" caption="Figure 2: Block diagram of a single-stage actuation system" >}}
+{{< figure src="/ox-hugo/du19_single_stage_control.png" caption="<span class=\"figure-number\">Figure 2: </span>Block diagram of a single-stage actuation system" >}}
 
 
 ### Dual-Stage Actuation Systems {#dual-stage-actuation-systems}
@@ -119,9 +119,9 @@ A typical closed-loop control system is shown on figure [2](#org3b2af5e), where
 Dual-stage actuation mechanism for the hard disk drives consists of a VCM actuator and a secondary actuator placed between the VCM and the sensor head.
 The VCM is used as the primary stage to provide long track seeking but with poor accuracy and slow response time, while the secondary stage actuator is used to provide higher positioning accuracy and faster response but with a stroke limit.
 
-<a id="org9af6d44"></a>
+<a id="figure--fig:dual-stage-control"></a>
 
-{{< figure src="/ox-hugo/du19_dual_stage_control.png" caption="Figure 3: Block diagram of dual-stage actuation system" >}}
+{{< figure src="/ox-hugo/du19_dual_stage_control.png" caption="<span class=\"figure-number\">Figure 3: </span>Block diagram of dual-stage actuation system" >}}
 
 
 ### Three-Stage Actuation Systems {#three-stage-actuation-systems}
@@ -145,7 +145,7 @@ In view of this, the controller design for dual-stage actuation systems adopts a
 
 ### Control Schemes {#control-schemes}
 
-A popular control scheme for dual-stage actuation system is the **decoupled structure** as shown in figure [4](#org0221f39).
+A popular control scheme for dual-stage actuation system is the **decoupled structure** as shown in [Figure 4](#figure--fig:decoupled-control).
 
 -   \\(C\_v(z)\\) and \\(C\_p(z)\\) are the controllers respectively, for the primary VCM actuator \\(P\_v(s)\\) and the secondary actuator \\(P\_p(s)\\).
 -   \\(\hat{P}\_p(z)\\) is an approximation of \\(P\_p\\) to estimate \\(y\_p\\).
@@ -153,9 +153,9 @@ A popular control scheme for dual-stage actuation system is the **decoupled stru
 -   \\(n\\) is the measurement noise
 -   \\(d\_u\\) stands for external vibration
 
-<a id="org0221f39"></a>
+<a id="figure--fig:decoupled-control"></a>
 
-{{< figure src="/ox-hugo/du19_decoupled_control.png" caption="Figure 4: Decoupled control structure for the dual-stage actuation system" >}}
+{{< figure src="/ox-hugo/du19_decoupled_control.png" caption="<span class=\"figure-number\">Figure 4: </span>Decoupled control structure for the dual-stage actuation system" >}}
 
 The open-loop transfer function from \\(pes\\) to \\(y\\) is
 \\[ G(z) = P\_p(z) C\_p(z) + P\_v(z) C\_v(z) + P\_v(z) C\_v(z) \hat{P}\_p(z) C\_p(z) \\]
@@ -175,16 +175,16 @@ The sensitivity functions of the VCM loop and the secondary actuator loop are
 And we obtain that the dual-stage sensitivity function \\(S(z)\\) is the product of \\(S\_v(z)\\) and \\(S\_p(z)\\).
 Thus, the dual-stage system control design can be decoupled into two independent controller designs.
 
-Another type of control scheme is the **parallel structure** as shown in figure [5](#org9edcb9b).
+Another type of control scheme is the **parallel structure** as shown in [Figure 5](#figure--fig:parallel-control-structure).
 The open-loop transfer function from \\(pes\\) to \\(y\\) is
 \\[ G(z) = P\_p(z) C\_p(z) + P\_v(z) C\_v(z) \\]
 
 The overall sensitivity function of the closed-loop system from \\(r\\) to \\(pes\\) is
 \\[ S(z) = \frac{1}{1 + G(z)} = \frac{1}{1 + P\_p(z) C\_p(z) + P\_v(z) C\_v(z)} \\]
 
-<a id="org9edcb9b"></a>
+<a id="figure--fig:parallel-control-structure"></a>
 
-{{< figure src="/ox-hugo/du19_parallel_control_structure.png" caption="Figure 5: Parallel control structure for the dual-stage actuator system" >}}
+{{< figure src="/ox-hugo/du19_parallel_control_structure.png" caption="<span class=\"figure-number\">Figure 5: </span>Parallel control structure for the dual-stage actuator system" >}}
 
 Because of the limited displacement range of the secondary actuator, the control efforts for the two actuators should be distributed properly when designing respective controllers to meet the required performance, make the actuators not conflict with each other, as well as prevent the saturation of the secondary actuator.
 
@@ -192,7 +192,7 @@ Because of the limited displacement range of the secondary actuator, the control
 ### Controller Design Method in the Continuous-Time Domain {#controller-design-method-in-the-continuous-time-domain}
 
 \\(\mathcal{H}\_\infty\\) loop shaping method is used to design the controllers for the primary and secondary actuators.
-The structure of the \\(\mathcal{H}\_\infty\\) loop shaping method is plotted in figure [6](#org24873cb) where \\(W(s)\\) is a weighting function relevant to the designed control system performance such as the sensitivity function.
+The structure of the \\(\mathcal{H}\_\infty\\) loop shaping method is plotted in [Figure 6](#figure--fig:h-inf-diagram) where \\(W(s)\\) is a weighting function relevant to the designed control system performance such as the sensitivity function.
 
 For a plant model \\(P(s)\\), a controller \\(C(s)\\) is to be designed such that the closed-loop system is stable and
 
@@ -202,11 +202,11 @@ For a plant model \\(P(s)\\), a controller \\(C(s)\\) is to be designed such tha
 
 is satisfied, where \\(T\_{zw}\\) is the transfer function from \\(w\\) to \\(z\\): \\(T\_{zw} = S(s) W(s)\\).
 
-<a id="org24873cb"></a>
+<a id="figure--fig:h-inf-diagram"></a>
 
-{{< figure src="/ox-hugo/du19_h_inf_diagram.png" caption="Figure 6: Block diagram for \\(\mathcal{H}\_\infty\\) loop shaping method to design the controller \\(C(s)\\) with the weighting function \\(W(s)\\)" >}}
+{{< figure src="/ox-hugo/du19_h_inf_diagram.png" caption="<span class=\"figure-number\">Figure 6: </span>Block diagram for \\(\mathcal{H}\_\infty\\) loop shaping method to design the controller \\(C(s)\\) with the weighting function \\(W(s)\\)" >}}
 
-Equation [1](#orga734f85) means that \\(S(s)\\) can be shaped similarly to the inverse of the chosen weighting function \\(W(s)\\).
+Equation [ 1](#orgcf76ccd) means that \\(S(s)\\) can be shaped similarly to the inverse of the chosen weighting function \\(W(s)\\).
 One form of \\(W(s)\\) is taken as
 
 \begin{equation}
@@ -219,18 +219,18 @@ The controller can then be synthesis using the linear matrix inequality (LMI) ap
 
 The primary and secondary actuator control loops are designed separately for the dual-stage control systems.
 But when designing their respective controllers, certain performances are required for the two actuators, so that control efforts for the two actuators are distributed properly and the actuators don't conflict with each other's control authority.
-As seen in figure [7](#orgb5c1410), the VCM primary actuator open loop has a higher gain at low frequencies, and the secondary actuator open loop has a higher gain in the high-frequency range.
+As seen in [Figure 7](#figure--fig:dual-stage-loop-gain), the VCM primary actuator open loop has a higher gain at low frequencies, and the secondary actuator open loop has a higher gain in the high-frequency range.
 
-<a id="orgb5c1410"></a>
+<a id="figure--fig:dual-stage-loop-gain"></a>
 
-{{< figure src="/ox-hugo/du19_dual_stage_loop_gain.png" caption="Figure 7: Frequency responses of \\(G\_v(s) = C\_v(s)P\_v(s)\\) (solid line) and \\(G\_p(s) = C\_p(s) P\_p(s)\\) (dotted line)" >}}
+{{< figure src="/ox-hugo/du19_dual_stage_loop_gain.png" caption="<span class=\"figure-number\">Figure 7: </span>Frequency responses of \\(G\_v(s) = C\_v(s)P\_v(s)\\) (solid line) and \\(G\_p(s) = C\_p(s) P\_p(s)\\) (dotted line)" >}}
 
-The sensitivity functions are shown in figure [8](#orgd91ec4c), where the hump of \\(S\_v\\) is arranged within the bandwidth of \\(S\_p\\) and the hump of \\(S\_p\\) is lowered as much as possible.
+The sensitivity functions are shown in [Figure 8](#figure--fig:dual-stage-sensitivity), where the hump of \\(S\_v\\) is arranged within the bandwidth of \\(S\_p\\) and the hump of \\(S\_p\\) is lowered as much as possible.
 This needs to decrease the bandwidth of the primary actuator loop and increase the bandwidth of the secondary actuator loop.
 
-<a id="orgd91ec4c"></a>
+<a id="figure--fig:dual-stage-sensitivity"></a>
 
-{{< figure src="/ox-hugo/du19_dual_stage_sensitivity.png" caption="Figure 8: Frequency response of \\(S\_v(s)\\) and \\(S\_p(s)\\)" >}}
+{{< figure src="/ox-hugo/du19_dual_stage_sensitivity.png" caption="<span class=\"figure-number\">Figure 8: </span>Frequency response of \\(S\_v(s)\\) and \\(S\_p(s)\\)" >}}
 
 A basic requirement of the dual-stage actuation control system is to make the individual primary and secondary loops stable.
 It also required that the primary actuator path has a higher gain than the secondary actuator path at low frequency range and the secondary actuator path has a higher gain than the primary actuator path in high-frequency range.
@@ -261,15 +261,15 @@ A VCM actuator is used as the first-stage actuator denoted by \\(P\_v(s)\\), a P
 
 ### Control Strategy and Controller Design {#control-strategy-and-controller-design}
 
-Figure [9](#org4bda714) shows the control structure for the three-stage actuation system.
+[Figure 9](#figure--fig:three-stage-control) shows the control structure for the three-stage actuation system.
 
 The control scheme is based on the decoupled master-slave dual-stage control and the third stage microactuator is added in parallel with the dual-stage control system.
 The parallel format is advantageous to the overall control bandwidth enhancement, especially for the microactuator having limited stroke which restricts the bandwidth of its own loop.
 The reason why the decoupled control structure is adopted here is that its overall sensitivity function is the product of those of the two individual loops, and the VCM and the PTZ controllers can be designed separately.
 
-<a id="org4bda714"></a>
+<a id="figure--fig:three-stage-control"></a>
 
-{{< figure src="/ox-hugo/du19_three_stage_control.png" caption="Figure 9: Control system for the three-stage actuation system" >}}
+{{< figure src="/ox-hugo/du19_three_stage_control.png" caption="<span class=\"figure-number\">Figure 9: </span>Control system for the three-stage actuation system" >}}
 
 The open-loop transfer function of the three-stage actuation system is derived as
 
@@ -280,8 +280,8 @@ The open-loop transfer function of the three-stage actuation system is derived a
 with
 
   \begin{align\*}
-  G\_v(z) &= P\_v(z) C\_v(z) \\\\\\
+  G\_v(z) &= P\_v(z) C\_v(z) \\\\
-  G\_p(z) &= P\_p(z) C\_p(z) \\\\\\
+  G\_p(z) &= P\_p(z) C\_p(z) \\\\
   G\_m(z) &= P\_m(z) C\_m(z)
 \end{align\*}
 
@@ -296,17 +296,17 @@ The PZT actuated milliactuator \\(P\_p(s)\\) works under a reasonably high bandw
 The third-stage actuator \\(P\_m(s)\\) is used to further push the bandwidth as high as possible.
 
 The control performances of both the VCM and the PZT actuators are limited by their dominant resonance modes.
-The open-loop frequency responses of the three stages are shown on figure [10](#orgded6e76).
+The open-loop frequency responses of the three stages are shown on [Figure 10](#figure--fig:open-loop-three-stage).
 
-<a id="orgded6e76"></a>
+<a id="figure--fig:open-loop-three-stage"></a>
 
-{{< figure src="/ox-hugo/du19_open_loop_three_stage.png" caption="Figure 10: Frequency response of the open-loop transfer function" >}}
+{{< figure src="/ox-hugo/du19_open_loop_three_stage.png" caption="<span class=\"figure-number\">Figure 10: </span>Frequency response of the open-loop transfer function" >}}
 
-The obtained sensitivity function is shown on figure [11](#orgde9819c).
+The obtained sensitivity function is shown on [Figure 11](#figure--fig:sensitivity-three-stage).
 
-<a id="orgde9819c"></a>
+<a id="figure--fig:sensitivity-three-stage"></a>
 
-{{< figure src="/ox-hugo/du19_sensitivity_three_stage.png" caption="Figure 11: Sensitivity function of the VCM single stage, the dual-stage and the three-stage loops" >}}
+{{< figure src="/ox-hugo/du19_sensitivity_three_stage.png" caption="<span class=\"figure-number\">Figure 11: </span>Sensitivity function of the VCM single stage, the dual-stage and the three-stage loops" >}}
 
 
 ### Performance Evaluation {#performance-evaluation}
@@ -319,13 +319,13 @@ Otherwise, saturation will occur in the control loop and the control system perf
 Therefore, the stroke specification of the actuators, especially milliactuator and microactuators, is very important for achievable control performance.
 Higher stroke actuators have stronger abilities to make sure that the control performances are not degraded in the presence of external vibrations.
 
-For the three-stage control architecture as shown on figure [9](#org4bda714), the position error is
+For the three-stage control architecture as shown on [Figure 9](#figure--fig:three-stage-control), the position error is
 \\[ e = -S(P\_v d\_1 + d\_2 + d\_e) + S n \\]
 The control signals and positions of the actuators are given by
 
 \begin{align\*}
-  u\_p &= C\_p e,\ y\_p = P\_p C\_p e \\\\\\
+  u\_p &= C\_p e,\ y\_p = P\_p C\_p e \\\\
-  u\_m &= C\_m e,\ y\_m = P\_m C\_m e \\\\\\
+  u\_m &= C\_m e,\ y\_m = P\_m C\_m e \\\\
   u\_v &= C\_v ( 1 + \hat{P}\_pC\_p ) e,\ y\_v = P\_v ( u\_v + d\_1 )
 \end{align\*}
 
@@ -335,11 +335,11 @@ Higher bandwidth/higher level of disturbance generally means high stroke needed.
 
 ### Different Configurations of the Control System {#different-configurations-of-the-control-system}
 
-A decoupled control structure can be used for the three-stage actuation system (see figure [12](#orga3b472d)).
+A decoupled control structure can be used for the three-stage actuation system (see [Figure 12](#figure--fig:three-stage-decoupled)).
 
 The overall sensitivity function is
 \\[ S(z) = \approx S\_v(z) S\_p(z) S\_m(z) \\]
-with \\(S\_v(z)\\) and \\(S\_p(z)\\) are defined in equation [1](#org442b5f7) and
+with \\(S\_v(z)\\) and \\(S\_p(z)\\) are defined in equation [ 1](#org40d0f02) and
 \\[ S\_m(z) = \frac{1}{1 + P\_m(z) C\_m(z)} \\]
 
 Denote the dual-stage open-loop transfer function as \\(G\_d\\)
@@ -348,23 +348,23 @@ Denote the dual-stage open-loop transfer function as \\(G\_d\\)
 The open-loop transfer function of the overall system is
 \\[ G(z) = G\_d(z) + G\_m(z) + G\_d(z) G\_m(z) \\]
 
-<a id="orga3b472d"></a>
+<a id="figure--fig:three-stage-decoupled"></a>
 
-{{< figure src="/ox-hugo/du19_three_stage_decoupled.png" caption="Figure 12: Decoupled control structure for the three-stage actuation system" >}}
+{{< figure src="/ox-hugo/du19_three_stage_decoupled.png" caption="<span class=\"figure-number\">Figure 12: </span>Decoupled control structure for the three-stage actuation system" >}}
 
 The control signals and the positions of the three actuators are
 
 \begin{align\*}
-  u\_p &= C\_p(1 + \hat{P}\_m C\_m) e, \ y\_p = P\_p u\_p \\\\\\
+  u\_p &= C\_p(1 + \hat{P}\_m C\_m) e, \ y\_p = P\_p u\_p \\\\
-  u\_m &= C\_m e, \ y\_m = P\_m M\_m e \\\\\\
+  u\_m &= C\_m e, \ y\_m = P\_m M\_m e \\\\
   u\_v &= C\_v(1 + \hat{P}\_p C\_p) (1 + \hat{P}\_m C\_m) e, \ y\_v = P\_v u\_v
 \end{align\*}
 
-The decoupled configuration makes the low frequency gain much higher, and consequently there is much better rejection capability at low frequency compared to the parallel architecture (see figure [13](#org5311716)).
+The decoupled configuration makes the low frequency gain much higher, and consequently there is much better rejection capability at low frequency compared to the parallel architecture (see [Figure 13](#figure--fig:three-stage-decoupled-loop-gain)).
 
-<a id="org5311716"></a>
+<a id="figure--fig:three-stage-decoupled-loop-gain"></a>
 
-{{< figure src="/ox-hugo/du19_three_stage_decoupled_loop_gain.png" caption="Figure 13: Frequency responses of the open-loop transfer functions for the three-stages parallel and decoupled structure" >}}
+{{< figure src="/ox-hugo/du19_three_stage_decoupled_loop_gain.png" caption="<span class=\"figure-number\">Figure 13: </span>Frequency responses of the open-loop transfer functions for the three-stages parallel and decoupled structure" >}}
 
 
 ### Conclusion {#conclusion}
@@ -671,7 +671,8 @@ Using PZT elements as a sensor to deal with high-frequency vibration beyond the
 As a more advanced concept, PZT elements being used as actuator and sensor simultaneously has also been addressed in this book with detailed scheme and controller design methodology for effective utilization.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org2403f17"></a>Du, Chunling, and Chee Khiang Pang. 2019. _Multi-Stage Actuation Systems and Control_. Boca Raton, FL: CRC Press.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Du, Chunling, and Chee Khiang Pang. 2019. <i>Multi-Stage Actuation Systems and Control</i>. Boca Raton, FL: CRC Press.</div>
+</div>

content/book/hatch00_vibrat_matlab_ansys.md

@@ -1,16 +1,16 @@
 +++
 title = "Vibration Simulation using Matlab and ANSYS"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 description = "Nice techniques to analyze resonant systems with Ansys and Matlab."
 keywords = ["Modal Analysis", "FEM"]
 draft = false
 +++
 
 Tags
-: [Finite Element Model]({{< relref "finite_element_model" >}})
+: [Finite Element Model]({{< relref "finite_element_model.md" >}})
 
 Reference
-: ([Hatch 2000](#org4036e02))
+: (<a href="#citeproc_bib_item_1">Hatch 2000</a>)
 
 Author(s)
 : Hatch, M. R.
@@ -23,17 +23,16 @@ Matlab Code form the book is available [here](https://in.mathworks.com/matlabcen
 
 ## Introduction {#introduction}
 
-<a id="org96f8e54"></a>
+<span class="org-target" id="org-target--sec-introduction"></span>
 
 The main goal of this book is to show how to take results of large dynamic finite element models and build small Matlab state space dynamic mechanical models for use in control system models.
 
 
 ### Modal Analysis {#modal-analysis}
 
-The diagram in Figure [1](#org97c03ca) shows the methodology for analyzing a lightly damped structure using normal modes.
+The diagram in [Figure 1](#figure--fig:hatch00-modal-analysis-flowchart) shows the methodology for analyzing a lightly damped structure using normal modes.
 
 <div class="important">
-  <div></div>
 
 The steps are:
 
@@ -48,9 +47,9 @@ The steps are:
 
 </div>
 
-<a id="org97c03ca"></a>
+<a id="figure--fig:hatch00-modal-analysis-flowchart"></a>
 
-{{< figure src="/ox-hugo/hatch00_modal_analysis_flowchart.png" caption="Figure 1: Modal analysis method flowchart" >}}
+{{< figure src="/ox-hugo/hatch00_modal_analysis_flowchart.png" caption="<span class=\"figure-number\">Figure 1: </span>Modal analysis method flowchart" >}}
 
 
 ### Model Size Reduction {#model-size-reduction}
@@ -58,9 +57,8 @@ The steps are:
 Because finite element models usually have a very large number of states, an important step is the reduction of the number of states while still providing correct responses for the forcing function input and desired output points.
 
 <div class="important">
-  <div></div>
 
-Figure [2](#orgdbb9ffa) shows such process, the steps are:
+[Figure 2](#figure--fig:hatch00-model-reduction-chart) shows such process, the steps are:
 
 -   start with the finite element model
 -   compute the eigenvalues and eigenvectors (as many as dof in the model)
@@ -73,18 +71,18 @@ Figure [2](#orgdbb9ffa) shows such process, the steps are:
 
 </div>
 
-<a id="orgdbb9ffa"></a>
+<a id="figure--fig:hatch00-model-reduction-chart"></a>
 
-{{< figure src="/ox-hugo/hatch00_model_reduction_chart.png" caption="Figure 2: Model size reduction flowchart" >}}
+{{< figure src="/ox-hugo/hatch00_model_reduction_chart.png" caption="<span class=\"figure-number\">Figure 2: </span>Model size reduction flowchart" >}}
 
 
 ### Notations {#notations}
 
-Tables [3](#org4819d7f), [2](#table--tab:notations-eigen-vectors-values) and [3](#table--tab:notations-stiffness-mass) summarize the notations of this document.
+[Figure 3](#figure--fig:hatch00-n-dof-zeros), [Table 2](#table--tab:notations-eigen-vectors-values) and [Table 3](#table--tab:notations-stiffness-mass) summarize the notations of this document.
 
 <a id="table--tab:notations-modes-nodes"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:notations-modes-nodes">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:notations-modes-nodes">Table 1</a>:</span>
   Notation for the modes and nodes
 </div>
 
@@ -99,7 +97,7 @@ Tables [3](#org4819d7f), [2](#table--tab:notations-eigen-vectors-values) and [3]
 
 <a id="table--tab:notations-eigen-vectors-values"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:notations-eigen-vectors-values">Table 2</a></span>:
+  <span class="table-number"><a href="#table--tab:notations-eigen-vectors-values">Table 2</a>:</span>
   Notation for the dofs, eigenvectors and eigenvalues
 </div>
 
@@ -114,7 +112,7 @@ Tables [3](#org4819d7f), [2](#table--tab:notations-eigen-vectors-values) and [3]
 
 <a id="table--tab:notations-stiffness-mass"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:notations-stiffness-mass">Table 3</a></span>:
+  <span class="table-number"><a href="#table--tab:notations-stiffness-mass">Table 3</a>:</span>
   Notation for the mass and stiffness matrices
 </div>
 
@@ -129,22 +127,21 @@ Tables [3](#org4819d7f), [2](#table--tab:notations-eigen-vectors-values) and [3]
 
 ## Zeros in SISO Mechanical Systems {#zeros-in-siso-mechanical-systems}
 
-<a id="orgca1a04d"></a>
+<span class="org-target" id="org-target--sec-zeros-siso-systems"></span>
 The origin and influence of poles are clear: they represent the resonant frequencies of the system, and for each resonance frequency, a mode shape can be defined to describe the motion at that frequency.
 
 We here which to give an intuitive understanding for **when to expect zeros in SISO mechanical systems** and **how to predict the frequencies at which they will occur**.
 
-Figure [3](#org4819d7f) shows a series arrangement of masses and springs, with a total of \\(n\\) masses and \\(n+1\\) springs.
+[Figure 3](#figure--fig:hatch00-n-dof-zeros) shows a series arrangement of masses and springs, with a total of \\(n\\) masses and \\(n+1\\) springs.
 The degrees of freedom are numbered from left to right, \\(z\_1\\) through \\(z\_n\\).
 
-<a id="org4819d7f"></a>
+<a id="figure--fig:hatch00-n-dof-zeros"></a>
 
-{{< figure src="/ox-hugo/hatch00_n_dof_zeros.png" caption="Figure 3: n dof system showing various SISO input/output configurations" >}}
+{{< figure src="/ox-hugo/hatch00_n_dof_zeros.png" caption="<span class=\"figure-number\">Figure 3: </span>n dof system showing various SISO input/output configurations" >}}
 
 <div class="important">
-  <div></div>
 
-([Miu 1993](#orgcda3e53)) shows that the zeros of any particular transfer function are the poles of the constrained system to the left and/or right of the system defined by constraining the one or two dof's defining the transfer function.
+(<a href="#citeproc_bib_item_2">Miu 1993</a>) shows that the zeros of any particular transfer function are the poles of the constrained system to the left and/or right of the system defined by constraining the one or two dof's defining the transfer function.
 
 The resonances of the "overhanging appendages" of the constrained system create the zeros.
 
@@ -153,17 +150,16 @@ The resonances of the "overhanging appendages" of the constrained system create
 
 ## State Space Analysis {#state-space-analysis}
 
-<a id="orgc4e6e06"></a>
+<span class="org-target" id="org-target--sec-state-space-analysis"></span>
 
 
 ## Modal Analysis {#modal-analysis}
 
-<a id="orge1af07f"></a>
+<span class="org-target" id="org-target--sec-modal-analysis"></span>
 
 Lightly damped structures are typically analyzed with the "normal mode" method described in this section.
 
 <div class="important">
-  <div></div>
 
 The modal method allows one to replace the n-coupled differential equations with n-uncoupled equations, where each uncoupled equation represents the motion of the system for that mode of vibration.
 
@@ -175,7 +171,6 @@ Heavily damped structures or structures which explicit damping elements, such as
 Thus, the present methods only works for lightly damped structures.
 
 <div class="important">
-  <div></div>
 
 Summarizing the modal analysis method of analyzing linear mechanical systems and the benefits derived:
 
@@ -198,34 +193,34 @@ Summarizing the modal analysis method of analyzing linear mechanical systems and
 
 #### Equation of Motion {#equation-of-motion}
 
-Let's consider the model shown in Figure [4](#orgde2ed42) with \\(k\_1 = k\_2 = k\\), \\(m\_1 = m\_2 = m\_3 = m\\) and \\(c\_1 = c\_2 = 0\\).
+Let's consider the model shown in [Figure 4](#figure--fig:hatch00-undamped-tdof-model) with \\(k\_1 = k\_2 = k\\), \\(m\_1 = m\_2 = m\_3 = m\\) and \\(c\_1 = c\_2 = 0\\).
 
-<a id="orgde2ed42"></a>
+<a id="figure--fig:hatch00-undamped-tdof-model"></a>
 
-{{< figure src="/ox-hugo/hatch00_undamped_tdof_model.png" caption="Figure 4: Undamped tdof model" >}}
+{{< figure src="/ox-hugo/hatch00_undamped_tdof_model.png" caption="<span class=\"figure-number\">Figure 4: </span>Undamped tdof model" >}}
 
 The equations of motions are:
 
 \begin{equation}
 \begin{bmatrix}
-  m & 0 & 0 \\\\\\
+  m & 0 & 0 \\\\
-  0 & m & 0 \\\\\\
+  0 & m & 0 \\\\
   0 & 0 & m
 \end{bmatrix} \begin{bmatrix}
-  \ddot{z}\_1 \\\\\\
+  \ddot{z}\_1 \\\\
-  \ddot{z}\_2 \\\\\\
+  \ddot{z}\_2 \\\\
   \ddot{z}\_3
 \end{bmatrix} + \begin{bmatrix}
-  k & -k & 0 \\\\\\
+  k & -k & 0 \\\\
-  -k & 2k & -k \\\\\\
+  -k & 2k & -k \\\\
   0 & -k & k
 \end{bmatrix} \begin{bmatrix}
-  z\_1 \\\\\\
+  z\_1 \\\\
-  z\_2 \\\\\\
+  z\_2 \\\\
   z\_3
 \end{bmatrix} = \begin{bmatrix}
-  0 \\\\\\
+  0 \\\\
-  0 \\\\\\
+  0 \\\\
   0
 \end{bmatrix} \label{eq:tdof\_eom}
 \end{equation}
@@ -236,7 +231,6 @@ The equations of motions are:
 Since the system is conservative (it has no damping), normal modes of vibration will exist.
 
 <div class="important">
-  <div></div>
 
 Having normal modes means that at certain frequencies all points in the system will vibrate at the same frequency and in phase, i.e., **all points in the system will reach their minimum and maximum displacements at the same point in time**.
 
@@ -258,7 +252,7 @@ where:
 
 #### Eigenvalues / Characteristic Equation {#eigenvalues-characteristic-equation}
 
-Re-injecting normal modes \eqref{eq:principal_mode} into the equation of motion \eqref{eq:tdof_eom} gives the eigenvalue problem:
+Re-injecting normal modes \eqref{eq:principal\_mode} into the equation of motion \eqref{eq:tdof\_eom} gives the eigenvalue problem:
 
 \begin{equation}
   (\bm{k} - \omega\_i^2 \bm{m}) \bm{z}\_{mi} = 0
@@ -285,45 +279,45 @@ One then find:
 
 \begin{equation}
   \bm{z}\_1 = \begin{bmatrix}
-    1 \\\\\\
+    1 \\\\
-    1 \\\\\\
+    1 \\\\
     1
   \end{bmatrix}, \quad \bm{z}\_2 = \begin{bmatrix}
-    1 \\\\\\
+    1 \\\\
-    0 \\\\\\
+    0 \\\\
     -1
   \end{bmatrix}, \quad \bm{z}\_3 = \begin{bmatrix}
-    1 \\\\\\
+    1 \\\\
-    -2 \\\\\\
+    -2 \\\\
     1
   \end{bmatrix}
 \end{equation}
 
-Virtual interpretation of the eigenvectors are shown in Figures [5](#orgc0f09b0), [6](#org88e7153) and [7](#org8225e3c).
+Virtual interpretation of the eigenvectors are shown in [Figure 5](#figure--fig:hatch00-tdof-mode-1), [Figure 6](#figure--fig:hatch00-tdof-mode-2) and [Figure 7](#figure--fig:hatch00-tdof-mode-3).
 
-<a id="orgc0f09b0"></a>
+<a id="figure--fig:hatch00-tdof-mode-1"></a>
 
-{{< figure src="/ox-hugo/hatch00_tdof_mode_1.png" caption="Figure 5: Rigid-Body Mode, 0rad/s" >}}
+{{< figure src="/ox-hugo/hatch00_tdof_mode_1.png" caption="<span class=\"figure-number\">Figure 5: </span>Rigid-Body Mode, 0rad/s" >}}
 
-<a id="org88e7153"></a>
+<a id="figure--fig:hatch00-tdof-mode-2"></a>
 
-{{< figure src="/ox-hugo/hatch00_tdof_mode_2.png" caption="Figure 6: Second Model, Middle Mass Stationary, 1rad/s" >}}
+{{< figure src="/ox-hugo/hatch00_tdof_mode_2.png" caption="<span class=\"figure-number\">Figure 6: </span>Second Model, Middle Mass Stationary, 1rad/s" >}}
 
-<a id="org8225e3c"></a>
+<a id="figure--fig:hatch00-tdof-mode-3"></a>
 
-{{< figure src="/ox-hugo/hatch00_tdof_mode_3.png" caption="Figure 7: Third Mode, 1.7rad/s" >}}
+{{< figure src="/ox-hugo/hatch00_tdof_mode_3.png" caption="<span class=\"figure-number\">Figure 7: </span>Third Mode, 1.7rad/s" >}}
 
 
 #### Modal Matrix {#modal-matrix}
 
-The modal matrix is an \\(n \times m\\) matrix with columns corresponding to the \\(m\\) system eigenvectors as shown in Eq. \eqref{eq:modal_matrix}
+The modal matrix is an \\(n \times m\\) matrix with columns corresponding to the \\(m\\) system eigenvectors as shown in Eq. \eqref{eq:modal\_matrix}
 
 \begin{equation}
   \bm{z}\_m = \begin{bmatrix}
   \bm{z}\_1 & \bm{z}\_2 & \bm{z}\_3
 \end{bmatrix} = \begin{bmatrix}
-  z\_{m11} & z\_{m12} & z\_{m13} \\\\\\
+  z\_{m11} & z\_{m12} & z\_{m13} \\\\
-  z\_{m21} & z\_{m22} & z\_{m23} \\\\\\
+  z\_{m21} & z\_{m22} & z\_{m23} \\\\
   z\_{m31} & z\_{m32} & z\_{m33}
 \end{bmatrix} \label{eq:modal\_matrix}
 \end{equation}
@@ -339,7 +333,6 @@ It is thus useful to **transform the n-coupled second order differential equatio
 In linear algebra terms, the transformation from physical to principal coordinates is known as a **change of basis**.
 
 <div class="important">
-  <div></div>
 
 There are many options for change of basis, but we will show that **when eigenvectors are used for the transformation, the principal coordinate system has a physical meaning: each of the uncoupled sdof systems represents the motion of a specific mode of vibration**.
 
@@ -348,11 +341,11 @@ There are many options for change of basis, but we will show that **when eigenve
 The n-uncoupled equations in the principal coordinate system can then be solved for the responses in the principal coordinate system using the well known solutions for the single dof systems.
 The n-responses in the principal coordinate system can then be **transformed back** to the physical coordinate system to provide the actual response in physical coordinate.
 
-This procedure is schematically shown in Figure [8](#org0f0be39).
+This procedure is schematically shown in [Figure 8](#figure--fig:hatch00-schematic-modal-solution).
 
-<a id="org0f0be39"></a>
+<a id="figure--fig:hatch00-schematic-modal-solution"></a>
 
-{{< figure src="/ox-hugo/hatch00_schematic_modal_solution.png" caption="Figure 8: Roadmap for Modal Solution" >}}
+{{< figure src="/ox-hugo/hatch00_schematic_modal_solution.png" caption="<span class=\"figure-number\">Figure 8: </span>Roadmap for Modal Solution" >}}
 
 The condition to guarantee diagonalization is the existence of n-linearly independent eigenvectors, which is always the case if either:
 
@@ -407,12 +400,12 @@ One method is to normalize with respect to unity, making the **largest** element
 
 \begin{equation}
   \bm{z}\_m = \begin{bmatrix}
-  1 & 1 & 1 \\\\\\
+  1 & 1 & 1 \\\\
-  1 & 0 & -2 \\\\\\
+  1 & 0 & -2 \\\\
   1 & -1 & 1
 \end{bmatrix} \Longrightarrow \bm{z}\_n \begin{bmatrix}
-  1 & 1 & -0.5 \\\\\\
+  1 & 1 & -0.5 \\\\
-  1 & 0 & 1 \\\\\\
+  1 & 0 & 1 \\\\
   1 & -1 & -0.5
 \end{bmatrix}
 \end{equation}
@@ -423,12 +416,12 @@ Transforming the mass and stiffness matrices give:
 
 \begin{equation}
   \bm{m}\_n = \bm{z}\_n^T \bm{m} \bm{z}\_n = \begin{bmatrix}
-  3m & 0 & 0 \\\\\\
+  3m & 0 & 0 \\\\
-  0 & 2m & 0 \\\\\\
+  0 & 2m & 0 \\\\
   0 & 0 & 1.5m
 \end{bmatrix}; \quad \bm{k}\_n = \bm{z}\_n^T \bm{k} \bm{z}\_n = \begin{bmatrix}
-  0 & 0 & 0 \\\\\\
+  0 & 0 & 0 \\\\
-  0 & 2k & 0 \\\\\\
+  0 & 2k & 0 \\\\
   0 & 0 & 4.5k
 \end{bmatrix}
 \end{equation}
@@ -455,12 +448,12 @@ And the normalized mass and stiffness matrices are:
 
 \begin{equation}
   \bm{m}\_n = \begin{bmatrix}
-  1 & 0 & 0 \\\\\\
+  1 & 0 & 0 \\\\
-  0 & 1 & 0 \\\\\\
+  0 & 1 & 0 \\\\
   0 & 0 & 1
 \end{bmatrix}; \quad \bm{k}\_n = \begin{bmatrix}
-  0 & 0 & 0 \\\\\\
+  0 & 0 & 0 \\\\
-  0 & 1 & 0 \\\\\\
+  0 & 1 & 0 \\\\
   0 & 0 & 3
 \end{bmatrix} \frac{k}{m}
 \end{equation}
@@ -471,7 +464,6 @@ The normalized stiffness matrix is known as the **spectral matrix**.
 Normalizing with respect to mass results in an identify principal mass matrix and squares of the eigenvalues on the diagonal in the principal stiffness matrix, this normalization technique is thus very useful for the following reason.
 
 <div class="important">
-  <div></div>
 
 Since we know the form of the principal matrices when normalizing with respect to mass, no multiplying of modal matrices is actually required: **the homogeneous principal equations of motion can be written by inspection knowing only the eigenvalues**.
 
@@ -498,7 +490,6 @@ Pre-multiplying by \\(\bm{z}\_n^T\\) and inserting \\(I = \bm{z}\_n \bm{z}\_n^{-
 Which is re-written in the following form:
 
 <div class="important">
-  <div></div>
 
 \begin{equation}
   \bm{m}\_p \ddot{\bm{z}}\_p + \bm{k}\_p \bm{z}\_p = \bm{F}\_p
@@ -517,7 +508,7 @@ where:
 The vectors of initial displacements \\(\bm{z}\_{op}\\) and velocities \\(\dot{\bm{z}}\_{op}\\) in the principal coordinate system can be expressed as:
 
 \begin{align}
-  \bm{z}\_{op} &= \bm{z}\_n^{-1} \bm{z}\_0 \\\\\\
+  \bm{z}\_{op} &= \bm{z}\_n^{-1} \bm{z}\_0 \\\\
   \dot{\bm{z}}\_{op} &= \bm{z}\_n^{-1} \dot{\bm{z}}\_0
 \end{align}
 
@@ -529,7 +520,6 @@ where \\(\bm{z}\_0\\) and \\(\dot{\bm{z}}\_0\\) are the vectors of initial displ
 We have now everything required to solve the equations in the principal coordinate system.
 
 <div class="important">
-  <div></div>
 
 The variables in physical coordinates are the positions and velocities of the masses.
 The variables in principal coordinates are the displacements and velocities of each mode of vibration.
@@ -568,12 +558,12 @@ Let's first examine the force transformation from physical to principal coordina
 
 \begin{equation}
   \bm{F}\_p = \bm{z}\_n^T \bm{F} = \begin{bmatrix}
-  z\_{n11} & z\_{n12} & z\_{n13} \\\\\\
+  z\_{n11} & z\_{n12} & z\_{n13} \\\\
-  z\_{n21} & z\_{n22} & z\_{n23} \\\\\\
+  z\_{n21} & z\_{n22} & z\_{n23} \\\\
   z\_{n31} & z\_{n32} & z\_{n33}
 \end{bmatrix}^T \begin{bmatrix}
-  F\_1 \\\\\\
+  F\_1 \\\\
-  F\_2 \\\\\\
+  F\_2 \\\\
   F\_3
 \end{bmatrix}
 \end{equation}
@@ -584,12 +574,12 @@ Let's now examine the displacement transformation from principal to physical coo
 
 \begin{equation}
   \bm{z} = \bm{z}\_n \bm{z}\_p = \begin{bmatrix}
-  z\_{n11} & z\_{n12} & z\_{n13} \\\\\\
+  z\_{n11} & z\_{n12} & z\_{n13} \\\\
-  z\_{n21} & z\_{n22} & z\_{n23} \\\\\\
+  z\_{n21} & z\_{n22} & z\_{n23} \\\\
   z\_{n31} & z\_{n32} & z\_{n33}
 \end{bmatrix} \begin{bmatrix}
-  z\_{p1} \\\\\\
+  z\_{p1} \\\\
-  z\_{p2} \\\\\\
+  z\_{p2} \\\\
   z\_{p3}
 \end{bmatrix}
 \end{equation}
@@ -597,7 +587,6 @@ Let's now examine the displacement transformation from principal to physical coo
 And thus, if we are only interested in the physical displacement of the mass 2 (\\(z\_2 = z\_{n21} z\_{p1} + z\_{n22} z\_{p2} + z\_{n23} z\_{p3}\\)), only the second row of the modal matrix is required to transform the three displacements \\(z\_{p1}\\), \\(z\_{p2}\\), \\(z\_{p3}\\) in principal coordinates to \\(z\_2\\).
 
 <div class="important">
-  <div></div>
 
 **Only the rows of the modal matrix that correspond to degrees of freedom to which forces are applied and/or for which displacements are desired are required to complete the model.**
 
@@ -698,7 +687,7 @@ Absolute damping is based on making \\(b = 0\\), in which case the percentage of
 
 ## Frequency Response: Modal Form {#frequency-response-modal-form}
 
-<a id="org027da35"></a>
+<span class="org-target" id="org-target--sec-frequency-response-modal-form"></span>
 
 The procedure to obtain the frequency response from a modal form is as follow:
 
@@ -706,11 +695,11 @@ The procedure to obtain the frequency response from a modal form is as follow:
 -   use Laplace transform to obtain the transfer functions in principal coordinates
 -   back-transform the transfer functions to physical coordinates where the individual mode contributions will be evident
 
-This will be applied to the model shown in Figure [9](#orgafc54fa).
+This will be applied to the model shown in [Figure 9](#figure--fig:hatch00-tdof-model).
 
-<a id="orgafc54fa"></a>
+<a id="figure--fig:hatch00-tdof-model"></a>
 
-{{< figure src="/ox-hugo/hatch00_tdof_model.png" caption="Figure 9: tdof undamped model for modal analysis" >}}
+{{< figure src="/ox-hugo/hatch00_tdof_model.png" caption="<span class=\"figure-number\">Figure 9: </span>tdof undamped model for modal analysis" >}}
 
 
 ### Review from Previous Results {#review-from-previous-results}
@@ -725,8 +714,8 @@ From previous analysis, we know the eigenvalues and eigenvectors normalized with
 
 \begin{equation}
   \bm{z}\_n = \frac{1}{\sqrt{m}} \begin{bmatrix}
-  \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} \\\\\\
+  \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} \\\\
-  \frac{1}{\sqrt{3}} & 0 & \frac{-2}{\sqrt{6}} \\\\\\
+  \frac{1}{\sqrt{3}} & 0 & \frac{-2}{\sqrt{6}} \\\\
   \frac{1}{\sqrt{3}} & \frac{-1}{\sqrt{2}} & \frac{1}{\sqrt{6}}
 \end{bmatrix}
 \end{equation}
@@ -735,13 +724,13 @@ Knowing that in principal coordinates the mass matrix is the identify matrix and
 
 \begin{equation}
   \bm{m}\_n = \begin{bmatrix}
-  1 & 0 & 0 \\\\\\
+  1 & 0 & 0 \\\\
-  0 & 1 & 0 \\\\\\
+  0 & 1 & 0 \\\\
   0 & 0 & 1
 \end{bmatrix}, \quad
   \bm{k}\_n = \begin{bmatrix}
-  0 & 0 & 0 \\\\\\
+  0 & 0 & 0 \\\\
-  0 & 1 & 0 \\\\\\
+  0 & 1 & 0 \\\\
   0 & 0 & 3
 \end{bmatrix} \frac{k}{m}
 \end{equation}
@@ -761,8 +750,8 @@ The equations of motion in principal coordinates are then:
 which give:
 
 \begin{align}
-  \ddot{z}\_{p1} &= (F\_1 + F\_2 + F\_3) \frac{1}{\sqrt{3m}} \\\\\\
+  \ddot{z}\_{p1} &= (F\_1 + F\_2 + F\_3) \frac{1}{\sqrt{3m}} \\\\
-  \ddot{z}\_{p2} + \frac{k}{m} z\_{p2} &= (F\_1 - F\_3) \frac{1}{\sqrt{2m}} \\\\\\
+  \ddot{z}\_{p2} + \frac{k}{m} z\_{p2} &= (F\_1 - F\_3) \frac{1}{\sqrt{2m}} \\\\
   \ddot{z}\_{p3} + \frac{3k}{m} z\_{p3} &= (F\_1 - 2 F\_2 + F\_3) \frac{1}{\sqrt{6m}}
 \end{align}
 
@@ -773,48 +762,48 @@ Taking the Laplace transform of each equation gives:
 
 \begin{equation}
   \begin{bmatrix}
-    \frac{z\_{p1}}{F\_{1}} \\\\\\
+    \frac{z\_{p1}}{F\_{1}} \\\\
-    \frac{z\_{p2}}{F\_{1}} \\\\\\
+    \frac{z\_{p2}}{F\_{1}} \\\\
     \frac{z\_{p3}}{F\_{1}}
   \end{bmatrix} = \begin{bmatrix}
-    \frac{1}{s^{2}\sqrt{3m}} \\\\\\
+    \frac{1}{s^{2}\sqrt{3m}} \\\\
-    \frac{1}{(s^{2} + \omega\_{2}^{2})\sqrt{2m}} \\\\\\
+    \frac{1}{(s^{2} + \omega\_{2}^{2})\sqrt{2m}} \\\\
     \frac{1}{(s^{2} + \omega\_{3}^{2})\sqrt{6m}}
   \end{bmatrix} = \begin{bmatrix}
-    z\_{p11} \\\\\\
+    z\_{p11} \\\\
-    z\_{p21} \\\\\\
+    z\_{p21} \\\\
     z\_{p31}
 \end{bmatrix}
 \end{equation}
 
 \begin{equation}
   \begin{bmatrix}
-    \frac{z\_{p1}}{F\_{2}} \\\\\\
+    \frac{z\_{p1}}{F\_{2}} \\\\
-    \frac{z\_{p2}}{F\_{2}} \\\\\\
+    \frac{z\_{p2}}{F\_{2}} \\\\
     \frac{z\_{p3}}{F\_{2}}
   \end{bmatrix} = \begin{bmatrix}
-    \frac{1}{s^{2}\sqrt{3m}} \\\\\\
+    \frac{1}{s^{2}\sqrt{3m}} \\\\
-    0 \\\\\\
+    0 \\\\
     \frac{-2}{(s^{2} + \omega\_{3}^{2})\sqrt{6m}}
   \end{bmatrix} = \begin{bmatrix}
-    z\_{p12} \\\\\\
+    z\_{p12} \\\\
-    z\_{p22} \\\\\\
+    z\_{p22} \\\\
     z\_{p32}
 \end{bmatrix}
 \end{equation}
 
 \begin{equation}
   \begin{bmatrix}
-    \frac{z\_{p1}}{F\_{3}} \\\\\\
+    \frac{z\_{p1}}{F\_{3}} \\\\
-    \frac{z\_{p2}}{F\_{3}} \\\\\\
+    \frac{z\_{p2}}{F\_{3}} \\\\
     \frac{z\_{p3}}{F\_{3}}
   \end{bmatrix} = \begin{bmatrix}
-    \frac{1}{s^{2}\sqrt{3m}} \\\\\\
+    \frac{1}{s^{2}\sqrt{3m}} \\\\
-    \frac{-1}{(s^{2} + \omega\_{2}^{2})\sqrt{2m}} \\\\\\
+    \frac{-1}{(s^{2} + \omega\_{2}^{2})\sqrt{2m}} \\\\
     \frac{1}{(s^{2} + \omega\_{3}^{2})\sqrt{6m}}
   \end{bmatrix} = \begin{bmatrix}
-    z\_{p13} \\\\\\
+    z\_{p13} \\\\
-    z\_{p23} \\\\\\
+    z\_{p23} \\\\
     z\_{p33}
 \end{bmatrix}
 \end{equation}
@@ -839,7 +828,7 @@ And the transfer functions \\(\frac{z\_i}{F\_j}\\) can be computed.
 For instance, the contributions to the transfer function \\(\frac{z\_1}{F\_1}\\) are:
 
 \begin{align}
-  \frac{z\_1}{F\_1} &= \underbrace{z\_{n11} z\_{p11}}\_{\text{1st mode}} + \underbrace{z\_{n12} z\_{p21}}\_{\text{2nd mode}} + \underbrace{z\_{n13} z\_{p31}}\_{\text{3rd mode}} \\\\\\
+  \frac{z\_1}{F\_1} &= \underbrace{z\_{n11} z\_{p11}}\_{\text{1st mode}} + \underbrace{z\_{n12} z\_{p21}}\_{\text{2nd mode}} + \underbrace{z\_{n13} z\_{p31}}\_{\text{3rd mode}} \\\\
   & = \frac{\frac{1}{3m}}{s^2} + \frac{\frac{1}{2m}}{s^2 + \omega\_2^2} + \frac{\frac{1}{6m}}{s^2 + \omega\_3^2}
 \end{align}
 
@@ -858,7 +847,6 @@ The forces transform in the principal coordinates using:
 \end{equation}
 
 <div class="important">
-  <div></div>
 
 Thus, if \\(\bm{F}\\) is aligned with \\(\bm{z}\_{ni}\\) (the i'th normalized eigenvector), then \\(\bm{F}\_p\\) will be null except for its i'th term and only the i'th mode will be excited.
 
@@ -870,7 +858,6 @@ Thus, if \\(\bm{F}\\) is aligned with \\(\bm{z}\_{ni}\\) (the i'th normalized ei
 Any transfer function derived from the modal analysis is an additive combination of sdof systems.
 
 <div class="important">
-  <div></div>
 
 Each single degree of freedom system has a gain determined by the appropriate eigenvector entries and a resonant frequency given by the appropriate eigenvalue.
 
@@ -886,33 +873,33 @@ If modes have some damping:
   \frac{z\_j}{F\_k} = \sum\_{i = 1}^m \frac{z\_{nji} z\_{nki}}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2} \label{eq:general\_add\_tf\_damp}
 \end{equation}
 
-Equations \eqref{eq:general_add_tf} and \eqref{eq:general_add_tf_damp} shows that in general every transfer function is made up of **additive combinations of single degree of freedom systems**, with each system having its DC gain determined by the appropriate eigenvector entry product divided by the square of the eigenvalue, \\(z\_{nji} z\_{nki}/\omega\_i^2\\), and with resonant frequency defined by the eigenvalue \\(\omega\_i\\).
+Equations \eqref{eq:general\_add\_tf} and \eqref{eq:general\_add\_tf\_damp} shows that in general every transfer function is made up of **additive combinations of single degree of freedom systems**, with each system having its DC gain determined by the appropriate eigenvector entry product divided by the square of the eigenvalue, \\(z\_{nji} z\_{nki}/\omega\_i^2\\), and with resonant frequency defined by the eigenvalue \\(\omega\_i\\).
 
 </div>
 
-Figure [10](#orgf64b6e5) shows the separate contributions of each mode to the total response \\(z\_1/F\_1\\).
+[Figure 10](#figure--fig:hatch00-z11-tf-example) shows the separate contributions of each mode to the total response \\(z\_1/F\_1\\).
 
-<a id="orgf64b6e5"></a>
+<a id="figure--fig:hatch00-z11-tf-example"></a>
 
-{{< figure src="/ox-hugo/hatch00_z11_tf.png" caption="Figure 10: Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_1\\)" >}}
+{{< figure src="/ox-hugo/hatch00_z11_tf.png" caption="<span class=\"figure-number\">Figure 10: </span>Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_1\\)" >}}
 
 The zeros for SISO transfer functions are the roots of the numerator, however, from modal analysis we can see that the zeros arise when modes combine with appropriate phase such that the resulting motion is null.
 
 
 ## SISO State Space Matlab Model from ANSYS Model {#siso-state-space-matlab-model-from-ansys-model}
 
-<a id="org39bd7f2"></a>
+<span class="org-target" id="org-target--sec-siso-state-space"></span>
 
 
 ### Introduction {#introduction}
 
-In this section is developed a SISO state space Matlab model from an ANSYS cantilever beam model as shown in Figure [11](#orgc285575).
+In this section is developed a SISO state space Matlab model from an ANSYS cantilever beam model as shown in [Figure 11](#figure--fig:hatch00-cantilever-beam).
 A z direction force is applied at the midpoint of the beam and z displacement at the tip is the output.
 The objective is to provide the smallest Matlab state space model that accurately represents the pertinent dynamics.
 
-<a id="orgc285575"></a>
+<a id="figure--fig:hatch00-cantilever-beam"></a>
 
-{{< figure src="/ox-hugo/hatch00_cantilever_beam.png" caption="Figure 11: Cantilever beam with forcing function at midpoint" >}}
+{{< figure src="/ox-hugo/hatch00_cantilever_beam.png" caption="<span class=\"figure-number\">Figure 11: </span>Cantilever beam with forcing function at midpoint" >}}
 
 The steps to define the smallest model are:
 
@@ -952,7 +939,7 @@ We will discuss in this section two methods of sorting, one which is applicable
 The general equation for the overall transfer function of undamped and damped systems are:
 
 \begin{align}
-  \frac{z\_j}{F\_k} &= \sum\_{i = 1}^m \frac{z\_{nji} z\_{nki}}{s^2 + \omega\_i^2} \\\\\\
+  \frac{z\_j}{F\_k} &= \sum\_{i = 1}^m \frac{z\_{nji} z\_{nki}}{s^2 + \omega\_i^2} \\\\
   \frac{z\_j}{F\_k} &= \sum\_{i = 1}^m \frac{z\_{nji} z\_{nki}}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2}
 \end{align}
 
@@ -989,7 +976,7 @@ If sorting of DC gain values is performed prior to the `truncate` operation, the
 
 ## Ground Acceleration Matlab Model From ANSYS Model {#ground-acceleration-matlab-model-from-ansys-model}
 
-<a id="org658f39a"></a>
+<span class="org-target" id="org-target--sec-ground-acceleration"></span>
 
 
 ### Model Description {#model-description}
@@ -1003,25 +990,25 @@ If sorting of DC gain values is performed prior to the `truncate` operation, the
 
 ## SISO Disk Drive Actuator Model {#siso-disk-drive-actuator-model}
 
-<a id="orgcd094f5"></a>
+<span class="org-target" id="org-target--sec-siso-disk-drive"></span>
 
-In this section we wish to extract a SISO state space model from a Finite Element model representing a Disk Drive Actuator (Figure [12](#org97a4ded)).
+In this section we wish to extract a SISO state space model from a Finite Element model representing a Disk Drive Actuator ([Figure 12](#figure--fig:hatch00-disk-drive-siso-model)).
 
 
 ### Actuator Description {#actuator-description}
 
-<a id="org97a4ded"></a>
+<a id="figure--fig:hatch00-disk-drive-siso-model"></a>
 
-{{< figure src="/ox-hugo/hatch00_disk_drive_siso_model.png" caption="Figure 12: Drawing of Actuator/Suspension system" >}}
+{{< figure src="/ox-hugo/hatch00_disk_drive_siso_model.png" caption="<span class=\"figure-number\">Figure 12: </span>Drawing of Actuator/Suspension system" >}}
 
-The primary motion of the actuator is rotation about the pivot bearing, therefore the final model has the coordinate system transformed from a Cartesian x,y,z coordinate system to a Cylindrical \\(r\\), \\(\theta\\) and \\(z\\) system, with the two origins coincident (Figure [13](#orga92b66d)).
+The primary motion of the actuator is rotation about the pivot bearing, therefore the final model has the coordinate system transformed from a Cartesian x,y,z coordinate system to a Cylindrical \\(r\\), \\(\theta\\) and \\(z\\) system, with the two origins coincident ([Figure 13](#figure--fig:hatch00-disk-drive-nodes-reduced-model)).
 
-<a id="orga92b66d"></a>
+<a id="figure--fig:hatch00-disk-drive-nodes-reduced-model"></a>
 
-{{< figure src="/ox-hugo/hatch00_disk_drive_nodes_reduced_model.png" caption="Figure 13: Nodes used for reduced Matlab model. Shown with partial finite element mesh at coil" >}}
+{{< figure src="/ox-hugo/hatch00_disk_drive_nodes_reduced_model.png" caption="<span class=\"figure-number\">Figure 13: </span>Nodes used for reduced Matlab model. Shown with partial finite element mesh at coil" >}}
 
 For reduced models, we only require eigenvector information for dof where forces are applied and where displacements are required.
-Figure [13](#orga92b66d) shows the nodes used for the reduced Matlab model.
+[Figure 13](#figure--fig:hatch00-disk-drive-nodes-reduced-model) shows the nodes used for the reduced Matlab model.
 The four nodes 24061, 24066, 24082 and 24087 are located in the center of the coil in the z direction and are used for simulating the VCM force.
 The arrows at the nodes indicate the direction of forces.
 
@@ -1045,10 +1032,8 @@ A recommended sequence for analyzing dynamic finite element models is:
 A small section of the exported `.eig` file from ANSYS is shown bellow..
 
 <div class="exampl">
-  <div></div>
 
 <div class="monoblock">
-  <div></div>
 
 LOAD STEP=     1  SUBSTEP=     1
  FREQ=    8.1532      LOAD CASE=   0
@@ -1089,7 +1074,7 @@ From Ansys, we have the eigenvalues \\(\omega\_i\\) and eigenvectors \\(\bm{z}\\
 
 ## Balanced Reduction {#balanced-reduction}
 
-<a id="org58a3a47"></a>
+<span class="org-target" id="org-target--sec-balanced-reduction"></span>
 
 In this chapter another method of reducing models, “balanced reduction”, will be introduced and compared with the DC and peak gain ranking methods.
 
@@ -1117,7 +1102,7 @@ A mode which cannot be excited by the applied force is said to be **uncontrollab
 For a state space system described by:
 
 \begin{align\*}
-  \dot{\bm{x}} &= \bm{A} \bm{x} + \bm{B} u \\\\\\
+  \dot{\bm{x}} &= \bm{A} \bm{x} + \bm{B} u \\\\
   \bm{y} &= \bm{C} \bm{x}
 \end{align\*}
 
@@ -1159,7 +1144,7 @@ A similar set of definitions can be made for observability:
 
     \begin{equation}
       \bm{\mathcal{O}} = \begin{bmatrix}
-        \bm{C} \\ \bm{C} \bm{A} \\ \bm{C} \bm{A}^{2} \\ \vdots \\ \bm{C} \bm{A}^{n-1}
+        \bm{C} \\\ \bm{C} \bm{A} \\\ \bm{C} \bm{A}^{2} \\\ \vdots \\\ \bm{C} \bm{A}^{n-1}
       \end{bmatrix}
     \end{equation}
 
@@ -1204,16 +1189,16 @@ The **states to be kept are the states with the largest diagonal terms**.
 
 ## MIMO Two Stage Actuator Model {#mimo-two-stage-actuator-model}
 
-<a id="orgf33e1dd"></a>
+<span class="org-target" id="org-target--sec-mimo-disk-drive"></span>
 
-In this section, a MIMO two-stage actuator model is derived from a finite element model (Figure [14](#org59e7525)).
+In this section, a MIMO two-stage actuator model is derived from a finite element model ([Figure 14](#figure--fig:hatch00-disk-drive-mimo-schematic)).
 
 
 ### Actuator Description {#actuator-description}
 
-<a id="org59e7525"></a>
+<a id="figure--fig:hatch00-disk-drive-mimo-schematic"></a>
 
-{{< figure src="/ox-hugo/hatch00_disk_drive_mimo_schematic.png" caption="Figure 14: Drawing of actuator/suspension system" >}}
+{{< figure src="/ox-hugo/hatch00_disk_drive_mimo_schematic.png" caption="<span class=\"figure-number\">Figure 14: </span>Drawing of actuator/suspension system" >}}
 
 A piezo-actuator is now bounded into one side of each of the arms.
 The piezo actuator consists of a ceramic element that changes size when a voltage is applied.
@@ -1221,7 +1206,6 @@ The piezo actuator consists of a ceramic element that changes size when a voltag
 Then the fine positioning motion of the piezo is used in conjunction with VCM's coarse positioning motion, higher servo bandwidth is possible.
 
 <div class="important">
-  <div></div>
 
 Instead of applying voltage as the input into the piezo elements, we will assume that we have calculated an equivalent set of forces which can be applied at the ends of the element that will replicate the voltage force function.
 In this model, we will be applying forces to multiple nodes at the ends of both piezo elements.
@@ -1233,11 +1217,11 @@ Since the same forces are being applied to both piezo elements, they represent t
 
 ### Ansys Model Description {#ansys-model-description}
 
-In Figure [15](#org5f31090) are shown the principal nodes used for the model.
+In [Figure 15](#figure--fig:hatch00-disk-drive-mimo-ansys) are shown the principal nodes used for the model.
 
-<a id="org5f31090"></a>
+<a id="figure--fig:hatch00-disk-drive-mimo-ansys"></a>
 
-{{< figure src="/ox-hugo/hatch00_disk_drive_mimo_ansys.png" caption="Figure 15: Nodes used for reduced Matlab model, shown with partial mesh at coil and piezo element" >}}
+{{< figure src="/ox-hugo/hatch00_disk_drive_mimo_ansys.png" caption="<span class=\"figure-number\">Figure 15: </span>Nodes used for reduced Matlab model, shown with partial mesh at coil and piezo element" >}}
 
 
 ### Matlab Model {#matlab-model}
@@ -1354,13 +1338,13 @@ And we note:
   G = zn * Gp;
 ```
 
-<a id="orgbe6df95"></a>
+<a id="figure--fig:hatch00-z13-tf"></a>
 
-{{< figure src="/ox-hugo/hatch00_z13_tf.png" caption="Figure 16: Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_3\\)" >}}
+{{< figure src="/ox-hugo/hatch00_z13_tf.png" caption="<span class=\"figure-number\">Figure 16: </span>Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_3\\)" >}}
 
-<a id="orgcec939e"></a>
+<a id="figure--fig:hatch00-z11-tf"></a>
 
-{{< figure src="/ox-hugo/hatch00_z11_tf.png" caption="Figure 17: Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_1\\)" >}}
+{{< figure src="/ox-hugo/hatch00_z11_tf.png" caption="<span class=\"figure-number\">Figure 17: </span>Mode contributions to the transfer function from \\(F\_1\\) to \\(z\_1\\)" >}}
 
 
 ## Matlab with ANSYS {#matlab-with-ansys}
@@ -1456,15 +1440,15 @@ State Space Model
 
 ### Simple mode truncation {#simple-mode-truncation}
 
-Let's plot the frequency of the modes (Figure [18](#org1183b44)).
+Let's plot the frequency of the modes ([Figure 18](#figure--fig:hatch00-cant-beam-modes-freq)).
 
-<a id="org1183b44"></a>
+<a id="figure--fig:hatch00-cant-beam-modes-freq"></a>
 
-{{< figure src="/ox-hugo/hatch00_cant_beam_modes_freq.png" caption="Figure 18: Frequency of the modes" >}}
+{{< figure src="/ox-hugo/hatch00_cant_beam_modes_freq.png" caption="<span class=\"figure-number\">Figure 18: </span>Frequency of the modes" >}}
 
-<a id="org350c1cb"></a>
+<a id="figure--fig:hatch00-cant-beam-unsorted-dc-gains"></a>
 
-{{< figure src="/ox-hugo/hatch00_cant_beam_unsorted_dc_gains.png" caption="Figure 19: Unsorted DC Gains" >}}
+{{< figure src="/ox-hugo/hatch00_cant_beam_unsorted_dc_gains.png" caption="<span class=\"figure-number\">Figure 19: </span>Unsorted DC Gains" >}}
 
 Let's keep only the first 10 modes.
 
@@ -1531,9 +1515,9 @@ Let's sort the modes by their DC gains and plot their sorted DC gains.
   [dc_gain_sort, index_sort] = sort(dc_gain, 'descend');
 ```
 
-<a id="orgd64190f"></a>
+<a id="figure--fig:hatch00-cant-beam-sorted-dc-gains"></a>
 
-{{< figure src="/ox-hugo/hatch00_cant_beam_sorted_dc_gains.png" caption="Figure 20: Sorted DC Gains" >}}
+{{< figure src="/ox-hugo/hatch00_cant_beam_sorted_dc_gains.png" caption="<span class=\"figure-number\">Figure 20: </span>Sorted DC Gains" >}}
 
 Let's keep only the first 10 **sorted** modes.
 
@@ -1875,9 +1859,9 @@ Then, we compute the controllability and observability gramians.
 
 And we plot the diagonal terms
 
-<a id="orgbdc6b3b"></a>
+<a id="figure--fig:hatch00-gramians"></a>
 
-{{< figure src="/ox-hugo/hatch00_gramians.png" caption="Figure 21: Observability and Controllability Gramians" >}}
+{{< figure src="/ox-hugo/hatch00_gramians.png" caption="<span class=\"figure-number\">Figure 21: </span>Observability and Controllability Gramians" >}}
 
 We use `balreal` to rank oscillatory states.
 
@@ -1893,9 +1877,9 @@ We use `balreal` to rank oscillatory states.
   [G_b, G, T, Ti] = balreal(G_m);
 ```
 
-<a id="org2787898"></a>
+<a id="figure--fig:hatch00-cant-beam-gramian-balanced"></a>
 
-{{< figure src="/ox-hugo/hatch00_cant_beam_gramian_balanced.png" caption="Figure 22: Sorted values of the Gramian of the balanced realization" >}}
+{{< figure src="/ox-hugo/hatch00_cant_beam_gramian_balanced.png" caption="<span class=\"figure-number\">Figure 22: </span>Sorted values of the Gramian of the balanced realization" >}}
 
 Now we can choose the number of states to keep.
 
@@ -2136,9 +2120,9 @@ Reduced Mass and Stiffness matrices in the physical coordinates:
 ```
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org4036e02"></a>Hatch, Michael R. 2000. _Vibration Simulation Using MATLAB and ANSYS_. CRC Press.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
-
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Hatch, Michael R. 2000. <i>Vibration Simulation Using MATLAB and ANSYS</i>. CRC Press.</div>
-<a id="orgcda3e53"></a>Miu, Denny K. 1993. _Mechatronics: Electromechanics and Contromechanics_. 1st ed. Mechanical Engineering Series. Springer-Verlag New York.
+  <div class="csl-entry"><a id="citeproc_bib_item_2"></a>Miu, Denny K. 1993. <i>Mechatronics: Electromechanics and Contromechanics</i>. 1st ed. Mechanical Engineering Series. Springer-Verlag New York.</div>
+</div>

content/book/horowitz15_art_of_elect_third_edition.md

@@ -1,16 +1,16 @@
 +++
 title = "The Art of Electronics - Third Edition"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 description = "One of the best book in electronics. Cover most topics (both analog and digital)."
 keywords = ["electronics"]
 draft = false
 +++
 
 Tags
-: [Reference Books]({{< relref "reference_books" >}}), [Electronics]({{< relref "electronics" >}})
+: [Reference Books]({{< relref "reference_books.md" >}}), [Electronics]({{< relref "electronics.md" >}})
 
 Reference
-: ([Horowitz 2015](#org8eab88c))
+: (<a href="#citeproc_bib_item_1">Horowitz 2015</a>)
 
 Author(s)
 : Horowitz, P.
@@ -19,7 +19,8 @@ Year
 : 2015
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org8eab88c"></a>Horowitz, Paul. 2015. _The Art of Electronics - Third Edition_. New York, NY, USA: Cambridge University Press.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Horowitz, Paul. 2015. <i>The Art of Electronics - Third Edition</i>. New York, NY, USA: Cambridge University Press.</div>
+</div>

content/book/leach14_fundam_princ_engin_nanom.md

@@ -1,15 +1,15 @@
 +++
 title = "Fundamental principles of engineering nanometrology"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 keywords = ["Metrology"]
-draft = true
+draft = false
 +++
 
 Tags
-: [Metrology]({{< relref "metrology" >}})
+: [Metrology]({{< relref "metrology.md" >}})
 
 Reference
-: ([Leach 2014](#org284df16))
+: (<a href="#citeproc_bib_item_1">Leach 2014</a>)
 
 Author(s)
 : Leach, R.
@@ -64,8 +64,8 @@ The second order nature means that cosine error quickly diminish as the alignmen
 ## Latest advances in displacement interferometry {#latest-advances-in-displacement-interferometry}
 
 Commercial interferometers
-=> fused silica optics housed in Invar mounts
+=&gt; fused silica optics housed in Invar mounts
-=> all the optical components are mounted to one central optic to reduce the susceptibility to thermal variations
+=&gt; all the optical components are mounted to one central optic to reduce the susceptibility to thermal variations
 
 One advantage that homodyme systems have over heterodyne systems is their ability to readily have the source fibre delivered to the interferometer.
 
@@ -88,7 +88,8 @@ The measurement of angles is then relative.
 This type of angular interferometer is used to measure small angles (less than \\(10deg\\)).
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org284df16"></a>Leach, Richard. 2014. _Fundamental Principles of Engineering Nanometrology_. Elsevier. <https://doi.org/10.1016/c2012-0-06010-3>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Leach, Richard. 2014. <i>Fundamental Principles of Engineering Nanometrology</i>. Elsevier. doi:<a href="https://doi.org/10.1016/c2012-0-06010-3">10.1016/c2012-0-06010-3</a>.</div>
+</div>

content/book/leach18_basic_precis_engin_edition.md

@@ -1,24 +1,25 @@
 +++
 title = "Basics of precision engineering - 1st edition"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 keywords = ["Metrology", "Mechatronics"]
 draft = true
 +++
 
 Tags
-: [Precision Engineering]({{< relref "precision_engineering" >}})
+: [Precision Engineering]({{< relref "precision_engineering.md" >}})
 
 Reference
-: ([Leach and Smith 2018](#org02e139c))
+: (<a href="#citeproc_bib_item_1">Leach and Smith 2018</a>)
 
 Author(s)
-: Leach, R., & Smith, S. T.
+: Leach, R., &amp; Smith, S. T.
 
 Year
 : 2018
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org02e139c"></a>Leach, Richard, and Stuart T. Smith. 2018. _Basics of Precision Engineering - 1st Edition_. CRC Press.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Leach, Richard, and Stuart T. Smith. 2018. <i>Basics of Precision Engineering - 1st Edition</i>. CRC Press.</div>
+</div>

content/book/lyons11_under_digit_signal_proces.md

@@ -0,0 +1,538 @@
++++
+title = "Understanding Digital Signal Processing"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+: [IRR and FIR Filters]({{< relref "irr_and_fir_filters.md" >}}), [Digital Filters]({{< relref "digital_filters.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Lyons 2011</a>)
+
+Author(s)
+: Lyons, R.
+
+Year
+: 2011
+
+
+## Discrete Sequences And Systems {#discrete-sequences-and-systems}
+
+
+### Discrete Sequences And Their Notation {#discrete-sequences-and-their-notation}
+
+
+### Signal Amplitude, Magnitude, Power {#signal-amplitude-magnitude-power}
+
+
+### Signal Processing Operational Symbols {#signal-processing-operational-symbols}
+
+
+### Introduction To Discrete Linear Time-Invariant Systems {#introduction-to-discrete-linear-time-invariant-systems}
+
+
+### Discrete Linear Systems {#discrete-linear-systems}
+
+
+### Time-Invariant Systems {#time-invariant-systems}
+
+
+### The Commutative Property Of Linear Time-Invariant Systems {#the-commutative-property-of-linear-time-invariant-systems}
+
+
+### Analyzing Linear Time-Invariant Systems {#analyzing-linear-time-invariant-systems}
+
+<a id="figure--fig:lyons11-lti-impulse-response"></a>
+
+{{< figure src="/ox-hugo/lyons11_lti_impulse_response.png" caption="<span class=\"figure-number\">Figure 1: </span>LTI system unit impulse response sequences. (a) system block diagram. (b) impulse input sequence \\(x(n)\\) and impulse reponse output sequence \\(y(n)\\)." >}}
+
+<a id="figure--fig:lyons11-moving-average"></a>
+
+{{< figure src="/ox-hugo/lyons11_moving_average.png" caption="<span class=\"figure-number\">Figure 2: </span>Analyzing a moving average filter. (a) averager block diagram; (b) impulse input and impulse response; (c) averager frequency magnitude reponse." >}}
+
+
+## Periodic Sampling {#periodic-sampling}
+
+
+### Aliasing: Signal Ambiguity In The Frequency Domain {#aliasing-signal-ambiguity-in-the-frequency-domain}
+
+<a id="figure--fig:lyons11-frequency-ambiguity"></a>
+
+{{< figure src="/ox-hugo/lyons11_frequency_ambiguity.png" caption="<span class=\"figure-number\">Figure 3: </span>Frequency ambiguity; (a) discrete time sequence of values; (b) two different sinewaves that pass through the points of discete sequence" >}}
+
+
+### Sampling Lowpass Signals {#sampling-lowpass-signals}
+
+<a id="figure--fig:lyons11-noise-spectral-replication"></a>
+
+{{< figure src="/ox-hugo/lyons11_noise_spectral_replication.png" caption="<span class=\"figure-number\">Figure 4: </span>Spectral replications; (a) original continuous signal plus noise spectrum; (b) discrete spectrum with noise contaminating the signal of interest" >}}
+
+<a id="figure--fig:lyons11-lowpass-sampling"></a>
+
+{{< figure src="/ox-hugo/lyons11_lowpass_sampling.png" caption="<span class=\"figure-number\">Figure 5: </span>Low pass analog filtering prior to sampling at a rate of \\(f\_s\\) Hz." >}}
+
+
+## The Discrete Fourier Transform {#the-discrete-fourier-transform}
+
+\begin{equation}
+X(f) = \int\_{-\infty}^{\infty} x(t) e^{-j2\pi f t} dt
+\end{equation}
+
+\begin{equation}
+X(m) = \sum\_{n = 0}^{N-1} x(n) e^{-j2 \pi n m /N}
+\end{equation}
+
+
+### Understanding The Dft Equation {#understanding-the-dft-equation}
+
+
+### Dft Symmetry {#dft-symmetry}
+
+
+### Dft Linearity {#dft-linearity}
+
+
+### Dft Magnitudes {#dft-magnitudes}
+
+
+### Dft Frequency Axis {#dft-frequency-axis}
+
+
+### Dft Shifting Theorem {#dft-shifting-theorem}
+
+
+### Inverse Dft {#inverse-dft}
+
+
+### Dft Leakage {#dft-leakage}
+
+
+### Windows {#windows}
+
+
+### Dft Scalloping Loss {#dft-scalloping-loss}
+
+
+### Dft Resolution, Zero Padding, And Frequency-Domain Sampling {#dft-resolution-zero-padding-and-frequency-domain-sampling}
+
+
+### Dft Processing Gain {#dft-processing-gain}
+
+
+### The Dft Of Rectangular Functions {#the-dft-of-rectangular-functions}
+
+
+### Interpreting The Dft Using The Discrete-Time Fourier Transform {#interpreting-the-dft-using-the-discrete-time-fourier-transform}
+
+
+## The Fast Fourier Transform {#the-fast-fourier-transform}
+
+
+### Relationship Of The Fft To The Dft {#relationship-of-the-fft-to-the-dft}
+
+
+### Hints On Using Ffts In Practice {#hints-on-using-ffts-in-practice}
+
+
+### Derivation Of The Radix-2 Fft Algorithm {#derivation-of-the-radix-2-fft-algorithm}
+
+
+### Fft Input/Output Data Index Bit Reversal {#fft-input-output-data-index-bit-reversal}
+
+
+### Radix-2 Fft Butterfly Structures {#radix-2-fft-butterfly-structures}
+
+
+### Alternate Single-Butterfly Structures {#alternate-single-butterfly-structures}
+
+
+## Finite Impulse Response Filters {#finite-impulse-response-filters}
+
+
+### An Introduction To Finite Impulse Response (Fir) Filters {#an-introduction-to-finite-impulse-response--fir--filters}
+
+
+### Convolution In Fir Filters {#convolution-in-fir-filters}
+
+
+### Lowpass Fir Filter Design {#lowpass-fir-filter-design}
+
+
+### Bandpass Fir Filter Design {#bandpass-fir-filter-design}
+
+
+### Highpass Fir Filter Design {#highpass-fir-filter-design}
+
+
+### Parks-Mcclellan Exchange Fir Filter Design Method {#parks-mcclellan-exchange-fir-filter-design-method}
+
+
+### Half-Band Fir Filters {#half-band-fir-filters}
+
+
+### Phase Response Of Fir Filters {#phase-response-of-fir-filters}
+
+
+### A Generic Description Of Discrete Convolution {#a-generic-description-of-discrete-convolution}
+
+
+### Analyzing Fir Filters {#analyzing-fir-filters}
+
+
+## Infinite Impulse Response Filters {#infinite-impulse-response-filters}
+
+
+### An Introduction To Infinite Impulse Response Filters {#an-introduction-to-infinite-impulse-response-filters}
+
+
+### The Laplace Transform {#the-laplace-transform}
+
+
+### The Z-Transform {#the-z-transform}
+
+
+### Using The Z-Transform To Analyze Iir Filters {#using-the-z-transform-to-analyze-iir-filters}
+
+
+### Using Poles And Zeros To Analyze Iir Filters {#using-poles-and-zeros-to-analyze-iir-filters}
+
+
+### Alternate Iir Filter Structures {#alternate-iir-filter-structures}
+
+
+### Pitfalls In Building Iir Filters {#pitfalls-in-building-iir-filters}
+
+
+### Improving Iir Filters With Cascaded Structures {#improving-iir-filters-with-cascaded-structures}
+
+
+### Scaling The Gain Of Iir Filters {#scaling-the-gain-of-iir-filters}
+
+
+### Impulse Invariance Iir Filter Design Method {#impulse-invariance-iir-filter-design-method}
+
+
+### Bilinear Transform Iir Filter Design Method {#bilinear-transform-iir-filter-design-method}
+
+
+### Optimized Iir Filter Design Method {#optimized-iir-filter-design-method}
+
+
+### A Brief Comparison Of Iir And Fir Filters {#a-brief-comparison-of-iir-and-fir-filters}
+
+
+## Specialized Digital Networks And Filters {#specialized-digital-networks-and-filters}
+
+
+### Differentiators {#differentiators}
+
+
+### Integrators {#integrators}
+
+
+### Matched Filters {#matched-filters}
+
+
+### Interpolated Lowpass Fir Filters {#interpolated-lowpass-fir-filters}
+
+
+### Frequency Sampling Filters: The Lost Art {#frequency-sampling-filters-the-lost-art}
+
+
+## Quadrature Signals {#quadrature-signals}
+
+
+### Why Care About Quadrature Signals? {#why-care-about-quadrature-signals}
+
+
+### The Notation Of Complex Numbers {#the-notation-of-complex-numbers}
+
+
+### Representing Real Signals Using Complex Phasors {#representing-real-signals-using-complex-phasors}
+
+
+### A Few Thoughts On Negative Frequency {#a-few-thoughts-on-negative-frequency}
+
+
+### Quadrature Signals In The Frequency Domain {#quadrature-signals-in-the-frequency-domain}
+
+
+### Bandpass Quadrature Signals In The Frequency Domain {#bandpass-quadrature-signals-in-the-frequency-domain}
+
+
+### Complex Down-Conversion {#complex-down-conversion}
+
+
+### A Complex Down-Conversion Example {#a-complex-down-conversion-example}
+
+
+### An Alternate Down-Conversion Method {#an-alternate-down-conversion-method}
+
+
+## The Discrete Hilbert Transform {#the-discrete-hilbert-transform}
+
+
+### Hilbert Transform Definition {#hilbert-transform-definition}
+
+
+### Why Care About The Hilbert Transform? {#why-care-about-the-hilbert-transform}
+
+
+### Impulse Response Of A Hilbert Transformer {#impulse-response-of-a-hilbert-transformer}
+
+
+### Designing A Discrete Hilbert Transformer {#designing-a-discrete-hilbert-transformer}
+
+
+### Time-Domain Analytic Signal Generation {#time-domain-analytic-signal-generation}
+
+
+### Comparing Analytical Signal Generation Methods {#comparing-analytical-signal-generation-methods}
+
+
+## 10 Sample Rate Conversion {#10-sample-rate-conversion}
+
+
+### 10.1 Decimation {#10-dot-1-decimation}
+
+
+### 10.2 Two-Stage Decimation {#10-dot-2-two-stage-decimation}
+
+
+### 10.3 Properties Of Downsampling {#10-dot-3-properties-of-downsampling}
+
+
+### 10.4 Interpolation {#10-dot-4-interpolation}
+
+
+### 10.5 Properties Of Interpolation {#10-dot-5-properties-of-interpolation}
+
+
+### 10.6 Combining Decimation And Interpolation {#10-dot-6-combining-decimation-and-interpolation}
+
+
+### 10.7 Polyphase Filters {#10-dot-7-polyphase-filters}
+
+
+### 10.8 Two-Stage Interpolation {#10-dot-8-two-stage-interpolation}
+
+
+### 10.9 Z-Transform Analysis Of Multirate Systems {#10-dot-9-z-transform-analysis-of-multirate-systems}
+
+
+### 10.10 Polyphase Filter Implementations {#10-dot-10-polyphase-filter-implementations}
+
+
+### 10.11 Sample Rate Conversion By Rational Factors {#10-dot-11-sample-rate-conversion-by-rational-factors}
+
+
+### 10.12 Sample Rate Conversion With Half-Band Filters {#10-dot-12-sample-rate-conversion-with-half-band-filters}
+
+
+### 10.13 Sample Rate Conversion With Ifir Filters {#10-dot-13-sample-rate-conversion-with-ifir-filters}
+
+
+### 10.14 Cascaded Integrator-Comb Filters {#10-dot-14-cascaded-integrator-comb-filters}
+
+
+## 11 Signal Averaging {#11-signal-averaging}
+
+
+### 11.1 Coherent Averaging {#11-dot-1-coherent-averaging}
+
+
+### 11.2 Incoherent Averaging {#11-dot-2-incoherent-averaging}
+
+
+### 11.3 Averaging Multiple Fast Fourier Transforms {#11-dot-3-averaging-multiple-fast-fourier-transforms}
+
+
+### 11.4 Averaging Phase Angles {#11-dot-4-averaging-phase-angles}
+
+
+### 11.5 Filtering Aspects Of Time-Domain Averaging {#11-dot-5-filtering-aspects-of-time-domain-averaging}
+
+
+### 11.6 Exponential Averaging {#11-dot-6-exponential-averaging}
+
+
+## 12 Digital Data Formats And Their Effects {#12-digital-data-formats-and-their-effects}
+
+
+### 12.1 Fixed-Point Binary Formats {#12-dot-1-fixed-point-binary-formats}
+
+
+### 12.2 Binary Number Precision And Dynamic Range {#12-dot-2-binary-number-precision-and-dynamic-range}
+
+
+### 12.3 Effects Of Finite Fixed-Point Binary Word Length {#12-dot-3-effects-of-finite-fixed-point-binary-word-length}
+
+
+### 12.4 Floating-Point Binary Formats {#12-dot-4-floating-point-binary-formats}
+
+
+### 12.5 Block Floating-Point Binary Format {#12-dot-5-block-floating-point-binary-format}
+
+
+## 13 Digital Signal Processing Tricks {#13-digital-signal-processing-tricks}
+
+
+### 13.1 Frequency Translation Without Multiplication {#13-dot-1-frequency-translation-without-multiplication}
+
+
+### 13.2 High-Speed Vector Magnitude Approximation {#13-dot-2-high-speed-vector-magnitude-approximation}
+
+
+### 13.3 Frequency-Domain Windowing {#13-dot-3-frequency-domain-windowing}
+
+
+### 13.4 Fast Multiplication Of Complex Numbers {#13-dot-4-fast-multiplication-of-complex-numbers}
+
+
+### 13.5 Efficiently Performing The Fft Of Real Sequences {#13-dot-5-efficiently-performing-the-fft-of-real-sequences}
+
+
+### 13.6 Computing The Inverse Fft Using The Forward Fft {#13-dot-6-computing-the-inverse-fft-using-the-forward-fft}
+
+
+### 13.7 Simplified Fir Filter Structure {#13-dot-7-simplified-fir-filter-structure}
+
+
+### 13.8 Reducing A/D Converter Quantization Noise {#13-dot-8-reducing-a-d-converter-quantization-noise}
+
+
+### 13.9 A/D Converter Testing Techniques {#13-dot-9-a-d-converter-testing-techniques}
+
+
+### 13.10 Fast Fir Filtering Using The Fft {#13-dot-10-fast-fir-filtering-using-the-fft}
+
+
+### 13.11 Generating Normally Distributed Random Data {#13-dot-11-generating-normally-distributed-random-data}
+
+
+### 13.12 Zero-Phase Filtering {#13-dot-12-zero-phase-filtering}
+
+
+### 13.13 Sharpened Fir Filters {#13-dot-13-sharpened-fir-filters}
+
+
+### 13.14 Interpolating A Bandpass Signal {#13-dot-14-interpolating-a-bandpass-signal}
+
+
+### 13.15 Spectral Peak Location Algorithm {#13-dot-15-spectral-peak-location-algorithm}
+
+
+### 13.16 Computing Fft Twiddle Factors {#13-dot-16-computing-fft-twiddle-factors}
+
+
+### 13.17 Single Tone Detection {#13-dot-17-single-tone-detection}
+
+
+### 13.18 The Sliding Dft {#13-dot-18-the-sliding-dft}
+
+
+### 13.19 The Zoom Fft {#13-dot-19-the-zoom-fft}
+
+
+### 13.20 A Practical Spectrum Analyzer {#13-dot-20-a-practical-spectrum-analyzer}
+
+
+### 13.21 An Efficient Arctangent Approximation {#13-dot-21-an-efficient-arctangent-approximation}
+
+
+### 13.22 Frequency Demodulation Algorithms {#13-dot-22-frequency-demodulation-algorithms}
+
+
+### 13.23 Dc Removal {#13-dot-23-dc-removal}
+
+
+### 13.24 Improving Traditional Cic Filters {#13-dot-24-improving-traditional-cic-filters}
+
+
+### 13.25 Smoothing Impulsive Noise {#13-dot-25-smoothing-impulsive-noise}
+
+
+### 13.26 Efficient Polynomial Evaluation {#13-dot-26-efficient-polynomial-evaluation}
+
+
+### 13.27 Designing Very High-Order Fir Filters {#13-dot-27-designing-very-high-order-fir-filters}
+
+
+### 13.28 Time-Domain Interpolation Using The Fft {#13-dot-28-time-domain-interpolation-using-the-fft}
+
+
+### 13.29 Frequency Translation Using Decimation {#13-dot-29-frequency-translation-using-decimation}
+
+
+### 13.30 Automatic Gain Control (Agc) {#13-dot-30-automatic-gain-control--agc}
+
+
+### 13.31 Approximate Envelope Detection {#13-dot-31-approximate-envelope-detection}
+
+
+### 13.32 A Quadrature Oscillator {#13-dot-32-a-quadrature-oscillator}
+
+
+### 13.33 Specialized Exponential Averaging {#13-dot-33-specialized-exponential-averaging}
+
+
+### 13.34 Filtering Narrowband Noise Using Filter Nulls {#13-dot-34-filtering-narrowband-noise-using-filter-nulls}
+
+
+### 13.35 Efficient Computation Of Signal Variance {#13-dot-35-efficient-computation-of-signal-variance}
+
+
+### 13.36 Real-Time Computation Of Signal Averages And Variances {#13-dot-36-real-time-computation-of-signal-averages-and-variances}
+
+
+### 13.37 Building Hilbert Transformers From Half-Band Filters {#13-dot-37-building-hilbert-transformers-from-half-band-filters}
+
+
+### 13.38 Complex Vector Rotation With Arctangents {#13-dot-38-complex-vector-rotation-with-arctangents}
+
+
+### 13.39 An Efficient Differentiating Network {#13-dot-39-an-efficient-differentiating-network}
+
+
+### 13.40 Linear-Phase Dc-Removal Filter {#13-dot-40-linear-phase-dc-removal-filter}
+
+
+### 13.41 Avoiding Overflow In Magnitude Computations {#13-dot-41-avoiding-overflow-in-magnitude-computations}
+
+
+### 13.42 Efficient Linear Interpolation {#13-dot-42-efficient-linear-interpolation}
+
+
+### 13.43 Alternate Complex Down-Conversion Schemes {#13-dot-43-alternate-complex-down-conversion-schemes}
+
+
+### 13.44 Signal Transition Detection {#13-dot-44-signal-transition-detection}
+
+
+### 13.45 Spectral Flipping Around Signal Center Frequency {#13-dot-45-spectral-flipping-around-signal-center-frequency}
+
+
+### 13.46 Computing Missing Signal Samples {#13-dot-46-computing-missing-signal-samples}
+
+
+### 13.47 Computing Large Dfts Using Small Ffts {#13-dot-47-computing-large-dfts-using-small-ffts}
+
+
+### 13.48 Computing Filter Group Delay Without Arctangents {#13-dot-48-computing-filter-group-delay-without-arctangents}
+
+
+### 13.49 Computing A Forward And Inverse Fft Using A Single Fft {#13-dot-49-computing-a-forward-and-inverse-fft-using-a-single-fft}
+
+
+### 13.50 Improved Narrowband Lowpass Iir Filters {#13-dot-50-improved-narrowband-lowpass-iir-filters}
+
+
+### 13.51 A Stable Goertzel Algorithm {#13-dot-51-a-stable-goertzel-algorithm}
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Lyons, Richard. 2011. <i>Understanding Digital Signal Processing</i>. Upper Saddle River, NJ: Prentice Hall.</div>
+</div>

content/book/morrison16_groun_shiel.md

@@ -1,16 +1,16 @@
 +++
 title = "Grounding and Shielding: Circuits and Interference"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 description = "Explains in a clear manner what is grounding and shielding and what are the fundamental physics behind these terms."
 keywords = ["Electronics"]
 draft = false
 +++
 
 Tags
-: [Electronics]({{< relref "electronics" >}})
+: [Electronics]({{< relref "electronics.md" >}})
 
 Reference
-: ([Morrison 2016](#org7a49345))
+: (<a href="#citeproc_bib_item_1">Morrison 2016</a>)
 
 Author(s)
 : Morrison, R.
@@ -22,7 +22,6 @@ Year
 ## Voltage and Capacitors {#voltage-and-capacitors}
 
 <div class="sum">
-  <div></div>
 
 This first chapter described the electric field that is basic to all electrical activity.
 The electric or \\(E\\) field represents forces between charges.
@@ -53,9 +52,9 @@ This displacement current flows when charges are added or removed from the plate
 
 ### Field representation {#field-representation}
 
-<a id="orga3615d0"></a>
+<a id="figure--fig:morrison16-E-field-charge"></a>
 
-{{< figure src="/ox-hugo/morrison16_E_field_charge.svg" caption="Figure 1: The force field lines around a positively chaged conducting sphere" >}}
+{{< figure src="/ox-hugo/morrison16_E_field_charge.svg" caption="<span class=\"figure-number\">Figure 1: </span>The force field lines around a positively chaged conducting sphere" >}}
 
 
 ### The definition of voltage {#the-definition-of-voltage}
@@ -64,22 +63,22 @@ This displacement current flows when charges are added or removed from the plate
 ### Equipotential surfaces {#equipotential-surfaces}
 
 
-### The force field or \\(E\\) field between two conducting plates {#the-force-field-or--e--field-between-two-conducting-plates}
+### The force field or \\(E\\) field between two conducting plates {#the-force-field-or-e-field-between-two-conducting-plates}
 
-<a id="org82b88ec"></a>
+<a id="figure--fig:morrison16-force-field-plates"></a>
 
-{{< figure src="/ox-hugo/morrison16_force_field_plates.svg" caption="Figure 2: The force field between two conducting plates with equal and opposite charges and spacing distance \\(h\\)" >}}
+{{< figure src="/ox-hugo/morrison16_force_field_plates.svg" caption="<span class=\"figure-number\">Figure 2: </span>The force field between two conducting plates with equal and opposite charges and spacing distance \\(h\\)" >}}
 
 
 ### Electric field patterns {#electric-field-patterns}
 
-<a id="org16f20a9"></a>
+<a id="figure--fig:morrison16-electric-field-ground-plane"></a>
 
-{{< figure src="/ox-hugo/morrison16_electric_field_ground_plane.svg" caption="Figure 3: The electric field pattern of one circuit trace and two circuit traces over a ground plane" >}}
+{{< figure src="/ox-hugo/morrison16_electric_field_ground_plane.svg" caption="<span class=\"figure-number\">Figure 3: </span>The electric field pattern of one circuit trace and two circuit traces over a ground plane" >}}
 
-<a id="org38210cb"></a>
+<a id="figure--fig:morrison16-electric-field-shielded-conductor"></a>
 
-{{< figure src="/ox-hugo/morrison16_electric_field_shielded_conductor.svg" caption="Figure 4: Field configuration around a shielded conductor" >}}
+{{< figure src="/ox-hugo/morrison16_electric_field_shielded_conductor.svg" caption="<span class=\"figure-number\">Figure 4: </span>Field configuration around a shielded conductor" >}}
 
 
 ### The energy stored in an electric field {#the-energy-stored-in-an-electric-field}
@@ -88,11 +87,11 @@ This displacement current flows when charges are added or removed from the plate
 ### Dielectrics {#dielectrics}
 
 
-### The \\(D\\) field {#the--d--field}
+### The \\(D\\) field {#the-d-field}
 
-<a id="org5a4329e"></a>
+<a id="figure--fig:morrison16-E-D-fields"></a>
 
-{{< figure src="/ox-hugo/morrison16_E_D_fields.svg" caption="Figure 5: The electric field pattern in the presence of a dielectric" >}}
+{{< figure src="/ox-hugo/morrison16_E_D_fields.svg" caption="<span class=\"figure-number\">Figure 5: </span>The electric field pattern in the presence of a dielectric" >}}
 
 
 ### Capacitance {#capacitance}
@@ -122,7 +121,6 @@ This displacement current flows when charges are added or removed from the plate
 ## Magnetics {#magnetics}
 
 <div class="sum">
-  <div></div>
 
 This chapter discusses magnetic fields.
 As in the electric field, there are two measures of the same magnetic field.
@@ -150,11 +148,11 @@ In a few elements, the atomic structure is such that atoms align to generate a n
 The flow of electrons is another way to generate a magnetic field.
 
 The letter \\(H\\) is reserved for the magnetic field generated by a current.
-Figure [6](#org9b0e888) shows the shape of the \\(H\\) field around a long, straight conductor carrying a direct current \\(I\\).
+[Figure 6](#figure--fig:morrison16-H-field) shows the shape of the \\(H\\) field around a long, straight conductor carrying a direct current \\(I\\).
 
-<a id="org9b0e888"></a>
+<a id="figure--fig:morrison16-H-field"></a>
 
-{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="Figure 6: The \\(H\\) field around a current-carrying conductor" >}}
+{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="<span class=\"figure-number\">Figure 6: </span>The \\(H\\) field around a current-carrying conductor" >}}
 
 The magnetic field is a force field.
 This force can only be exerted on another magnetic field.
@@ -169,7 +167,7 @@ Ampere's law states that the integral of the \\(H\\) field intensity in a closed
 \boxed{\oint H dl = I}
 \end{equation}
 
-The simplest path to use for this integration is the one of the concentric circles in Figure [6](#org9b0e888), where \\(H\\) is constant and \\(r\\) is the distance from the conductor.
+The simplest path to use for this integration is the one of the concentric circles in [Figure 6](#figure--fig:morrison16-H-field), where \\(H\\) is constant and \\(r\\) is the distance from the conductor.
 Solving for \\(H\\), we obtain
 
 \begin{equation}
@@ -181,29 +179,29 @@ And we see that \\(H\\) has units of amperes per meter.
 
 ### The solenoid {#the-solenoid}
 
-The magnetic field of a solenoid is shown in Figure [7](#orgd3a9cf9).
+The magnetic field of a solenoid is shown in [Figure 7](#figure--fig:morrison16-solenoid).
 The field intensity inside the solenoid is nearly constant, while outside its intensity falls of rapidly.
 
-Using Ampere's law \eqref{eq:ampere_law}:
+Using Ampere's law \eqref{eq:ampere\_law:}
 
 \begin{equation}
 \oint H dl \approx n I l
 \end{equation}
 
-<a id="orgd3a9cf9"></a>
+<a id="figure--fig:morrison16-solenoid"></a>
 
-{{< figure src="/ox-hugo/morrison16_solenoid.svg" caption="Figure 7: The \\(H\\) field around a solenoid" >}}
+{{< figure src="/ox-hugo/morrison16_solenoid.svg" caption="<span class=\"figure-number\">Figure 7: </span>The \\(H\\) field around a solenoid" >}}
 
 
 ### Faraday's law and the induction field {#faraday-s-law-and-the-induction-field}
 
 When a conducting coil is moved through a magnetic field, a voltage appears at the open ends of the coil.
-This is illustrated in Figure [8](#org4b2f5c1).
+This is illustrated in [Figure 8](#figure--fig:morrison16-voltage-moving-coil).
 The voltage depends on the number of turns in the coil and the rate at which the flux is changing.
 
-<a id="org4b2f5c1"></a>
+<a id="figure--fig:morrison16-voltage-moving-coil"></a>
 
-{{< figure src="/ox-hugo/morrison16_voltage_moving_coil.svg" caption="Figure 8: A voltage induced into a moving coil" >}}
+{{< figure src="/ox-hugo/morrison16_voltage_moving_coil.svg" caption="<span class=\"figure-number\">Figure 8: </span>A voltage induced into a moving coil" >}}
 
 The magnetic field has two measured.
 The \\(H\\) or magnetic field that is proportional to current flow.
@@ -232,14 +230,13 @@ The inverse is also true.
 ### The definition of inductance {#the-definition-of-inductance}
 
 <div class="definition">
-  <div></div>
 
 Inductance is defined as the ratio of magnetic flux generated per unit current.
 The unit of inductance if the henry.
 
 </div>
 
-For the  coil in Figure [7](#orgd3a9cf9):
+For the  coil in [Figure 7](#figure--fig:morrison16-solenoid):
 
 \begin{equation} \label{eq:inductance\_coil}
 V = n^2 A k \mu\_0 \frac{dI}{dt} = L \frac{dI}{dt}
@@ -247,12 +244,12 @@ V = n^2 A k \mu\_0 \frac{dI}{dt} = L \frac{dI}{dt}
 
 where \\(k\\) relates to the geometry of the coil.
 
-Equation \eqref{eq:inductance_coil} states that if \\(V\\) is one volt, then for an inductance of one henry, the current will rise at the rate of one ampere per second.
+Equation \eqref{eq:inductance\_coil} states that if \\(V\\) is one volt, then for an inductance of one henry, the current will rise at the rate of one ampere per second.
 
 
 ### The energy stored in an inductance {#the-energy-stored-in-an-inductance}
 
-One way to calculate the work stored in a magnetic field is to use Eq. \eqref{eq:inductance_coil}.
+One way to calculate the work stored in a magnetic field is to use Eq. \eqref{eq:inductance\_coil}.
 The voltage \\(V\\) applied to a coil results in a linearly increasing current.
 At any time \\(t\\), the power \\(P\\) supplied is equal to \\(VI\\).
 Power is the rate of change of energy or \\(P = d\bm{E}/dt\\) where \\(\bm{E}\\) is the stored energy in the inductance.
@@ -263,7 +260,6 @@ We then have the stored energy in an inductance:
 \end{equation}
 
 <div class="important">
-  <div></div>
 
 An inductor stores field energy.
 It does not dissipate energy.
@@ -275,7 +271,6 @@ The movement of energy into the inductor thus requires both an electric and a ma
 This is due to the Faraday's law that requires a voltage when changing magnetic flux couples to a coil.
 
 <div class="exampl">
-  <div></div>
 
 Consider a 1mH inductor carrying a current of 0.1A.
 The stored energy is \\(5 \times 10^{-4} J\\).
@@ -309,7 +304,6 @@ In a typical circuit, conductor carrying current, the average electron velocity
 ## Digital Electronics {#digital-electronics}
 
 <div class="sum">
-  <div></div>
 
 This chapter shows that both electric and magnetic field are needed to move energy over pairs of conductors.
 The idea of transporting electrical energy in field is extended to traces and conducting planes on printed circuit boards.
@@ -415,7 +409,6 @@ Radiation occurs at the leading edge of a wave as it moves down the transmission
 ## Analog Circuits {#analog-circuits}
 
 <div class="sum">
-  <div></div>
 
 This chapter treats the general problem of analog instrumentation.
 The signals of interest are often generated while testing functioning hardware.
@@ -451,7 +444,6 @@ There are many transducers that can measure temperature, strain, stress, positio
 The signals generated are usually in the milli-volt range and must be amplified, conditioned, and then recorded for later analysis.
 
 <div class="important">
-  <div></div>
 
 It can be very difficult to verify that the measurement is valid.
 For example, signals that overload an input stage can produce noise that may look like signal.
@@ -459,7 +451,6 @@ For example, signals that overload an input stage can produce noise that may loo
 </div>
 
 <div class="definition">
-  <div></div>
 
 1.  **Reference Conductor**.
     Any conductor used as the zero of voltage.
@@ -485,39 +476,39 @@ For example, signals that overload an input stage can produce noise that may loo
 
 ### The basic shield enclosure {#the-basic-shield-enclosure}
 
-Consider the simple amplifier circuit shown in Figure [9](#org3286d62) with:
+Consider the simple amplifier circuit shown in [Figure 9](#figure--fig:morrison16-parasitic-capacitance-amp) with:
 
 -   \\(V\_1\\) the input lead
 -   \\(V\_2\\) the output lead
 -   \\(V\_3\\) the conducting enclosure which is floating and taken as the reference conductor
 -   \\(V\_4\\) a signal common or reference conductor
 
-Every conductor pair has a mutual capacitance, which are shown in Figure [9](#org3286d62) (b).
+Every conductor pair has a mutual capacitance, which are shown in [Figure 9](#figure--fig:morrison16-parasitic-capacitance-amp) (b).
-The equivalent circuit is shown in Figure [9](#org3286d62) (c) and it is apparent that there is some feedback from the output to the input or the amplifier.
+The equivalent circuit is shown in [Figure 9](#figure--fig:morrison16-parasitic-capacitance-amp) (c) and it is apparent that there is some feedback from the output to the input or the amplifier.
 
-<a id="org3286d62"></a>
+<a id="figure--fig:morrison16-parasitic-capacitance-amp"></a>
 
-{{< figure src="/ox-hugo/morrison16_parasitic_capacitance_amp.svg" caption="Figure 9: Parasitic capacitances in a simple circuit. (a) Field lines in a circuit. (b) Mutual capacitance diagram. (b) Circuit representation" >}}
+{{< figure src="/ox-hugo/morrison16_parasitic_capacitance_amp.svg" caption="<span class=\"figure-number\">Figure 9: </span>Parasitic capacitances in a simple circuit. (a) Field lines in a circuit. (b) Mutual capacitance diagram. (b) Circuit representation" >}}
 
-It is common practice in analog design to connect the enclosure to circuit common (Figure [10](#org9f3c9db)).
+It is common practice in analog design to connect the enclosure to circuit common ([Figure 10](#figure--fig:morrison16-grounding-shield-amp)).
 When this connection is made, the feedback is removed and the enclosure no longer couples signals into the feedback structure.
 The conductive enclosure is called a **shield**.
 Connecting the signal common to the conductive enclosure is called "**grounding the shield**".
 This "grounding" usually removed "hum" from the circuit.
 
-<a id="org9f3c9db"></a>
+<a id="figure--fig:morrison16-grounding-shield-amp"></a>
 
-{{< figure src="/ox-hugo/morrison16_grounding_shield_amp.svg" caption="Figure 10: Grounding the shield to limit feedback" >}}
+{{< figure src="/ox-hugo/morrison16_grounding_shield_amp.svg" caption="<span class=\"figure-number\">Figure 10: </span>Grounding the shield to limit feedback" >}}
 
 Most practical circuits provide connections to external points.
 To see the effect of making a _single_ external connection, open the conductive enclosure and connect the input circuit common to an external ground.
-Figure [11](#orgc4242ae) (a) shows this grounded connection surrounded by an extension of the enclosure called the _cable shield_.
+[Figure 11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (a) shows this grounded connection surrounded by an extension of the enclosure called the _cable shield_.
 A problem can be caused by an incorrect location of the connection between the cable shield and the enclosure.
-In Figure [11](#orgc4242ae) (a), the electromagnetic field in the area induces a voltage in the loop and a resulting current to flow in conductor (1)-(2).
+In [Figure 11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (a), the electromagnetic field in the area induces a voltage in the loop and a resulting current to flow in conductor (1)-(2).
-This conductor being the common ground that might have a resistance \\(R\\) or \\(1\,\Omega\\), this current induced voltage that it added to the transmitted signal.
+This conductor being the common ground that might have a resistance \\(R\\) or \\(1\\,\Omega\\), this current induced voltage that it added to the transmitted signal.
 Our goal in this chapter is to find ways of keeping interference currents from flowing in any input signal conductor.
 To remove this coupling, the shield connection to circuit common must be made at the point, where the circuit common connects to the external ground.
-This connection is shown in Figure [11](#orgc4242ae) (b).
+This connection is shown in [Figure 11](#figure--fig:morrison16-enclosure-shield-1-2-leads) (b).
 This connection keeps the circulation of interference current on the outside of the shield.
 
 There is only one point of zero signal potential external to the enclosure and that is where the signal common connects to an external hardware ground.
@@ -527,7 +518,6 @@ If there is an external electromagnetic field, there will be current flow in the
 A voltage gradient will couple interference capacitively to the signal conductors.
 
 <div class="important">
-  <div></div>
 
 An input circuit shield should connect to the circuit common, where the signal common makes its connection to the source of signal.
 Any other shield connection will introduce interference.
@@ -535,16 +525,15 @@ Any other shield connection will introduce interference.
 </div>
 
 <div class="important">
-  <div></div>
 
 Shielding is not an issue of finding a "really good ground".
 It is an issue of using the _right_ ground.
 
 </div>
 
-<a id="orgc4242ae"></a>
+<a id="figure--fig:morrison16-enclosure-shield-1-2-leads"></a>
 
-{{< figure src="/ox-hugo/morrison16_enclosure_shield_1_2_leads.png" caption="Figure 11: (a) The problem of bringing one lead out of a shielded region. Unwanted current circulates in the signal lead 2. (b) The \\(E\\) field circulate current in the shield, not in the signal conductor." >}}
+{{< figure src="/ox-hugo/morrison16_enclosure_shield_1_2_leads.png" caption="<span class=\"figure-number\">Figure 11: </span>(a) The problem of bringing one lead out of a shielded region. Unwanted current circulates in the signal lead 2. (b) The \\(E\\) field circulate current in the shield, not in the signal conductor." >}}
 
 
 ### The enclosure and utility power {#the-enclosure-and-utility-power}
@@ -554,9 +543,9 @@ The power transformer couples fields from the external environment into the encl
 The obvious coupling results from capacitance between the primary coil and the secondary coil.
 Note that the secondary coil is connected to the circuit common conductor.
 
-<a id="org5995e31"></a>
+<a id="figure--fig:morrison16-power-transformer-enclosure"></a>
 
-{{< figure src="/ox-hugo/morrison16_power_transformer_enclosure.png" caption="Figure 12: A power transformer added to the circuit enclosure" >}}
+{{< figure src="/ox-hugo/morrison16_power_transformer_enclosure.png" caption="<span class=\"figure-number\">Figure 12: </span>A power transformer added to the circuit enclosure" >}}
 
 
 ### The two-ground problem {#the-two-ground-problem}
@@ -566,9 +555,9 @@ Note that the secondary coil is connected to the circuit common conductor.
 
 The basic analog problem is to condition a signal associated with one ground reference potential and transport this signal to a second ground reference potential without adding interference.
 
-<a id="org3228c82"></a>
+<a id="figure--fig:morrison16-two-ground-problem"></a>
 
-{{< figure src="/ox-hugo/morrison16_two_ground_problem.svg" caption="Figure 13: The two-circuit enclosures used to transport signals between grounds" >}}
+{{< figure src="/ox-hugo/morrison16_two_ground_problem.svg" caption="<span class=\"figure-number\">Figure 13: </span>The two-circuit enclosures used to transport signals between grounds" >}}
 
 
 ### Strain-gauge instrumentation {#strain-gauge-instrumentation}
@@ -582,9 +571,9 @@ The basic analog problem is to condition a signal associated with one ground ref
 
 ### The basic low-gain differential amplifier (forward referencing amplifier) {#the-basic-low-gain-differential-amplifier--forward-referencing-amplifier}
 
-<a id="org4f33add"></a>
+<a id="figure--fig:morrison16-low-gain-diff-amp"></a>
 
-{{< figure src="/ox-hugo/morrison16_low_gain_diff_amp.svg" caption="Figure 14: The low-gain differential amplifier applied to the two-ground problem" >}}
+{{< figure src="/ox-hugo/morrison16_low_gain_diff_amp.svg" caption="<span class=\"figure-number\">Figure 14: </span>The low-gain differential amplifier applied to the two-ground problem" >}}
 
 
 ### Shielding in power transformers {#shielding-in-power-transformers}
@@ -599,7 +588,6 @@ The basic analog problem is to condition a signal associated with one ground ref
 ### Signal flow paths in analog circuits {#signal-flow-paths-in-analog-circuits}
 
 <div class="important">
-  <div></div>
 
 Here are a few rule that will help in analog board layout:
 
@@ -625,13 +613,13 @@ Here are a few rule that will help in analog board layout:
 
 ### Feedback theory {#feedback-theory}
 
-<a id="org4a09d89"></a>
+<a id="figure--fig:morrison16-basic-feedback-circuit"></a>
 
-{{< figure src="/ox-hugo/morrison16_basic_feedback_circuit.svg" caption="Figure 15: The basic feedback circuit" >}}
+{{< figure src="/ox-hugo/morrison16_basic_feedback_circuit.svg" caption="<span class=\"figure-number\">Figure 15: </span>The basic feedback circuit" >}}
 
-<a id="orgf414d06"></a>
+<a id="figure--fig:morrison16-LR-stabilizing-network"></a>
 
-{{< figure src="/ox-hugo/morrison16_LR_stabilizing_network.svg" caption="Figure 16: An LR-stabilizing network" >}}
+{{< figure src="/ox-hugo/morrison16_LR_stabilizing_network.svg" caption="<span class=\"figure-number\">Figure 16: </span>An LR-stabilizing network" >}}
 
 
 ### Output loads and circuit stability {#output-loads-and-circuit-stability}
@@ -667,27 +655,26 @@ If the resistors are replaced by capacitors, the gain is the ratio of reactances
 This feedback circuit is called a **charge converter**.
 The charge on the input capacitor is transferred to the feedback capacitor.
 If the feedback capacitor is smaller than the transducer capacitance by a factor of 100, then the voltage across the feedback capacitor will be 100 times greater than the open-circuit transducer voltage.
-This feedback arrangement is shown in Figure [17](#org74f6090).
+This feedback arrangement is shown in [Figure 17](#figure--fig:morrison16-charge-amplifier).
 The open-circuit input signal voltage is \\(Q/C\_T\\).
 The output voltage is \\(Q/C\_{FB}\\).
 The voltage gain is therefore \\(C\_T/C\_{FB}\\).
 Note that there is essentially no voltage at the summing node \\(s\_p\\).
 
 <div class="important">
-  <div></div>
 
 A charge converter does not amplifier charge.
 It converts a charge signal to a voltage.
 
 </div>
 
-<a id="org74f6090"></a>
+<a id="figure--fig:morrison16-charge-amplifier"></a>
 
-{{< figure src="/ox-hugo/morrison16_charge_amplifier.svg" caption="Figure 17: A basic charge amplifier" >}}
+{{< figure src="/ox-hugo/morrison16_charge_amplifier.svg" caption="<span class=\"figure-number\">Figure 17: </span>A basic charge amplifier" >}}
 
-<a id="orgb9f996c"></a>
+<a id="figure--fig:morrison16-charge-amplifier-feedback-resistor"></a>
 
-{{< figure src="/ox-hugo/morrison16_charge_amplifier_feedback_resistor.svg" caption="Figure 18: The resistor feedback arrangement to control the low-frequency response" >}}
+{{< figure src="/ox-hugo/morrison16_charge_amplifier_feedback_resistor.svg" caption="<span class=\"figure-number\">Figure 18: </span>The resistor feedback arrangement to control the low-frequency response" >}}
 
 
 ### DC power supplies {#dc-power-supplies}
@@ -705,7 +692,6 @@ It converts a charge signal to a voltage.
 ## Utility Power and Facility Grounding {#utility-power-and-facility-grounding}
 
 <div class="sum">
-  <div></div>
 
 This chapter discusses the relationship between utility power and the performance of electrical circuits.
 Utility installations in facilities are controller by the NEC (National Electrical Code).
@@ -798,7 +784,7 @@ Listed equipment
 ### Neutral conductors {#neutral-conductors}
 
 
-### \\(k\\) factor in transformers {#k--factor-in-transformers}
+### \\(k\\) factor in transformers {#k-factor-in-transformers}
 
 
 ### Power factor correction {#power-factor-correction}
@@ -858,7 +844,6 @@ Listed equipment
 ## Radiation {#radiation}
 
 <div class="sum">
-  <div></div>
 
 This chapter discusses radiation from circuit boards, transmission lines, conductor loops, and antennas.
 The frequency spectrum of square waves and pulses is presented.
@@ -917,7 +902,6 @@ Simple tools for locating sources of radiation are suggested.
 ## Shielding from Radiation {#shielding-from-radiation}
 
 <div class="sum">
-  <div></div>
 
 Cable shields are often made of aluminum foil or tinned copper braid.
 Drain wires make it practical to connect to the foil.
@@ -1033,7 +1017,8 @@ To transport RF power without reflections, the source impedance and the terminat
 ### Shielded and screen rooms {#shielded-and-screen-rooms}
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org7a49345"></a>Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Morrison, Ralph. 2016. <i>Grounding and Shielding: Circuits and Interference</i>. John Wiley &#38; Sons.</div>
+</div>

content/book/pintelon12_system_ident.md

@@ -0,0 +1,24 @@
++++
+title = "System identification : a frequency domain approach"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+: [System Identification]({{< relref "system_identification.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Pintelon and Schoukens 2012</a>)
+
+Author(s)
+: Pintelon, R., &amp; Schoukens, J.
+
+Year
+: 2012
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Pintelon, Rik, and Johan Schoukens. 2012. <i>System Identification : a Frequency Domain Approach</i>. Hoboken, N.J. Piscataway, NJ: Wiley IEEE Press. doi:<a href="https://doi.org/10.1002/9781118287422">10.1002/9781118287422</a>.</div>
+</div>

content/book/preumont18_vibrat_contr_activ_struc_fourt_edition.md

@@ -1,16 +1,16 @@
 +++
 title = "Vibration Control of Active Structures - Fourth Edition"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 description = "Gives a broad overview of vibration control."
 keywords = ["Control", "Vibration"]
 draft = false
 +++
 
 Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Reference Books]({{< relref "reference_books" >}}), [Stewart Platforms]({{< relref "stewart_platforms" >}}), [HAC-HAC]({{< relref "hac_hac" >}})
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Reference Books]({{< relref "reference_books.md" >}}), [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [HAC-HAC]({{< relref "hac_hac.md" >}})
 
 Reference
-: ([Preumont 2018](#orgf75c814))
+: (<a href="#citeproc_bib_item_1">Preumont 2018</a>)
 
 Author(s)
 : Preumont, A.
@@ -63,11 +63,11 @@ There are two radically different approached to disturbance rejection: feedback
 
 #### Feedback {#feedback}
 
-<a id="org30e8b62"></a>
+<a id="figure--fig:classical-feedback-small"></a>
 
-{{< figure src="/ox-hugo/preumont18_classical_feedback_small.png" caption="Figure 1: Principle of feedback control" >}}
+{{< figure src="/ox-hugo/preumont18_classical_feedback_small.png" caption="<span class=\"figure-number\">Figure 1: </span>Principle of feedback control" >}}
 
-The principle of feedback is represented on figure [1](#org30e8b62). The output \\(y\\) of the system is compared to the reference signal \\(r\\), and the error signal \\(\epsilon = r-y\\) is passed into a compensator \\(K(s)\\) and applied to the system \\(G(s)\\), \\(d\\) is the disturbance.
+The principle of feedback is represented on [Figure 1](#figure--fig:classical-feedback-small). The output \\(y\\) of the system is compared to the reference signal \\(r\\), and the error signal \\(\epsilon = r-y\\) is passed into a compensator \\(K(s)\\) and applied to the system \\(G(s)\\), \\(d\\) is the disturbance.
 The design problem consists of finding the appropriate compensator \\(K(s)\\) such that the closed-loop system is stable and behaves in the appropriate manner.
 
 In the control of lightly damped structures, feedback control is used for two distinct and complementary purposes: **active damping** and **model-based feedback**.
@@ -89,23 +89,23 @@ The objective is to control a variable \\(y\\) to a desired value \\(r\\) in spi
 
 #### Feedforward {#feedforward}
 
-<a id="org0cb2cac"></a>
+<a id="figure--fig:feedforward-adaptative"></a>
 
-{{< figure src="/ox-hugo/preumont18_feedforward_adaptative.png" caption="Figure 2: Principle of feedforward control" >}}
+{{< figure src="/ox-hugo/preumont18_feedforward_adaptative.png" caption="<span class=\"figure-number\">Figure 2: </span>Principle of feedforward control" >}}
 
 The method relies on the availability of a **reference signal correlated to the primary disturbance**.
-The idea is to produce a second disturbance such that is cancels the effect of the primary disturbance at the location of the sensor error. Its principle is explained in figure [2](#org0cb2cac).
+The idea is to produce a second disturbance such that is cancels the effect of the primary disturbance at the location of the sensor error. Its principle is explained in [Figure 2](#figure--fig:feedforward-adaptative).
 
 The filter coefficients are adapted in such a way that the error signal at one or several critical points is minimized.
 
 There is no guarantee that the global response is reduced at other locations. This method is therefor considered as a local one.
 Because it is less sensitive to phase lag than feedback, it can be used at higher frequencies (\\(\omega\_c \approx \omega\_s/10\\)).
 
-The table [1](#table--tab:adv-dis-type-control) summarizes the main features of the two approaches.
+The [Table 1](#table--tab:adv-dis-type-control) summarizes the main features of the two approaches.
 
 <a id="table--tab:adv-dis-type-control"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:adv-dis-type-control">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:adv-dis-type-control">Table 1</a>:</span>
   Advantages and Disadvantages of some types of control
 </div>
 
@@ -125,11 +125,11 @@ The table [1](#table--tab:adv-dis-type-control) summarizes the main features of
 
 ### The Various Steps of the Design {#the-various-steps-of-the-design}
 
-<a id="org5fed023"></a>
+<a id="figure--fig:design-steps"></a>
 
-{{< figure src="/ox-hugo/preumont18_design_steps.png" caption="Figure 3: The various steps of the design" >}}
+{{< figure src="/ox-hugo/preumont18_design_steps.png" caption="<span class=\"figure-number\">Figure 3: </span>The various steps of the design" >}}
 
-The various steps of the design of a controlled structure are shown in figure [3](#org5fed023).
+The various steps of the design of a controlled structure are shown in [Figure 3](#figure--fig:design-steps).
 
 The **starting point** is:
 
@@ -156,21 +156,20 @@ If the dynamics of the sensors and actuators may significantly affect the behavi
 
 ### Plant Description, Error and Control Budget {#plant-description-error-and-control-budget}
 
-From the block diagram of the control system (figure [4](#orgc558cd1)):
+From the block diagram of the control system ([Figure 4](#figure--fig:general-plant)):
 
 \begin{align\*}
-y &= (I - G\_{yu}H)^{-1} G\_{yw} w\\\\\\
+y &= (I - G\_{yu}H)^{-1} G\_{yw} w\\\\
 z &= T\_{zw} w = [G\_{zw} + G\_{zu}H(I - G\_{yu}H)^{-1} G\_{yw}] w
 \end{align\*}
 
-<a id="orgc558cd1"></a>
+<a id="figure--fig:general-plant"></a>
 
-{{< figure src="/ox-hugo/preumont18_general_plant.png" caption="Figure 4: Block diagram of the control System" >}}
+{{< figure src="/ox-hugo/preumont18_general_plant.png" caption="<span class=\"figure-number\">Figure 4: </span>Block diagram of the control System" >}}
 
 The frequency content of the disturbance \\(w\\) is usually described by its **power spectral density** \\(\Phi\_w (\omega)\\) which describes the frequency distribution of the meas-square value.
 
 <div class="cbox">
-  <div></div>
 
 \\[\sigma\_w = \sqrt{\int\_0^\infty \Phi\_w(\omega) d\omega}\\]
 
@@ -179,7 +178,6 @@ The frequency content of the disturbance \\(w\\) is usually described by its **p
 Even more interesting for the design is the **Cumulative Mean Square** response defined by the integral of the PSD in the frequency range \\([\omega, \infty[\\).
 
 <div class="cbox">
-  <div></div>
 
 \\[\sigma\_z^2(\omega) = \int\_\omega^\infty \Phi\_z(\nu) d\nu = \int\_\omega^\infty |T\_{zw}|^2 \Phi\_w(\nu) d\nu \\]
 
@@ -188,14 +186,14 @@ Even more interesting for the design is the **Cumulative Mean Square** response
 It is a monotonously decreasing function of frequency and describes the contribution of all frequencies above \\(\omega\\) to the mean-square value of \\(z\\).
 \\(\sigma\_z(0)\\) is then the global RMS response.
 
-A typical plot of \\(\sigma\_z(\omega)\\) is shown figure [5](#orgd0ed9cf).
+A typical plot of \\(\sigma\_z(\omega)\\) is shown [Figure 5](#figure--fig:cas-plot).
 It is useful to **identify the critical modes** in a design, at which the effort should be targeted.
 
 The diagram can also be used to **assess the control laws** and compare different actuator and sensor configuration.
 
-<a id="orgd0ed9cf"></a>
+<a id="figure--fig:cas-plot"></a>
 
-{{< figure src="/ox-hugo/preumont18_cas_plot.png" caption="Figure 5: Error budget distribution in OL and CL for increasing gains" >}}
+{{< figure src="/ox-hugo/preumont18_cas_plot.png" caption="<span class=\"figure-number\">Figure 5: </span>Error budget distribution in OL and CL for increasing gains" >}}
 
 
 ### Pseudo-inverse {#pseudo-inverse}
@@ -254,7 +252,6 @@ This will have usually little impact of the fitting error while reducing conside
 The general form of the equation of motion governing the dynamic equilibrium between the external, elastic, inertia and damping forces acting on a discrete, flexible structure with a finite number \\(n\\) of degrees of freedom is
 
 <div class="cbox">
-  <div></div>
 
 \begin{equation}
   M \ddot{x} + C \dot{x} + K x = f
@@ -271,7 +268,6 @@ With:
 The damping matrix \\(C\\) represents the various dissipation mechanisms in the structure, which are usually poorly known. One of the popular hypotheses is the Rayleigh damping.
 
 <div class="cbox">
-  <div></div>
 
 \begin{equation}
   C = \alpha M + \beta K
@@ -299,14 +295,14 @@ The number of mode shapes is equal to the number of degrees of freedom \\(n\\).
 The mode shapes are orthogonal with respect to the stiffness and mass matrices:
 
 \begin{align}
-  \phi\_i^T M \phi\_j &= \mu\_i \delta\_{ij} \\\\\\
+  \phi\_i^T M \phi\_j &= \mu\_i \delta\_{ij} \\\\
   \phi\_i^T K \phi\_j &= \mu\_i \omega\_i^2 \delta\_{ij}
 \end{align}
 
 With \\(\mu\_i\\) the **modal mass** (also called the generalized mass) of mode \\(i\\).
 
 
-### [Modal Decomposition]({{< relref "modal_decomposition" >}}) {#modal-decomposition--modal-decomposition-dot-md}
+### [Modal Decomposition]({{< relref "modal_decomposition.md" >}}) {#modal-decomposition--modal-decomposition-dot-md}
 
 
 #### Structure Without Rigid Body Modes {#structure-without-rigid-body-modes}
@@ -314,7 +310,6 @@ With \\(\mu\_i\\) the **modal mass** (also called the generalized mass) of mode
 Let perform a change of variable from physical coordinates \\(x\\) to modal coordinates \\(z\\).
 
 <div class="cbox">
-  <div></div>
 
 \begin{equation}
   x = \Phi z
@@ -336,12 +331,11 @@ If we left multiply the equation by \\(\Phi^T\\) and we use the orthogonalily re
 If \\(\Phi^T C \Phi\\) is diagonal, the **damping is said classical or normal**. In this case:
 \\[ \Phi^T C \Phi = diag(2 \xi\_i \mu\_i \omega\_i) \\]
 
-One can verify that the Rayleigh damping \eqref{eq:rayleigh_damping} complies with this condition with modal damping ratios \\(\xi\_i = \frac{1}{2} ( \frac{\alpha}{\omega\_i} + \beta\omega\_i )\\).
+One can verify that the Rayleigh damping \eqref{eq:rayleigh\_damping} complies with this condition with modal damping ratios \\(\xi\_i = \frac{1}{2} ( \frac{\alpha}{\omega\_i} + \beta\omega\_i )\\).
 
-And we obtain decoupled modal equations \eqref{eq:modal_eom}.
+And we obtain decoupled modal equations \eqref{eq:modal\_eom}.
 
 <div class="cbox">
-  <div></div>
 
 \begin{equation}
   \ddot{z} + 2 \xi \Omega \dot{z} + \Omega^2 z = z^{-1} \Phi^T f
@@ -355,11 +349,11 @@ with:
 
 </div>
 
-Typical values of the modal damping ratio are summarized on table [tab:damping_ratio](#tab:damping_ratio).
+Typical values of the modal damping ratio are summarized on table <tab:damping_ratio>.
 
 <a id="table--tab:damping-ratio"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:damping-ratio">Table 2</a></span>:
+  <span class="table-number"><a href="#table--tab:damping-ratio">Table 2</a>:</span>
   Typical Damping ratio
 </div>
 
@@ -372,15 +366,15 @@ Typical values of the modal damping ratio are summarized on table [tab:damping_r
 
 The assumption of classical damping is often justified for light damping, but it is questionable when the damping is large.
 
-If one accepts the assumption of classical damping, the only difference between equation \eqref{eq:general_eom} and \eqref{eq:modal_eom} lies in the change of coordinates.
+If one accepts the assumption of classical damping, the only difference between equation \eqref{eq:general\_eom} and \eqref{eq:modal\_eom} lies in the change of coordinates.
 However, in physical coordinates, the number of degrees of freedom is usually very large.
-If a structure is excited in by a band limited excitation, its response is dominated by the modes whose natural frequencies are inside the bandwidth of the excitation and the equation \eqref{eq:modal_eom} can often be restricted to theses modes.
+If a structure is excited in by a band limited excitation, its response is dominated by the modes whose natural frequencies are inside the bandwidth of the excitation and the equation \eqref{eq:modal\_eom} can often be restricted to theses modes.
 Therefore, the number of degrees of freedom contribution effectively to the response is **reduced drastically** in modal coordinates.
 
 
 #### Dynamic Flexibility Matrix {#dynamic-flexibility-matrix}
 
-If we consider the steady-state response of equation \eqref{eq:general_eom} to harmonic excitation \\(f=F e^{j\omega t}\\), the response is also harmonic \\(x = Xe^{j\omega t}\\). The amplitude of \\(F\\) and \\(X\\) is related by:
+If we consider the steady-state response of equation \eqref{eq:general\_eom} to harmonic excitation \\(f=F e^{j\omega t}\\), the response is also harmonic \\(x = Xe^{j\omega t}\\). The amplitude of \\(F\\) and \\(X\\) is related by:
 \\[ X = G(\omega) F \\]
 
 Where \\(G(\omega)\\) is called the **Dynamic flexibility Matrix**:
@@ -400,11 +394,11 @@ With:
   D\_i(\omega) = \frac{1}{1 - \omega^2/\omega\_i^2 + 2 j \xi\_i \omega/\omega\_i}
 \end{equation}
 
-<a id="orgeec9f86"></a>
+<a id="figure--fig:neglected-modes"></a>
 
-{{< figure src="/ox-hugo/preumont18_neglected_modes.png" caption="Figure 6: Fourier spectrum of the excitation \\(F\\) and dynamic amplitification \\(D\_i\\) of mode \\(i\\) and \\(k\\) such that \\(\omega\_i < \omega\_b\\) and \\(\omega\_k \gg \omega\_b\\)" >}}
+{{< figure src="/ox-hugo/preumont18_neglected_modes.png" caption="<span class=\"figure-number\">Figure 6: </span>Fourier spectrum of the excitation \\(F\\) and dynamic amplitification \\(D\_i\\) of mode \\(i\\) and \\(k\\) such that \\(\omega\_i < \omega\_b\\) and \\(\omega\_k \gg \omega\_b\\)" >}}
 
-If the excitation has a limited bandwidth \\(\omega\_b\\), the contribution of the high frequency modes \\(\omega\_k \gg \omega\_b\\) can be evaluated by assuming \\(D\_k(\omega) \approx 1\\) (as shown on figure [6](#orgeec9f86)).
+If the excitation has a limited bandwidth \\(\omega\_b\\), the contribution of the high frequency modes \\(\omega\_k \gg \omega\_b\\) can be evaluated by assuming \\(D\_k(\omega) \approx 1\\) (as shown on [Figure 6](#figure--fig:neglected-modes)).
 
 And \\(G(\omega)\\) can be rewritten on terms of the **low frequency modes only**:
 \\[ G(\omega) \approx \sum\_{i=1}^m \frac{\phi\_i \phi\_i^T}{\mu\_i \omega\_i^2} D\_i(\omega) + R \\]
@@ -418,7 +412,6 @@ The quasi-static correction of the high frequency modes \\(R\\) is called the **
 ### Collocated Control System {#collocated-control-system}
 
 <div class="cbox">
-  <div></div>
 
 A **collocated control system** is a control system where:
 
@@ -429,7 +422,7 @@ A **collocated control system** is a control system where:
 
 <a id="table--tab:dual-actuator-sensor"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:dual-actuator-sensor">Table 3</a></span>:
+  <span class="table-number"><a href="#table--tab:dual-actuator-sensor">Table 3</a>:</span>
   Examples of dual actuators and sensors
 </div>
 
@@ -443,30 +436,28 @@ The open-loop FRF of a collocated system corresponds to a diagonal component of
 If we assumes that the collocated system is undamped and is attached to the DoF \\(k\\), the open-loop FRF is purely real:
 \\[ G\_{kk}(\omega) = \sum\_{i=1}^m \frac{\phi\_i^2(k)}{\mu\_i (\omega\_i^2 - \omega^2)} + R\_{kk} \\]
 
-\\(G\_{kk}\\) is a monotonously increasing function of \\(\omega\\) (figure [7](#org2389144)).
+\\(G\_{kk}\\) is a monotonously increasing function of \\(\omega\\) ([Figure 7](#figure--fig:collocated-control-frf)).
 
-<a id="org2389144"></a>
+<a id="figure--fig:collocated-control-frf"></a>
 
-{{< figure src="/ox-hugo/preumont18_collocated_control_frf.png" caption="Figure 7: Open-Loop FRF of an undamped structure with collocated actuator/sensor pair" >}}
+{{< figure src="/ox-hugo/preumont18_collocated_control_frf.png" caption="<span class=\"figure-number\">Figure 7: </span>Open-Loop FRF of an undamped structure with collocated actuator/sensor pair" >}}
 
 The amplitude of the FRF goes from \\(-\infty\\) at the resonance frequencies \\(\omega\_i\\) to \\(+\infty\\) at the next resonance frequency \\(\omega\_{i+1}\\). Therefore, in every interval, there is a frequency \\(z\_i\\) such that \\(\omega\_i < z\_i < \omega\_{i+1}\\) where the amplitude of the FRF vanishes. The frequencies \\(z\_i\\) are called **anti-resonances**.
 
 <div class="cbox">
-  <div></div>
 
 Undamped **collocated control systems** have **alternating poles and zeros** on the imaginary axis.
 For lightly damped structure, the poles and zeros are just moved a little bit in the left-half plane, but they are still interlacing.
 
 </div>
 
-If the undamped structure is excited harmonically by the actuator at the frequency of the transmission zero \\(z\_i\\), the amplitude of the response of the collocated sensor vanishes. That means that the structure oscillates at the frequency \\(z\_i\\) according to the mode shape shown in dotted line figure [8](#org9a738f7).
+If the undamped structure is excited harmonically by the actuator at the frequency of the transmission zero \\(z\_i\\), the amplitude of the response of the collocated sensor vanishes. That means that the structure oscillates at the frequency \\(z\_i\\) according to the mode shape shown in dotted line [Figure 8](#figure--fig:collocated-zero).
 
-<a id="org9a738f7"></a>
+<a id="figure--fig:collocated-zero"></a>
 
-{{< figure src="/ox-hugo/preumont18_collocated_zero.png" caption="Figure 8: Structure with collocated actuator and sensor" >}}
+{{< figure src="/ox-hugo/preumont18_collocated_zero.png" caption="<span class=\"figure-number\">Figure 8: </span>Structure with collocated actuator and sensor" >}}
 
 <div class="cbox">
-  <div></div>
 
 The frequency of the transmission zero \\(z\_i\\) and the mode shape associated are the **natural frequency** and the **mode shape** of the system obtained by **constraining the d.o.f. on which the control systems acts**.
 
@@ -476,11 +467,11 @@ The open-loop poles are independant of the actuator and sensor configuration whi
 
 </div>
 
-By looking at figure [7](#org2389144), we see that neglecting the residual mode in the modelling amounts to translating the FRF diagram vertically. That produces a shift in the location of the transmission zeros to the right.
+By looking at [Figure 7](#figure--fig:collocated-control-frf), we see that neglecting the residual mode in the modelling amounts to translating the FRF diagram vertically. That produces a shift in the location of the transmission zeros to the right.
 
-<a id="org52c26c5"></a>
+<a id="figure--fig:alternating-p-z"></a>
 
-{{< figure src="/ox-hugo/preumont18_alternating_p_z.png" caption="Figure 9: Bode plot of a lighly damped structure with collocated actuator and sensor" >}}
+{{< figure src="/ox-hugo/preumont18_alternating_p_z.png" caption="<span class=\"figure-number\">Figure 9: </span>Bode plot of a lighly damped structure with collocated actuator and sensor" >}}
 
 The open-loop transfer function of a lighly damped structure with a collocated actuator/sensor pair can be written:
 
@@ -488,7 +479,7 @@ The open-loop transfer function of a lighly damped structure with a collocated a
   G(s) = G\_0 \frac{\Pi\_i(s^2/z\_i^2 + 2 \xi\_i s/z\_i + 1)}{\Pi\_j(s^2/\omega\_j^2 + 2 \xi\_j s /\omega\_j + 1)}
 \end{equation}
 
-The corresponding Bode plot is represented in figure [9](#org52c26c5). Every imaginary pole at \\(\pm j\omega\_i\\) introduces a \\(\SI{180}{\degree}\\) phase lag and every imaginary zero at \\(\pm jz\_i\\) introduces a phase lead of \\(\SI{180}{\degree}\\).
+The corresponding Bode plot is represented in [Figure 9](#figure--fig:alternating-p-z). Every imaginary pole at \\(\pm j\omega\_i\\) introduces a \\(\SI{180}{\degree}\\) phase lag and every imaginary zero at \\(\pm jz\_i\\) introduces a phase lead of \\(\SI{180}{\degree}\\).
 In this way, the phase diagram is always contained between \\(\SI{0}{\degree}\\) and \\(\SI{-180}{\degree}\\) as a consequence of the interlacing property.
 
 
@@ -510,14 +501,14 @@ Two broad categories of actuators can be distinguish:
 
 A voice coil transducer is an energy transformer which converts electrical power into mechanical power and vice versa.
 
-The system consists of (see figure [10](#orga1a9b67)):
+The system consists of (see [Figure 10](#figure--fig:voice-coil-schematic)):
 
 -   A permanent magnet which produces a uniform flux density \\(B\\) normal to the gap
 -   A coil which is free to move axially
 
-<a id="orga1a9b67"></a>
+<a id="figure--fig:voice-coil-schematic"></a>
 
-{{< figure src="/ox-hugo/preumont18_voice_coil_schematic.png" caption="Figure 10: Physical principle of a voice coil transducer" >}}
+{{< figure src="/ox-hugo/preumont18_voice_coil_schematic.png" caption="<span class=\"figure-number\">Figure 10: </span>Physical principle of a voice coil transducer" >}}
 
 We note:
 
@@ -527,7 +518,6 @@ We note:
 -   \\(i\\) the current into the coil
 
 <div class="cbox">
-  <div></div>
 
 **Faraday's law**:
 
@@ -553,11 +543,11 @@ Thus, at any time, there is an equilibrium between the electrical power absorbed
 
 #### Proof-Mass Actuator {#proof-mass-actuator}
 
-A reaction mass \\(m\\) is conected to the support structure by a spring \\(k\\) , and damper \\(c\\) and a force actuator \\(f = T i\\) (figure [11](#orgc439137)).
+A reaction mass \\(m\\) is conected to the support structure by a spring \\(k\\) , and damper \\(c\\) and a force actuator \\(f = T i\\) ([Figure 11](#figure--fig:proof-mass-actuator)).
 
-<a id="orgc439137"></a>
+<a id="figure--fig:proof-mass-actuator"></a>
 
-{{< figure src="/ox-hugo/preumont18_proof_mass_actuator.png" caption="Figure 11: Proof-mass actuator" >}}
+{{< figure src="/ox-hugo/preumont18_proof_mass_actuator.png" caption="<span class=\"figure-number\">Figure 11: </span>Proof-mass actuator" >}}
 
 If we apply the second law of Newton on the mass:
 \\[ m\ddot{x} + c\dot{x} + kx = f = Ti \\]
@@ -571,7 +561,6 @@ The total force applied on the support is:
 The transfer function between the total force and the current \\(i\\) applied to the coil is :
 
 <div class="cbox">
-  <div></div>
 
 \begin{equation}
   \frac{F}{i} = \frac{-s^2 T}{s^2 + 2\xi\_p \omega\_p s + \omega\_p^2}
@@ -585,11 +574,11 @@ with:
 
 </div>
 
-Above some critical frequency \\(\omega\_c \approx 2\omega\_p\\), **the proof-mass actuator can be regarded as an ideal force generator** (figure [12](#org3b93a8e)).
+Above some critical frequency \\(\omega\_c \approx 2\omega\_p\\), **the proof-mass actuator can be regarded as an ideal force generator** ([Figure 12](#figure--fig:proof-mass-tf)).
 
-<a id="org3b93a8e"></a>
+<a id="figure--fig:proof-mass-tf"></a>
 
-{{< figure src="/ox-hugo/preumont18_proof_mass_tf.png" caption="Figure 12: Bode plot \\(F/i\\) of the proof-mass actuator" >}}
+{{< figure src="/ox-hugo/preumont18_proof_mass_tf.png" caption="<span class=\"figure-number\">Figure 12: </span>Bode plot \\(F/i\\) of the proof-mass actuator" >}}
 
 
 #### Geophone {#geophone}
@@ -600,7 +589,7 @@ The voltage \\(e\\) of the coil is used as the sensor output.
 If \\(x\_0\\) is the displacement of the support and if the voice coil is open (\\(i=0\\)), the governing equations are:
 
 \begin{align\*}
-  m\ddot{x} + c(\dot{x}-\dot{x\_0}) + k(x-x\_0) &= 0\\\\\\
+  m\ddot{x} + c(\dot{x}-\dot{x\_0}) + k(x-x\_0) &= 0\\\\
   T(\dot{x}-\dot{x\_0}) &= e
 \end{align\*}
 
@@ -612,25 +601,25 @@ By using the two equations, we obtain:
 
 Above the corner frequency, the gain of the geophone is equal to the transducer constant \\(T\\).
 
-<a id="org7ded49f"></a>
+<a id="figure--fig:geophone"></a>
 
-{{< figure src="/ox-hugo/preumont18_geophone.png" caption="Figure 13: Model of a geophone based on a voice coil transducer" >}}
+{{< figure src="/ox-hugo/preumont18_geophone.png" caption="<span class=\"figure-number\">Figure 13: </span>Model of a geophone based on a voice coil transducer" >}}
 
 Designing geophones with very low corner frequency is in general difficult. Active geophones where the frequency is lowered electronically may constitute a good alternative option.
 
 
 ### General Electromechanical Transducer {#general-electromechanical-transducer}
 
-The consitutive behavior of a wide class of electromechanical transducers can be modelled as in figure [14](#org82c090c).
+The consitutive behavior of a wide class of electromechanical transducers can be modelled as in [Figure 14](#figure--fig:electro-mechanical-transducer).
 
-<a id="org82c090c"></a>
+<a id="figure--fig:electro-mechanical-transducer"></a>
 
-{{< figure src="/ox-hugo/preumont18_electro_mechanical_transducer.png" caption="Figure 14: Electrical analog representation of an electromechanical transducer" >}}
+{{< figure src="/ox-hugo/preumont18_electro_mechanical_transducer.png" caption="<span class=\"figure-number\">Figure 14: </span>Electrical analog representation of an electromechanical transducer" >}}
 
 In Laplace form the constitutive equations read:
 
 \begin{align}
-  e & = Z\_e    i + T\_{em} v \label{eq:gen\_trans\_e} \\\\\\
+  e & = Z\_e    i + T\_{em} v \label{eq:gen\_trans\_e} \\\\
   f & = T\_{em} i + Z\_m    v \label{eq:gen\_trans\_f}
 \end{align}
 
@@ -645,10 +634,10 @@ With:
 -   \\(T\_{me}\\) is the transduction coefficient representing the force acting on the mechanical terminals to balance the electromagnetic force induced per unit current input (in \\(\si{\newton\per\ampere}\\))
 -   \\(Z\_m\\) is the mechanical impedance measured when \\(i=0\\)
 
-Equation \eqref{eq:gen_trans_e} shows that the voltage across the electrical terminals of any electromechanical transducer is the sum of a contribution proportional to the current applied and a contribution proportional to the velocity of the mechanical terminals.
+Equation \eqref{eq:gen\_trans\_e} shows that the voltage across the electrical terminals of any electromechanical transducer is the sum of a contribution proportional to the current applied and a contribution proportional to the velocity of the mechanical terminals.
 Thus, if \\(Z\_ei\\) can be measured and substracted from \\(e\\), a signal proportional to the velocity is obtained.
 
-To do so, the bridge circuit as shown on figure [15](#org8e1c5fb) can be used.
+To do so, the bridge circuit as shown on [Figure 15](#figure--fig:bridge-circuit) can be used.
 
 We can show that
 
@@ -658,19 +647,19 @@ We can show that
 
 which is indeed a linear function of the velocity \\(v\\) at the mechanical terminals.
 
-<a id="org8e1c5fb"></a>
+<a id="figure--fig:bridge-circuit"></a>
 
-{{< figure src="/ox-hugo/preumont18_bridge_circuit.png" caption="Figure 15: Bridge circuit for self-sensing actuation" >}}
+{{< figure src="/ox-hugo/preumont18_bridge_circuit.png" caption="<span class=\"figure-number\">Figure 15: </span>Bridge circuit for self-sensing actuation" >}}
 
 
 ### Smart Materials {#smart-materials}
 
 Smart materials have the ability to respond significantly to stimuli of different physical nature.
-Figure [16](#org29efe87) lists various effects that are observed in materials in response to various inputs.
+[Figure 16](#figure--fig:smart-materials) lists various effects that are observed in materials in response to various inputs.
 
-<a id="org29efe87"></a>
+<a id="figure--fig:smart-materials"></a>
 
-{{< figure src="/ox-hugo/preumont18_smart_materials.png" caption="Figure 16: Stimulus response relations indicating various effects in materials. The smart materials corresponds to the non-diagonal cells" >}}
+{{< figure src="/ox-hugo/preumont18_smart_materials.png" caption="<span class=\"figure-number\">Figure 16: </span>Stimulus response relations indicating various effects in materials. The smart materials corresponds to the non-diagonal cells" >}}
 
 
 ### Piezoelectric Transducer {#piezoelectric-transducer}
@@ -678,14 +667,12 @@ Figure [16](#org29efe87) lists various effects that are observed in materials in
 Piezoelectric materials exhibits two effects described below.
 
 <div class="cbox">
-  <div></div>
 
 Ability to generate an electrical charge in proportion to an external applied force.
 
 </div>
 
 <div class="cbox">
-  <div></div>
 
 An electric filed parallel to the direction of polarization induces an expansion of the material.
 
@@ -696,11 +683,10 @@ The most popular piezoelectric materials are Lead-Zirconate-Titanate (PZT) which
 We here consider a transducer made of one-dimensional piezoelectric material.
 
 <div class="cbox">
-  <div></div>
 
 \begin{subequations}
   \begin{align}
-    D & = \epsilon^T E + d\_{33} T\\\\\\
+    D & = \epsilon^T E + d\_{33} T\\\\
     S & = d\_{33} E     + s^E T
   \end{align}
 \end{subequations}
@@ -720,16 +706,16 @@ With:
 
 #### Constitutive Relations of a Discrete Transducer {#constitutive-relations-of-a-discrete-transducer}
 
-The set of equations \eqref{eq:piezo_eq} can be written in a matrix form:
+The set of equations \eqref{eq:piezo\_eq} can be written in a matrix form:
 
 \begin{equation}
-\begin{bmatrix}D\\S\end{bmatrix}
+\begin{bmatrix}D\\\S\end{bmatrix}
 =
 \begin{bmatrix}
-\epsilon^T & d\_{33}\\\\\\
+\epsilon^T & d\_{33}\\\\
 d\_{33}     & s^E
 \end{bmatrix}
-\begin{bmatrix}E\\T\end{bmatrix}
+\begin{bmatrix}E\\\T\end{bmatrix}
 \end{equation}
 
 Where \\((E, T)\\) are the independent variables and \\((D, S)\\) are the dependent variable.
@@ -737,13 +723,13 @@ Where \\((E, T)\\) are the independent variables and \\((D, S)\\) are the depend
 If \\((E, S)\\) are taken as independant variables:
 
 \begin{equation}
-\begin{bmatrix}D\\T\end{bmatrix}
+\begin{bmatrix}D\\\T\end{bmatrix}
 =
 \begin{bmatrix}
-\epsilon^T(1-k^2) & e\_{33}\\\\\\
+\epsilon^T(1-k^2) & e\_{33}\\\\
 -e\_{33}           & c^E
 \end{bmatrix}
-\begin{bmatrix}E\\S\end{bmatrix}
+\begin{bmatrix}E\\\S\end{bmatrix}
 \end{equation}
 
 With:
@@ -752,7 +738,6 @@ With:
 -   \\(e\_{33} = \frac{d\_{33}}{s^E}\\) is the constant relating the electric displacement to the strain for short-circuited electrodes \\([C/m^2]\\)
 
 <div class="cbox">
-  <div></div>
 
 \begin{equation}
   k^2 = \frac{{d\_{33}}^2}{s^E \epsilon^T} = \frac{{e\_{33}}^2}{c^E \epsilon^T}
@@ -763,16 +748,16 @@ It measures the efficiency of the conversion of the mechanical energy into elect
 
 </div>
 
-If one assumes that all the electrical and mechanical quantities are uniformly distributed in a linear transducer formed by a **stack** (see figure [17](#org226015b)) of \\(n\\) disks of thickness \\(t\\) and cross section \\(A\\), the global constitutive equations of the transducer are obtained by integrating \eqref{eq:piezo_eq_matrix_bis} over the volume of the transducer:
+If one assumes that all the electrical and mechanical quantities are uniformly distributed in a linear transducer formed by a **stack** (see [Figure 17](#figure--fig:piezo-stack)) of \\(n\\) disks of thickness \\(t\\) and cross section \\(A\\), the global constitutive equations of the transducer are obtained by integrating \eqref{eq:piezo\_eq\_matrix\_bis} over the volume of the transducer:
 
 \begin{equation}
-\begin{bmatrix}Q\\\Delta\end{bmatrix}
+\begin{bmatrix}Q\\\\Delta\end{bmatrix}
 =
 \begin{bmatrix}
-C & nd\_{33}\\\\\\
+C & nd\_{33}\\\\
 nd\_{33} & 1/K\_a
 \end{bmatrix}
-\begin{bmatrix}V\\f\end{bmatrix}
+\begin{bmatrix}V\\\f\end{bmatrix}
 \end{equation}
 
 where
@@ -784,27 +769,27 @@ where
 -   \\(C = \epsilon^T A n^2/l\\) is the capacitance of the transducer with no external load (\\(f = 0\\))
 -   \\(K\_a = A/s^El\\) is the stiffness with short-circuited electrodes (\\(V = 0\\))
 
-<a id="org226015b"></a>
+<a id="figure--fig:piezo-stack"></a>
 
-{{< figure src="/ox-hugo/preumont18_piezo_stack.png" caption="Figure 17: Piezoelectric linear transducer" >}}
+{{< figure src="/ox-hugo/preumont18_piezo_stack.png" caption="<span class=\"figure-number\">Figure 17: </span>Piezoelectric linear transducer" >}}
 
-Equation \eqref{eq:piezo_stack_eq} can be inverted to obtain
+Equation \eqref{eq:piezo\_stack\_eq} can be inverted to obtain
 
 \begin{equation}
-\begin{bmatrix}V\\f\end{bmatrix}
+\begin{bmatrix}V\\\f\end{bmatrix}
 =
 \frac{K\_a}{C(1-k^2)}
 \begin{bmatrix}
-1/K\_a & -nd\_{33}\\\\\\
+1/K\_a & -nd\_{33}\\\\
 -nd\_{33} & C
 \end{bmatrix}
-\begin{bmatrix}Q\\\Delta\end{bmatrix}
+\begin{bmatrix}Q\\\\Delta\end{bmatrix}
 \end{equation}
 
 
 #### Energy Stored in the Piezoelectric Transducer {#energy-stored-in-the-piezoelectric-transducer}
 
-Let us write the total stored electromechanical energy of a discrete piezoelectric transducer as shown on figure [18](#org4316115).
+Let us write the total stored electromechanical energy of a discrete piezoelectric transducer as shown on [Figure 18](#figure--fig:piezo-discrete).
 
 The total power delivered to the transducer is the sum of electric power \\(V i\\) and the mechanical power \\(f \dot{\Delta}\\). The net work of the transducer is
 
@@ -812,11 +797,11 @@ The total power delivered to the transducer is the sum of electric power \\(V i\
   dW = V i dt + f \dot{\Delta} dt = V dQ + f d\Delta
 \end{equation}
 
-<a id="org4316115"></a>
+<a id="figure--fig:piezo-discrete"></a>
 
-{{< figure src="/ox-hugo/preumont18_piezo_discrete.png" caption="Figure 18: Discrete Piezoelectric Transducer" >}}
+{{< figure src="/ox-hugo/preumont18_piezo_discrete.png" caption="<span class=\"figure-number\">Figure 18: </span>Discrete Piezoelectric Transducer" >}}
 
-By integrating equation \eqref{eq:piezo_work} and using the constitutive equations \eqref{eq:piezo_stack_eq_inv}, we obtain the analytical expression of the stored electromechanical energy for the discrete transducer:
+By integrating equation \eqref{eq:piezo\_work} and using the constitutive equations \eqref{eq:piezo\_stack\_eq\_inv}, we obtain the analytical expression of the stored electromechanical energy for the discrete transducer:
 
 \begin{equation}
   W\_e(\Delta, Q) = \frac{Q^2}{2 C (1 - k^2)} - \frac{n d\_{33} K\_a}{C(1-k^2)} Q\Delta + \frac{K\_a}{1-k^2}\frac{\Delta^2}{2}
@@ -830,7 +815,7 @@ The constitutive equations can be recovered by differentiate the stored energy:
 \\[ f = \frac{\partial W\_e}{\partial \Delta}, \quad V = \frac{\partial W\_e}{\partial Q} \\]
 
 
-#### Interpretation of \\(k^2\\) {#interpretation-of--k-2}
+#### Interpretation of \\(k^2\\) {#interpretation-of-k-2}
 
 Consider a piezoelectric transducer subjected to the following mechanical cycle: first, it is loaded with a force \\(F\\) with short-circuited electrodes; the resulting extension is \\(\Delta\_1 = F/K\_a\\) where \\(K\_a = A/(s^El)\\) is the stiffness with short-circuited electrodes.
 The energy stored in the system is:
@@ -846,12 +831,12 @@ The ratio between the remaining stored energy and the initial stored energy is
 
 #### Admittance of the Piezoelectric Transducer {#admittance-of-the-piezoelectric-transducer}
 
-Consider the system of figure [19](#orgcdbb831), where the piezoelectric transducer is assumed massless and is connected to a mass \\(M\\).
+Consider the system of [Figure 19](#figure--fig:piezo-stack-admittance), where the piezoelectric transducer is assumed massless and is connected to a mass \\(M\\).
 The force acting on the mass is negative of that acting on the transducer, \\(f = -M \ddot{x}\\).
 
-<a id="orgcdbb831"></a>
+<a id="figure--fig:piezo-stack-admittance"></a>
 
-{{< figure src="/ox-hugo/preumont18_piezo_stack_admittance.png" caption="Figure 19: Elementary dynamical model of the piezoelectric transducer" >}}
+{{< figure src="/ox-hugo/preumont18_piezo_stack_admittance.png" caption="<span class=\"figure-number\">Figure 19: </span>Elementary dynamical model of the piezoelectric transducer" >}}
 
 From the constitutive equations, one finds
 
@@ -868,11 +853,11 @@ And one can see that
   \frac{z^2 - p^2}{z^2} = k^2
 \end{equation}
 
-Equation \eqref{eq:distance_p_z} constitutes a practical way to determine the electromechanical coupling factor from the poles and zeros of the admittance measurement (figure [20](#org15dd7b6)).
+Equation \eqref{eq:distance\_p\_z} constitutes a practical way to determine the electromechanical coupling factor from the poles and zeros of the admittance measurement ([Figure 20](#figure--fig:piezo-admittance-curve)).
 
-<a id="org15dd7b6"></a>
+<a id="figure--fig:piezo-admittance-curve"></a>
 
-{{< figure src="/ox-hugo/preumont18_piezo_admittance_curve.png" caption="Figure 20: Typical admittance FRF of the transducer" >}}
+{{< figure src="/ox-hugo/preumont18_piezo_admittance_curve.png" caption="<span class=\"figure-number\">Figure 20: </span>Typical admittance FRF of the transducer" >}}
 
 
 ## Piezoelectric Beam, Plate and Truss {#piezoelectric-beam-plate-and-truss}
@@ -1004,13 +989,12 @@ Equation \eqref{eq:distance_p_z} constitutes a practical way to determine the el
 #### Equivalent Damping Ratio {#equivalent-damping-ratio}
 
 
-## Collocated Versus Non-collocated Control {#collocated-versus-non-collocated-control}
+## BKMK Collocated Versus Non-collocated Control {#bkmk-collocated-versus-non-collocated-control}
 
 
 ### Pole-Zero Flipping {#pole-zero-flipping}
 
 <div class="cbox">
-  <div></div>
 
 The Root Locus shows, in a graphical form, the evolution of the poles of the closed-loop system as a function of the scalar gain \\(g\\) applied to the compensator.
 The Root Locus is the locus of the solution \\(s\\) of the closed loop characteristic equation \\(1 + gG(s)H(s) = 0\\) when \\(g\\) goes from zero to infinity.
@@ -1380,7 +1364,7 @@ Weakness of LQG:
 -   use frequency independant cost function
 -   use noise statistics with uniform distribution
 
-To overcome the weakness => frequency shaping either by:
+To overcome the weakness =&gt; frequency shaping either by:
 
 -   considering a frequency dependant cost function
 -   using colored noise statistics
@@ -1568,7 +1552,7 @@ Their design requires a model of the structure, and there is usually a trade-off
 
 When collocated actuator/sensor pairs can be used, stability can be achieved using positivity concepts, but in many situations, collocated pairs are not feasible for HAC.
 
-The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure [21](#org0c9fed0).
+The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in [Figure 21](#figure--fig:hac-lac-control).
 The inner loop uses a set of collocated actuator/sensor pairs for decentralized active damping with guaranteed stability ; the outer loop consists of a non-collocated HAC based on a model of the actively damped structure.
 This approach has the following advantages:
 
@@ -1576,9 +1560,9 @@ This approach has the following advantages:
 -   The active damping makes it easier to gain-stabilize the modes outside the bandwidth of the output loop (improved gain margin)
 -   The larger damping of the modes within the controller bandwidth makes them more robust to the parmetric uncertainty (improved phase margin)
 
-<a id="org0c9fed0"></a>
+<a id="figure--fig:hac-lac-control"></a>
 
-{{< figure src="/ox-hugo/preumont18_hac_lac_control.png" caption="Figure 21: Principle of the dual-loop HAC/LAC control" >}}
+{{< figure src="/ox-hugo/preumont18_hac_lac_control.png" caption="<span class=\"figure-number\">Figure 21: </span>Principle of the dual-loop HAC/LAC control" >}}
 
 
 #### Wide-Band Position Control {#wide-band-position-control}
@@ -1818,7 +1802,8 @@ This approach has the following advantages:
 ### Problems {#problems}
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgf75c814"></a>Preumont, Andre. 2018. _Vibration Control of Active Structures - Fourth Edition_. Solid Mechanics and Its Applications. Springer International Publishing. <https://doi.org/10.1007/978-3-319-72296-2>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Preumont, Andre. 2018. <i>Vibration Control of Active Structures - Fourth Edition</i>. Solid Mechanics and Its Applications. Springer International Publishing. doi:<a href="https://doi.org/10.1007/978-3-319-72296-2">10.1007/978-3-319-72296-2</a>.</div>
+</div>

content/book/schmidt20_desig_high_perfor_mechat_third_revis_edition.md

@@ -1,19 +1,19 @@
 +++
 title = "The design of high performance mechatronics - third revised edition"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 description = "Awesome book that gives great overview of high performance mechatronic systems"
 keywords = ["Metrology", "Mechatronics", "Control"]
 draft = false
 +++
 
 Tags
-: [Reference Books]({{< relref "reference_books" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})
+: [Reference Books]({{< relref "reference_books.md" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting.md" >}})
 
 Reference
-: ([Schmidt, Schitter, and Rankers 2020](#org4e5c703))
+: (<a href="#citeproc_bib_item_1">Schmidt, Schitter, and Rankers 2020</a>)
 
 Author(s)
-: Schmidt, R. M., Schitter, G., & Rankers, A.
+: Schmidt, R. M., Schitter, G., &amp; Rankers, A.
 
 Year
 : 2020
@@ -66,9 +66,9 @@ Year
 
 #### Electric Field {#electric-field}
 
-<a id="org16b370d"></a>
+<a id="figure--fig:schmidt20-electrical-field"></a>
 
-{{< figure src="/ox-hugo/schmidt20_electrical_field.svg" caption="Figure 1: Charges have an electric field" >}}
+{{< figure src="/ox-hugo/schmidt20_electrical_field.svg" caption="<span class=\"figure-number\">Figure 1: </span>Charges have an electric field" >}}
 
 
 ##### Potential Difference and Capacitance {#potential-difference-and-capacitance}
@@ -172,14 +172,13 @@ The term "rms" refers to Root Mean Square, named from the action of taking the r
 The RMS value is a well known term used to characterize the "useful" value of the energy supply with a signal by comparing it with an equivalent DC voltage that would cause the same power in a resistive load.
 
 <div class="exampl">
-  <div></div>
 
 For a sinusoidal signal \\(V(t) = V\_p \sin(\omega t)\\), the equivalent DC voltage becomes:
 
 \begin{equation}
 \begin{aligned}
-V\_{\text{rms}} &= \sqrt{\frac{1}{T} \int\_0^T \left< V\_p\sin(\omega t) \right>^2 dt} \\\\\\
+V\_{\text{rms}} &= \sqrt{\frac{1}{T} \int\_0^T \left< V\_p\sin(\omega t) \right>^2 dt} \\\\
-               &= \dots \\\\\\
+               &= \dots \\\\
                &= \frac{V\_p}{\sqrt{2}} \quad [V]
 \end{aligned}
 \end{equation}
@@ -213,7 +212,7 @@ Its inverse, the spatial period length called _wavelength_ \\(\lambda\\) [m] is
 The relation between the above defined terms is:
 
 \begin{align}
-  \lambda &= \frac{1}{\nu} = c\_p T = \frac{c\_p}{f} \quad [m] \\\\\\
+  \lambda &= \frac{1}{\nu} = c\_p T = \frac{c\_p}{f} \quad [m] \\\\
   v\_p     &= \frac{f}{\nu} \quad [m/s]
 \end{align}
 
@@ -221,11 +220,11 @@ The relation between the above defined terms is:
 ##### Mechanical Waves {#mechanical-waves}
 
 The propagation speed value of a mechanical wave is mostly determined by the density and elasticity of the medium.
-The wave propagation through an elastic material can be qualitatively explained with the help of a simplified lumped element model, consisting of a chain of springs and bodies as shown in Figure [2](#orgaa33fb8).
+The wave propagation through an elastic material can be qualitatively explained with the help of a simplified lumped element model, consisting of a chain of springs and bodies as shown in Figure [2](#figure--fig:schmidt20-mechanical-wave).
 
-<a id="orgaa33fb8"></a>
+<a id="figure--fig:schmidt20-mechanical-wave"></a>
 
-{{< figure src="/ox-hugo/schmidt20_mechanical_wave.svg" caption="Figure 2: Lumped element model of one wavelength of a mechanical wave." >}}
+{{< figure src="/ox-hugo/schmidt20_mechanical_wave.svg" caption="<span class=\"figure-number\">Figure 2: </span>Lumped element model of one wavelength of a mechanical wave." >}}
 
 To explain the principle of energy transfer, the longitudinal wave is taken as example.
 When a movement of mass \\(m\_1\\) is introduced in the propagation direction of the chain, this will first cause a compression of the elastic coupling \\(k\_1\\).
@@ -234,7 +233,6 @@ This process is repeated over the total chain until the original movement reache
 With this mechanism the kinetic energy from mass \\(m\_1\\) is converted into potential energy in \\(k\_1\\), which in turn is transferred into kinetic energy of \\(m\_2\\), and so on.
 
 <div class="important">
-  <div></div>
 
 This phenomenon of transfer of energy in an elastic body is important in mechatronic systems because driving forces are also transported through the body as a wave and as a consequence will experience a delay between the actuator and the sensor when they are located separately.
 
@@ -247,7 +245,6 @@ The propagation speed \\(c\_p\\) is determined by the density \\(\rho\_m\\) and
 \end{equation}
 
 <div class="exampl">
-  <div></div>
 
 The propagation speed in stainless steel varies between 3500 m/s for transversal waves and 5500 m/s for longitudinal waves.
 With for instance half a meter of steel this gives a delay of about 0.1ms, resulting in a phase delay of 36 degrees at 1kHz, which can be significant from a control point of view.
@@ -384,7 +381,7 @@ The values are given in Table [1](#table--tab:relation-slope-decade) for a decad
 
 <a id="table--tab:relation-slope-decade"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:relation-slope-decade">Table 1</a></span>:
+  <span class="table-number"><a href="#table--tab:relation-slope-decade">Table 1</a>:</span>
   Relation between the order of the slope of a bode plot and the magnitude ration in dB, amplitude ratio and power ration, per <b>decade</b> (\(f_1 = 10 f_2\))
 </div>
 
@@ -398,7 +395,7 @@ The values are given in Table [1](#table--tab:relation-slope-decade) for a decad
 
 <a id="table--tab:relation-slope-octave"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:relation-slope-octave">Table 2</a></span>:
+  <span class="table-number"><a href="#table--tab:relation-slope-octave">Table 2</a>:</span>
   Relation between the order of the slope of a bode plot and the magnitude ration in dB, amplitude ratio and power ration, per <b>octave</b> (\(f_1 = 2 f_2\))
 </div>
 
@@ -589,7 +586,8 @@ The values are given in Table [1](#table--tab:relation-slope-decade) for a decad
 
 ### Summary on Dynamics {#summary-on-dynamics}
 
-<summary>
+<div class="sum">
+
 In this chapter some important lessons have been learned, which are summarised as follows:
 
 -   Stiffness, whether it is created mechanically or by means of a control system, is determinative for precision
@@ -604,7 +602,8 @@ In this chapter some important lessons have been learned, which are summarised a
 -   Modal analysis is a powerful and widely applied tool to investigate the dynamics of a mechanical structure.
 
 Finally it can be concluded, that these insights help in designing actively controlled dynamic motion systems with optimally located actuators and sensors, which reduce the sensitivity for modal dynamic problems.
-</summary>
+
+</div>
 
 
 ## Motion Control {#motion-control}
@@ -612,15 +611,15 @@ Finally it can be concluded, that these insights help in designing actively cont
 
 ### A Walk around the Control Loop {#a-walk-around-the-control-loop}
 
-Figure [3](#org6432052) shows a basic control loop of a positioning system.
+Figure [3](#figure--fig:schmidt20-walk-control-loop) shows a basic control loop of a positioning system.
 First, the A/D and D/A converters are used to translate analog signals into time-discrete digital signals and vice versa.
 Secondly, the impact locations of several disturbances are shown, which play a large role in determining what reqwuirements the controller needs to fulfil.
 The core of the control system is the _plant_, which is the physical system that needs to be controlled.
 
 <a id="table--tab:walk-control-loop"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:walk-control-loop">Table 3</a></span>:
+  <span class="table-number"><a href="#table--tab:walk-control-loop">Table 3</a>:</span>
-  Symbols used in Figure <a href="#org6432052">10</a>
+  Symbols used in Figure <a href="#org4b1b612">3</a>
 </div>
 
 | Symbol     | Meaning                              | Unit |
@@ -634,16 +633,16 @@ The core of the control system is the _plant_, which is the physical system that
 | \\(y\\)    | Measured output motion               | [m]  |
 | \\(y\_m\\) | Measurement value                    | [m]  |
 
-<a id="org6432052"></a>
+<a id="figure--fig:schmidt20-walk-control-loop"></a>
 
-{{< figure src="/ox-hugo/schmidt20_walk_control_loop.svg" caption="Figure 3: Block diagram of a motion control system, including feedforward and feedback control." >}}
+{{< figure src="/ox-hugo/schmidt20_walk_control_loop.svg" caption="<span class=\"figure-number\">Figure 3: </span>Block diagram of a motion control system, including feedforward and feedback control." >}}
 
-The plant combines the mechanical structure, amplifiers and actuators, as they all deal with energy conversion in close interaction (Figure [4](#org21aa9c3)).
+The plant combines the mechanical structure, amplifiers and actuators, as they all deal with energy conversion in close interaction (Figure [4](#figure--fig:schmidt20-energy-actuator-system)).
 They interact in both directions in such a way that each element not only determines the input of the next element, but also influences the previous element by its dynamic load.
 
-<a id="org21aa9c3"></a>
+<a id="figure--fig:schmidt20-energy-actuator-system"></a>
 
-{{< figure src="/ox-hugo/schmidt20_energy_actuator_system.svg" caption="Figure 4: The energy converting part of a mechatronic system consists of a the amplifier, the actuator and the mechanical structure." >}}
+{{< figure src="/ox-hugo/schmidt20_energy_actuator_system.svg" caption="<span class=\"figure-number\">Figure 4: </span>The energy converting part of a mechatronic system consists of a the amplifier, the actuator and the mechanical structure." >}}
 
 
 #### Poles and Zeros in Motion Control {#poles-and-zeros-in-motion-control}
@@ -672,7 +671,7 @@ Fortunately the effect is mostly so small that it can be neglected.
 
 #### Overview Feedforward Control {#overview-feedforward-control}
 
-Figure [5](#org4b3a329) shows the typical basic configuration for feedforward control, which is also called _open-loop control_ as it is equal to a situation where the measured output is not connected to the input for feedback.
+Figure [5](#figure--fig:schmidt20-feedforward-control-diagram) shows the typical basic configuration for feedforward control, which is also called _open-loop control_ as it is equal to a situation where the measured output is not connected to the input for feedback.
 
 The reference signal \\(r\\) [m] is applied to the controller, which as a reference transfer function \\(C\_{ff}(s)\\) in [N/m].
 The output \\(u\\) in [N] of the controller is connected to the input of the motion system, which has a transfer function \\(G(s)\\) in [m/N] giving the output \\(x\\) in [m].
@@ -684,12 +683,11 @@ If one would like to achieve perfect control, which means that there is no diffe
 G\_{t,ff}(s) = \frac{x}{r} = C\_{ff}(s)G(s) = 1 \quad \Longrightarrow \quad C\_{ff}(s) = G^{-1}(s)
 \end{equation}
 
-<a id="org4b3a329"></a>
+<a id="figure--fig:schmidt20-feedforward-control-diagram"></a>
 
-{{< figure src="/ox-hugo/schmidt20_feedforward_control_diagram.svg" caption="Figure 5: Block diagram of a feedforward controller motion system with one input and output (SISO)." >}}
+{{< figure src="/ox-hugo/schmidt20_feedforward_control_diagram.svg" caption="<span class=\"figure-number\">Figure 5: </span>Block diagram of a feedforward controller motion system with one input and output (SISO)." >}}
 
 <div class="important">
-  <div></div>
 
 Feedforward control is a very useful and preferred first step in the control of a complex dynamic motion system as it provides the following advantages:
 
@@ -702,7 +700,6 @@ Feedforward control is a very useful and preferred first step in the control of
 </div>
 
 <div class="important">
-  <div></div>
 
 The drawbacks and limitations of feedforward control are:
 
@@ -718,21 +715,20 @@ The drawbacks and limitations of feedforward control are:
 
 In feedback control the actuator status of the motion system is monitored by a sensor and the controller generates a control action based on the difference between the desired motion (reference signal) and the actuator system status (sensor signal).
 
-The block diagram of Figure [6](#org3bccc77) shows a SISO feedback loop for a motion system without the A/D and D/A converters.
+The block diagram of Figure [6](#figure--fig:schmidt20-feedback-control-diagram) shows a SISO feedback loop for a motion system without the A/D and D/A converters.
 The output \\(x\\) in [m] is the total motion of the plant on all its parts and details, while \\(y\\) is the measured motion with a measured value \\(y\_m\\) measured on a selected location in the plant.
 This measured is compared with \\(r\_f\\), which is the reference \\(r\\) after filtering.
 The result of this comparison is used as input for the feedback controller.
 
 <div class="note">
-  <div></div>
 
 The transfer function of any input to any output in a closed-loop feedback controlled dynamic system is equal to the forward path from the input to the output divided by one plus the transfer function of the total feedback path.
 
 </div>
 
-<a id="org3bccc77"></a>
+<a id="figure--fig:schmidt20-feedback-control-diagram"></a>
 
-{{< figure src="/ox-hugo/schmidt20_feedback_control_diagram.svg" caption="Figure 6: Block diagram of a SISO feedback controlled motion system." >}}
+{{< figure src="/ox-hugo/schmidt20_feedback_control_diagram.svg" caption="<span class=\"figure-number\">Figure 6: </span>Block diagram of a SISO feedback controlled motion system." >}}
 
 In control design, one has the freedom to choose \\(F(s)\\) and particularly \\(C\_{fb}(s)\\) such that the total transfer function fulfills the desired specifications.
 Feedback control allows to directly place the system poles at values that are more useful for the operation of the motion system that their natural locations.
@@ -743,7 +739,6 @@ It is mainly used to present unwanted signals from entering the system.
 This can be signals that drive the system into its "incapability" region where the system can no longer perform as required due to limitations in the hardware.
 
 <div class="important">
-  <div></div>
 
 Feedback is an addition to feedforward control with the following benefits:
 
@@ -754,7 +749,6 @@ Feedback is an addition to feedforward control with the following benefits:
 </div>
 
 <div class="important">
-  <div></div>
 
 Also, some pitfalls have to be dealt with:
 
@@ -769,9 +763,9 @@ Also, some pitfalls have to be dealt with:
 
 #### Summary {#summary}
 
-<a id="table--tab:feedback-feedforward-summary"></a>
+<a id="table--tab:feedback-feedforward-sum"></a>
 <div class="table-caption">
-  <span class="table-number"><a href="#table--tab:feedback-feedforward-summary">Table 4</a></span>:
+  <span class="table-number"><a href="#table--tab:feedback-feedforward-sum">Table 4</a>:</span>
   Summary of Feedback and Feedforward control
 </div>
 
@@ -795,11 +789,11 @@ Also, some pitfalls have to be dealt with:
 #### Model-Based Feedforward Control {#model-based-feedforward-control}
 
 In the following an example of a model-based feedforward controller is introduced.
-The measured frequency-response of the scanning unit taken as as an example is shown in Figure [7](#org77061d7).
+The measured frequency-response of the scanning unit taken as as an example is shown in Figure [7](#figure--fig:schmidt20-bode-plot-scanning).
 
-<a id="org77061d7"></a>
+<a id="figure--fig:schmidt20-bode-plot-scanning"></a>
 
-{{< figure src="/ox-hugo/schmidt20_bode_plot_scanning.svg" caption="Figure 7: Bode plot of a piezoelectric-actuator based scanning unit for nanometer resolution positioning. It shows the measured response (solid line) and the second order model, which is fitted for the low-frewquency system behaviour (dashed line)." >}}
+{{< figure src="/ox-hugo/schmidt20_bode_plot_scanning.svg" caption="<span class=\"figure-number\">Figure 7: </span>Bode plot of a piezoelectric-actuator based scanning unit for nanometer resolution positioning. It shows the measured response (solid line) and the second order model, which is fitted for the low-frewquency system behaviour (dashed line)." >}}
 
 A mathematical model of a seconder-order mass-spring system with a force input is fitted to this measured response:
 
@@ -815,7 +809,7 @@ This means that the transfer function of the feedforward controller is:
 C\_{ff}(s) = \frac{s^2 + 2 \xi\_f \omega\_0 s + \omega\_0^2}{\omega\_0^2}
 \end{equation}
 
-However, such controller needs to be modified in such a way that it becomes realizable.
+However, such controller needs to be modified in such a way that it becomes _realizable_.
 In this case, it is decided to create a resulting overall transfer function of the controller and the plant that acts like a well damped mass-spring system with the same natural frequency as the plant and an additional reduction of the excitation of high frequency eigen-modes.
 In order to realize this controller, first two poles have to be added:
 
@@ -835,17 +829,17 @@ C\_{ff}(s) = \frac{s^2 + 2 \xi\_f \omega\_0 s + \omega\_0^2}{(s + \omega\_0)(s^2
 Then this controller is connected in series with the scanning unit, the anti-resonance of the controller and the resonance of the piezo-scanner cancel each other out:
 
 \begin{align}
-G\_{t,ff}(s) &= G(s)G\_{ff}(s) \\\\\\
+G\_{t,ff}(s) &= G(s)G\_{ff}(s) \\\\
-            &= \frac{C\_f}{s^2 + 2 \xi\_f \omega\_0 s + \omega\_0^2} \frac{s^2 + 2 \xi\_f \omega\_0 s + \omega\_0^2}{(s + \omega\_0){s^2 + 2 \omega\_0 s + \omega\_0^2}} \\\\\\
+            &= \frac{C\_f}{s^2 + 2 \xi\_f \omega\_0 s + \omega\_0^2} \frac{s^2 + 2 \xi\_f \omega\_0 s + \omega\_0^2}{(s + \omega\_0){s^2 + 2 \omega\_0 s + \omega\_0^2}} \\\\
             &= \frac{C\_f}{(s + \omega\_0){s^2 + 2 \omega\_0 s + \omega\_0^2}}
 \end{align}
 
-The bode plot of the resulting dynamics is shown in Figure [8](#org1f513e4).
+The bode plot of the resulting dynamics is shown in Figure [8](#figure--fig:schmidt20-bode-plot-feedfoward-example).
 The controlled system has low-pass characteristics, rolling of at the scanner's natural frequency.
 
-<a id="org1f513e4"></a>
+<a id="figure--fig:schmidt20-bode-plot-feedfoward-example"></a>
 
-{{< figure src="/ox-hugo/schmidt20_bode_plot_feedfoward_example.svg" caption="Figure 8: Bode plot of the feedforward-controlled scanning unit" >}}
+{{< figure src="/ox-hugo/schmidt20_bode_plot_feedfoward_example.svg" caption="<span class=\"figure-number\">Figure 8: </span>Bode plot of the feedforward-controlled scanning unit" >}}
 
 
 #### Input-Shaping {#input-shaping}
@@ -861,16 +855,16 @@ The oscillation caused by each individual step are 180 degrees out of phase and
 This method is clearly very different form pole-zero cancellation.
 In the frequency domain, these sampled adaptations to the input create a frequency spectrum with a multiple of notch filters at the harmonic of the frequency where these adaptations are applied.
 
-Applying input-shaping to the triangular scanning signal results in the introduction of a plateau instead of the sharp peak, where the width of the plateau corresponds to half the period of the scanner's resonance as can be seen in Figure [9](#orgddd25e4).
+Applying input-shaping to the triangular scanning signal results in the introduction of a plateau instead of the sharp peak, where the width of the plateau corresponds to half the period of the scanner's resonance as can be seen in Figure [9](#figure--fig:schmidt20-input-shaping-example).
 
-<a id="orgddd25e4"></a>
+<a id="figure--fig:schmidt20-input-shaping-example"></a>
 
-{{< figure src="/ox-hugo/schmidt20_input_shaping_example.svg" caption="Figure 9: Input-shaping control of the triangular scanning signal in a scanning probe microscope." >}}
+{{< figure src="/ox-hugo/schmidt20_input_shaping_example.svg" caption="<span class=\"figure-number\">Figure 9: </span>Input-shaping control of the triangular scanning signal in a scanning probe microscope." >}}
 
 
 #### Adaptive Feedforward Control {#adaptive-feedforward-control}
 
-Both examples of feedforward control, the model-based pole-zero cancellation and the input-shaping, only work reliably as long as the dynamic properties of the total plant are known and remain constant.
+Both examples of feedforward control, the model-based pole-zero cancellation and the input-shaping, only work reliably as long as the dynamic properties of the total plant are known and _remain constant_.
 There is always some deviation between the parameters in the model and the reality.
 This deviation can be partly solved by _adaptive feedforward control_, adapting the feedforward signal by measuring the real behavior of the system.
 This method requires a sensor to obtain information about the response of the system and for that reason it is often applied in combination with feedback.
@@ -891,13 +885,13 @@ The limitations of the actuators and electronics in a controlled motion system a
 Of at least the levels of Jerk and preferable also Snap should be limited.
 The standard method to cope with these limitations involves shaping the input of a mechatronic motion system by means of _trajectory profile generation_ or _path-planning_.
 
-Figure [10](#orge30b109) shows a fourth order trajectory profile of a displacement, which means that all derivatives including the fourth derivative are defined in the path planning.
+Figure [10](#figure--fig:schmidt20-trajectory-profile) shows a fourth order trajectory profile of a displacement, which means that all derivatives including the fourth derivative are defined in the path planning.
 A third order trajectory would show a square profile for the jerk indicating an infinite Snap and the round of the acceleration would be gone.
 A second order trajectory would show a square acceleration profile with infinite Jerk and sharp edges on the velocity.
 
-<a id="orge30b109"></a>
+<a id="figure--fig:schmidt20-trajectory-profile"></a>
 
-{{< figure src="/ox-hugo/schmidt20_trajectory_profile.svg" caption="Figure 10: Figure caption" >}}
+{{< figure src="/ox-hugo/schmidt20_trajectory_profile.svg" caption="<span class=\"figure-number\">Figure 10: </span>Figure caption" >}}
 
 
 ### Feedback Control {#feedback-control}
@@ -915,29 +909,29 @@ Feedback control is more complex and critical to design than feedforward control
 In general, a feedback controlled motion system is to perform a certain predetermined motion task defined by the reference input \\(r\\), while reducing the effects of other inputs like external vibrations and noise from the electronics.
 All these input signals, whether desired of undesired, are treated by the feedback loop as disturbances and it is the sensitivity of the desired output signal to all input signals that determine the performance of the feedback controller.
 
-<a id="org39f635c"></a>
+<a id="figure--fig:schmidt20-feedback-full-simplified"></a>
 
-{{< figure src="/ox-hugo/schmidt20_feedback_full_simplified.svg" caption="Figure 11: Full and simplified representation of a feedback loop in order to determine the influence of the reference signal and most important disturbance sources on real motion output of the plant \\(x\\), the feedback controller output \\(u\\) and the measured motion output \\(y\\). \\(y\_m = y\\) when the measurement system is set at unity gain and the sensor disturbance is included in the output disturbance." >}}
+{{< figure src="/ox-hugo/schmidt20_feedback_full_simplified.svg" caption="<span class=\"figure-number\">Figure 11: </span>Full and simplified representation of a feedback loop in order to determine the influence of the reference signal and most important disturbance sources on real motion output of the plant \\(x\\), the feedback controller output \\(u\\) and the measured motion output \\(y\\). \\(y\_m = y\\) when the measurement system is set at unity gain and the sensor disturbance is included in the output disturbance." >}}
 
 Several standard sensitivity functions have been defined to quantify the performance of feedback controlled dynamic systems.
-There are derived from a simplified version of the generic feedback loop as shown in Figure [11](#org39f635c).
+There are derived from a simplified version of the generic feedback loop as shown in Figure [11](#figure--fig:schmidt20-feedback-full-simplified).
 The first simplification is made by approximating the measurement system to have a unity-gain transfer function.
 For further simplification the sensor disturbance in the measurement system is included in the output disturbance \\(n\\), thereby defining the output of the system \\(y\\) as the measured output.
 With this simplified model, the transfer functions of the different inputs of the system to three relevant output variables in the loop are written down in a set of equations.
-Six different transfer functions are obtained and summarized in equation \eqref{eq:gang_of_six}.
+Six different transfer functions are obtained and summarized in equation <eq:gang_of_six>.
 
 \begin{equation} \label{eq:gang\_of\_six}
 \begin{aligned}
- \frac{x}{r} &= \frac{y}{r} = \frac{GCF}{1 + GC} \\\\\\
+ \frac{x}{r} &= \frac{y}{r} = \frac{GCF}{1 + GC} \\\\
--\frac{x}{n} &= -\frac{u}{d} = \frac{GC}{1 + GC} \\\\\\
+-\frac{x}{n} &= -\frac{u}{d} = \frac{GC}{1 + GC} \\\\
- \frac{x}{d} &= \frac{y}{d} = \frac{G}{1 + GC} \\\\\\
+ \frac{x}{d} &= \frac{y}{d} = \frac{G}{1 + GC} \\\\
- \frac{u}{r} &= \frac{CF}{1 + GC} \\\\\\
+ \frac{u}{r} &= \frac{CF}{1 + GC} \\\\
- \frac{u}{n} &= \frac{C}{1 + GC} \\\\\\
+ \frac{u}{n} &= \frac{C}{1 + GC} \\\\
  \frac{y}{n} &= \frac{1}{1 + GC}
 \end{aligned}
 \end{equation}
 
-In case no input filter is applied \\(F\\) is equal to one and the set of six equations is reduced to a set of four equations as shown in equation \eqref{eq:gang_of_four}.
+In case no input filter is applied \\(F\\) is equal to one and the set of six equations is reduced to a set of four equations as shown in equation <eq:gang_of_four>.
 This short set of equations also corresponds to the situation without a reference signal.
 
 The most important transfer function is named the _Sensitivity Function_ (no unit):
@@ -968,9 +962,9 @@ For that reason the most relevant motion system performance criteria are the Sen
 
 \begin{equation} \label{eq:gang\_of\_four}
 \boxed{\begin{aligned}
-\frac{x}{r} &= \frac{y}{r} = -\frac{x}{n} = -\frac{u}{d} = \frac{GC}{1 + GC} \\\\\\
+\frac{x}{r} &= \frac{y}{r} = -\frac{x}{n} = -\frac{u}{d} = \frac{GC}{1 + GC} \\\\
-\frac{x}{d} &= \frac{y}{d} = \frac{G}{1 + GC} \\\\\\
+\frac{x}{d} &= \frac{y}{d} = \frac{G}{1 + GC} \\\\
-\frac{u}{r} &= \frac{u}{n} = \frac{C}{1 + GC} \\\\\\
+\frac{u}{r} &= \frac{u}{n} = \frac{C}{1 + GC} \\\\
 \frac{y}{n} &= \frac{1}{1 + GC}
 \end{aligned}}
 \end{equation}
@@ -1001,17 +995,17 @@ To achieve sufficient robustness against instability in closed-loop feedback con
 
 The condition for robustness of closed-loop stability is that the total phase-lag of the **total feedback-loop**, consisting of the feedback controller in series with the mechatronic system, must be less than 180 degrees in the frequency region of the _unity-gain cross-over frequency_.
 
-The Nyquist plot of the feedback loop, like the example shown in Figure [12](#org6e48553), is most appropriate to analyze the robustness on stability of a feedback system.
+The Nyquist plot of the feedback loop, like the example shown in Figure [12](#figure--fig:schmidt20-nyquist-plot-stable), is most appropriate to analyze the robustness on stability of a feedback system.
 It is an analysis tool that shows the frequency response of the **feedback-loop** combining magnitude and phase in one plot.
 In this figure, two graphs are shown, designed for a different purpose.
 The first graph from the left shows margin circles related to the capability of the closed-loop feedback controlled system to follow a reference according to the complementary sensitivity.
 The second graph shows a margin circle related to the capability of the closed-loop feedback controlled system to suppress disturbances according to the sensitivity function.
 
-<a id="org6e48553"></a>
+<a id="figure--fig:schmidt20-nyquist-plot-stable"></a>
 
-{{< figure src="/ox-hugo/schmidt20_nyquist_plot_stable.svg" caption="Figure 12: Nyquist plot of the feedback-loop response of a stable feedback controlled motion system. Stability is guaranteed as the \\(-1\\) point is kept at the left hand side of the feedback loop repsonse line upon passing with increased frequency, even though the phase-lag is more than 180 degrees at low frequencies." >}}
+{{< figure src="/ox-hugo/schmidt20_nyquist_plot_stable.svg" caption="<span class=\"figure-number\">Figure 12: </span>Nyquist plot of the feedback-loop response of a stable feedback controlled motion system. Stability is guaranteed as the \\(-1\\) point is kept at the left hand side of the feedback loop repsonse line upon passing with increased frequency, even though the phase-lag is more than 180 degrees at low frequencies." >}}
 
-Three values are shown in Figure [12](#org6e48553) related to the robustness of the closed-loop feedback system:
+Three values are shown in Figure [12](#figure--fig:schmidt20-nyquist-plot-stable) related to the robustness of the closed-loop feedback system:
 
 -   **The gain margin** determines by which factor the feedback loop gain additionally can increase before the closed-loop goes unstable.
 -   **The phase margin** determines how much additional phase-lab at the unity-gain cross-over frequency is acceptable before the closed-loop system becomes unstable.
@@ -1024,14 +1018,14 @@ Higher margins corresponds to a higher level of damping.
 The Nyquist plot has one significant disadvantage as it does not show directly the frequency along the plot.
 For that reason many designers prefer to use the Bode plot.
 
-Fortunately it is also possible to indicate the phase and gain margin in the Bode plot as is shown in Figure [13](#orgc932364).
+Fortunately it is also possible to indicate the phase and gain margin in the Bode plot as is shown in Figure [13](#figure--fig:schmidt20-phase-gain-margin-bode).
 
 In many not too complicated cases, these two margins are sufficient to tune a feedback motion controller.
 In more complicated control systems, it remains useful to also use the Nyquist plot as it also gives the Modulus margin.
 
-<a id="orgc932364"></a>
+<a id="figure--fig:schmidt20-phase-gain-margin-bode"></a>
 
-{{< figure src="/ox-hugo/schmidt20_phase_gain_margin_bode.svg" caption="Figure 13: The gain and phase margin in the Bode plot" >}}
+{{< figure src="/ox-hugo/schmidt20_phase_gain_margin_bode.svg" caption="<span class=\"figure-number\">Figure 13: </span>The gain and phase margin in the Bode plot" >}}
 
 
 ### PID Feedback Control {#pid-feedback-control}
@@ -1152,11 +1146,11 @@ However, analogue controllers have three important disadvantages:
 
 The digital implementation of filters overcome these problems as well as allows more complex algorithm such as adaptive control, real-time optimization, nonlinear control and learning control methods.
 
-In Figure [14](#org4b95e2a) two elements were introduced, the _analogue-to-digital converter_ (ADC) and the _digital-to-analogue converter_ (DAC), which together transfer the signals between the analogue and the digital domain.
+In Figure [14](#figure--fig:schmidt20-digital-implementation) two elements were introduced, the _analogue-to-digital converter_ (ADC) and the _digital-to-analogue converter_ (DAC), which together transfer the signals between the analogue and the digital domain.
 
-<a id="org4b95e2a"></a>
+<a id="figure--fig:schmidt20-digital-implementation"></a>
 
-{{< figure src="/ox-hugo/schmidt20_digital_implementation.svg" caption="Figure 14: Overview of a digital implementation of a feedback controller, emphasising the analog-to-digital and digital-to-analog converters with their required analogue filters" >}}
+{{< figure src="/ox-hugo/schmidt20_digital_implementation.svg" caption="<span class=\"figure-number\">Figure 14: </span>Overview of a digital implementation of a feedback controller, emphasising the analog-to-digital and digital-to-analog converters with their required analogue filters" >}}
 
 Anti-aliasing filter is needed at the input of the ADC to limit the frequency range at the input to less than half the sampling frequency, according to the Nyquist-Shannon sampling theorem.
 
@@ -1176,7 +1170,7 @@ Fixed point arithmetic has been favored in the past, because of the less complex
 A main drawback is, that the developer must pay attention to truncation, overflow, underflow and round-off errors that occur during mathematical operations.
 Fixed points numbers are equally spaced over the whole range, separated by the gap which is denoted by the least significant bit.
 The two's complement is the most used format for representing positive and negative numbers.
-For representing a fixed point fractional number of two's complement notation, the so called \\(Q\_{m,n}\\) format is often used (see Figure [15](#orgf73916a)).
+For representing a fixed point fractional number of two's complement notation, the so called \\(Q\_{m,n}\\) format is often used (see Figure [15](#figure--fig:schmidt20-digital-number-representation)).
 \\(m\\) denotes the number of integer bits and \\(n\\) denotes the number of fractional bits.
 \\(m+n+1=N\\) bits are necessary to store a signed \\(Q\_{m,n}\\) number.
 If the binary representation is given, the decimal value can be calculated to:
@@ -1185,11 +1179,11 @@ If the binary representation is given, the decimal value can be calculated to:
 x = \frac{1}{2^n} \left( -2^{N-1 }b\_{N-1} + \sum\_{i=0}^{N-2} 2^i b\_i \right)
 \end{equation}
 
-where \\(b\\) indicate the bit position, starting with \\(b\_0\\) from the right in Figure [15](#orgf73916a).
+where \\(b\\) indicate the bit position, starting with \\(b\_0\\) from the right in Figure [15](#figure--fig:schmidt20-digital-number-representation).
 
-<a id="orgf73916a"></a>
+<a id="figure--fig:schmidt20-digital-number-representation"></a>
 
-{{< figure src="/ox-hugo/schmidt20_digital_number_representation.svg" caption="Figure 15: Example of a \\(Q\_{m.n}\\) fixed point number representation and a single precision floating point number" >}}
+{{< figure src="/ox-hugo/schmidt20_digital_number_representation.svg" caption="<span class=\"figure-number\">Figure 15: </span>Example of a \\(Q\_{m.n}\\) fixed point number representation and a single precision floating point number" >}}
 
 Floating point arithmetic has a higher dynamic range than fixed point arithmetic, given by the largest and smallest number that can be represented, has a higher precision due to the smaller gaps between adjacent numbers, less quantization noise, and it is easier to handle in terms of programming.
 A floating point number is represented by a multiplication of a _mantissa_ \\(M\\) with a _base_ \\(b\\) to the power of the _exponent_ \\(q\\):
@@ -1209,41 +1203,41 @@ x = -1^i M 2^{E-127}
 The term \\(E\\) in the exponent is stored as a positive number ranging from \\(0 \le E < 256\\) with 8 bits.
 An offset of \\(-127\\) is added in order to allow very small to very large numbers.
 The decimal value is normalized, meaning that only one nonzero digit is noted at the left of the decimal point.
-The storage register is divided into three groups, as shown in Figure [15](#orgf73916a).
+The storage register is divided into three groups, as shown in Figure [15](#figure--fig:schmidt20-digital-number-representation).
 1 bit represents the sign, the exponent term \\(E\\) is represented by 8 bits, and the mantissa is stored in 23 bits.
 
 
 #### Digital Filter Theory {#digital-filter-theory}
 
-<a id="org3a2480f"></a>
+<a id="figure--fig:schmidt20-s-z-planes"></a>
 
-{{< figure src="/ox-hugo/schmidt20_s_z_planes.svg" caption="Figure 16: Corresponding points and area in s and z planes" >}}
+{{< figure src="/ox-hugo/schmidt20_s_z_planes.svg" caption="<span class=\"figure-number\">Figure 16: </span>Corresponding points and area in s and z planes" >}}
 
 
 #### Finite Impulse Response (FIR) Filter {#finite-impulse-response--fir--filter}
 
-<a id="org4983bdd"></a>
+<a id="figure--fig:schmidt20-transversal-filter-structure"></a>
 
-{{< figure src="/ox-hugo/schmidt20_transversal_filter_structure.svg" caption="Figure 17: Transversal filter structure of a FIR filter. The term \\(z^{-1}\\) each represent a sampling period which means that \\(b\_0\\) is the gain of the last sample, \\(b\_1\\) is the gain of the precious sample etcetera." >}}
+{{< figure src="/ox-hugo/schmidt20_transversal_filter_structure.svg" caption="<span class=\"figure-number\">Figure 17: </span>Transversal filter structure of a FIR filter. The term \\(z^{-1}\\) each represent a sampling period which means that \\(b\_0\\) is the gain of the last sample, \\(b\_1\\) is the gain of the precious sample etcetera." >}}
 
-<a id="org936becf"></a>
+<a id="figure--fig:schmidt20-optimized-fir-filter-structure"></a>
 
-{{< figure src="/ox-hugo/schmidt20_optimized_fir_filter_structure.svg" caption="Figure 18: Optimized FIR filter structure with symmetric filter coefficients" >}}
+{{< figure src="/ox-hugo/schmidt20_optimized_fir_filter_structure.svg" caption="<span class=\"figure-number\">Figure 18: </span>Optimized FIR filter structure with symmetric filter coefficients" >}}
 
-<a id="org8ea00c7"></a>
+<a id="figure--fig:schmidt20-dir-filter-cascaded-sos"></a>
 
-{{< figure src="/ox-hugo/schmidt20_dir_filter_cascaded_sos.svg" caption="Figure 19: Higher-order FIR filter realization with cascade SOS filter structures" >}}
+{{< figure src="/ox-hugo/schmidt20_dir_filter_cascaded_sos.svg" caption="<span class=\"figure-number\">Figure 19: </span>Higher-order FIR filter realization with cascade SOS filter structures" >}}
 
 
 #### Infinite Impulse Response (IIR) Filter {#infinite-impulse-response--iir--filter}
 
-<a id="org696a8aa"></a>
+<a id="figure--fig:schmidt20-irr-structure"></a>
 
-{{< figure src="/ox-hugo/schmidt20_irr_structure.svg" caption="Figure 20: (a:) IIR structure in DF-1 realization and (b:) IIR structure in DF-2 realization" >}}
+{{< figure src="/ox-hugo/schmidt20_irr_structure.svg" caption="<span class=\"figure-number\">Figure 20: </span>(a:) IIR structure in DF-1 realization and (b:) IIR structure in DF-2 realization" >}}
 
-<a id="orge99cdac"></a>
+<a id="figure--fig:schmidt20-irr-sos-structure"></a>
 
-{{< figure src="/ox-hugo/schmidt20_irr_sos_structure.svg" caption="Figure 21: IIR SOS structure in DF-2 realization" >}}
+{{< figure src="/ox-hugo/schmidt20_irr_sos_structure.svg" caption="<span class=\"figure-number\">Figure 21: </span>IIR SOS structure in DF-2 realization" >}}
 
 
 #### Converting Continuous to Discrete-Time Filters {#converting-continuous-to-discrete-time-filters}
@@ -1275,7 +1269,8 @@ The storage register is divided into three groups, as shown in Figure [15](#orgf
 
 ### Conclusion on Motion Control {#conclusion-on-motion-control}
 
-<summary>
+<div class="sum">
+
 Motion control is essential for Precision Mechatronic Systems and consists of two complementary elements:
 
 -   **Extremely accurate Feedforward Control** is required when the motion system must execute a user defined motion to within maximum user defined position error limits.
@@ -1283,7 +1278,8 @@ Motion control is essential for Precision Mechatronic Systems and consists of tw
 -   **High Performance Feedback Control** is required when the motion system must be able to follow an unknown motion of a target, stabilize an otherwise unstable system and reduce the impact of disturbing forces and vibrations, such that the position error remains below a maximum user defined level.
     Due to the fact that a feedback controller can become unstable, sufficient robustness must be guaranteed.
     These is a conflicting relation between stability and performance.
-</summary>
+
+</div>
 
 
 ## Electromechanic Actuators {#electromechanic-actuators}
@@ -2237,4 +2233,6 @@ Motion control is essential for Precision Mechatronic Systems and consists of tw
 
 ## Bibliography {#bibliography}
 
-<a id="org4e5c703"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2020. _The Design of High Performance Mechatronics - Third Revised Edition_. Ios Press.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Schmidt, R Munnig, Georg Schitter, and Adrian Rankers. 2020. <i>The Design of High Performance Mechatronics - Third Revised Edition</i>. Ios Press.</div>
+</div>

content/book/slocum92_precis_machin_desig.md

@@ -0,0 +1,20 @@
++++
+title = "Precision Machine Design"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: <slocum92_precis_machin_desig>
+
+Author(s)
+: Slocum, A. H.
+
+Year
+: 1992
+
+<./biblio/references.bib>

content/book/smith99_scien_engin_guide_digit_signal.md

@@ -1,15 +1,15 @@
 +++
 title = "The scientist and engineer's guide to digital signal processing - second edition"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 keywords = ["Signal Processing"]
 draft = true
 +++
 
 Tags
-: [Digital Signal Processing]({{< relref "digital_signal_processing" >}})
+: [Digital Signal Processing]({{< relref "digital_signal_processing.md" >}})
 
 Reference
-: ([Smith 1999](#org023917a))
+: (<a href="#citeproc_bib_item_1">Smith 1999</a>)
 
 Author(s)
 : Smith, S. W.
@@ -18,7 +18,8 @@ Year
 : 1999
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org023917a"></a>Smith, Steven W. 1999. _The Scientist and Engineer’s Guide to Digital Signal Processing - Second Edition_. California Technical Publishing.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Smith, Steven W. 1999. <i>The Scientist and Engineer’s Guide to Digital Signal Processing - Second Edition</i>. California Technical Publishing.</div>
+</div>

content/inproceedings/abramovitch23_tutor_real_time_comput_issues_contr_system.md

@@ -0,0 +1,22 @@
++++
+title = "A tutorial on real-time computing issues for control systems"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (<a href="#citeproc_bib_item_1">Abramovitch et al. 2023</a>)
+
+Author(s)
+: Abramovitch, D. Y., Andersson, S., Leang, K. K., Nagel, W., &amp; Ruben, S.
+
+Year
+: 2023
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Abramovitch, Daniel Y., Sean Andersson, Kam K. Leang, William Nagel, and Shalom Ruben. 2023. “A Tutorial on Real-Time Computing Issues for Control Systems.” In <i>2023 American Control Conference (ACC)</i>, 3751–68. doi:<a href="https://doi.org/10.23919/acc55779.2023.10156102">10.23919/acc55779.2023.10156102</a>.</div>
+</div>

content/inproceedings/heertjes20_contr.md

@@ -1,7 +1,7 @@
 +++
 title = "Control of wafer scanners: methods and developments"
 author = ["Thomas Dehaeze"]
-draft = false
+draft = true
 +++
 
 Tags
@@ -9,7 +9,7 @@ Tags
 
 
 Reference
-: ([Heertjes et al. 2020](#org38a977c))
+: ([Heertjes et al. 2020](#org3f3475f))
 
 Author(s)
 : Heertjes, Marcel Fran\ccois, Butler, H., Dirkx, N., van der Meulen, S., Ahlawat, R., O'Brien, K., Simonelli, J., …
@@ -20,4 +20,4 @@ Year
 
 ## Bibliography {#bibliography}
 
-<a id="org38a977c"></a>Heertjes, Marcel François, Hans Butler, NJ Dirkx, SH van der Meulen, R Ahlawat, K O’Brien, J Simonelli, KT Teng, and Y Zhao. 2020. “Control of Wafer Scanners: Methods and Developments.” In _2020 American Control Conference (ACC)_, 3686–3703. IEEE.
+<a id="org3f3475f"></a>Heertjes, Marcel François, Hans Butler, NJ Dirkx, SH van der Meulen, R Ahlawat, K O’Brien, J Simonelli, KT Teng, and Y Zhao. 2020. “Control of Wafer Scanners: Methods and Developments.” In _2020 American Control Conference (ACC)_, 3686–3703. IEEE.

content/inproceedings/henein10_flexur.md

@@ -0,0 +1,24 @@
++++
+title = "Flexures: simply subtle"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (<a href="#citeproc_bib_item_1">Henein 2010</a>)
+
+Author(s)
+: Henein, S.
+
+Year
+: 2010
+
+## References
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Henein, Simon. 2010. “Flexures: Simply Subtle.” In <i>Diamond Light Source Proceedings, Medsi 2010</i>. Cambridge University Press.</div>
+</div>

content/inproceedings/mcinroy03_proper_stewar.md

@@ -1,6 +1,6 @@
 +++
 title = "Properties of orthogonal stewart platform"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = true
 +++
 
@@ -9,7 +9,7 @@ Tags
 
 
 Reference
-: ([McInroy 2003](#orgb7c0811))
+: (<a href="#citeproc_bib_item_1">McInroy 2003</a>)
 
 Author(s)
 : McInroy, J. E.
@@ -20,4 +20,6 @@ Year
 
 ## Bibliography {#bibliography}
 
-<a id="orgb7c0811"></a>McInroy, John E. 2003. “Properties of Orthogonal Stewart Platform.” In _Smart Structures and Materials 2003: Smart Structures and Integrated Systems_, nil. <https://doi.org/10.1117/12.483460>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>McInroy, John E. 2003. “Properties of Orthogonal Stewart Platform.” In <i>Smart Structures and Materials 2003: Smart Structures and Integrated Systems</i>, nil. doi:<a href="https://doi.org/10.1117/12.483460">10.1117/12.483460</a>.</div>
+</div>

content/phdthesis/afzali-far16_vibrat_dynam_isotr_hexap_analy_studies.md

@@ -1,14 +1,16 @@
 +++
 title = "Vibrations and dynamic isotropy in hexapods-analytical studies"
 author = ["Thomas Dehaeze"]
-draft = true
+draft = false
+ref_author = "Afzali-Far, B."
+ref_year = 2016
 +++
 
 Tags
 : [Stewart Platforms]({{<relref "stewart_platforms.md#" >}}), [Isotropy of Parallel Manipulator]({{<relref "isotropy_of_parallel_manipulator.md#" >}})
 
 Reference
-: ([Afzali-Far 2016](#orga93b30a))
+: ([Afzali-Far 2016](#org28bc5f9))
 
 Author(s)
 : Afzali-Far, B.
@@ -95,7 +97,7 @@ Dynamic isotropy for the Stewart platform leads to a series of restrictive condi
 
 When considering inertia of the struts, conditions are becoming more complex.
 
-<a id="org64466c7"></a>
+<a id="org75888b1"></a>
 
 {{< figure src="/ox-hugo/afzali-far16_isotropic_hexapod_example.png" caption="Figure 1: Architecture of the obtained dynamically isotropic hexapod" >}}
 
@@ -115,25 +117,28 @@ where \\(\sigma I\\) is a scaled identity matrix.
 The isotropic constrain of the standard hexapod imposes special inertia of the top platform which may not be wanted in practice (\\(I\_{zz} = 4 I\_{yy} = 4 I\_{xx}\\)).
 
 A class of generalized Gough-Stewart platforms are proposed to eliminate the above constrains.
-Figure [2](#orgfab85fb) shows a schematic of proposed generalized hexapod.
+Figure [2](#org09a0134) shows a schematic of proposed generalized hexapod.
 
-<a id="orgfab85fb"></a>
+<a id="org09a0134"></a>
 
 {{< figure src="/ox-hugo/afzali-far16_proposed_generalized_hexapod.png" caption="Figure 2: Parametrization of the proposed generalized hexapod" >}}
 
 
 ## Conclusions {#conclusions}
 
-<summary>
+<div class="sum">
+  <div></div>
+
 The main findings of this dissertation are:
 
 -   Comprehensive and fully parametric model of the hexapod for symmetric configurations are established both in the Cartesian and joint space.
 -   Inertia of the struts are taken into account to refine the model.
 -   A novel approach in order to obtain dynamically isotropic hexapods is proposed.
--   A novel architecture of hexapod is introduced (Figure [2](#orgfab85fb)) which is dynamically isotropic for a wide range of inertia properties.
+-   A novel architecture of hexapod is introduced (Figure [2](#org09a0134)) which is dynamically isotropic for a wide range of inertia properties.
-</summary>
+
+</div>
 
 
 ## Bibliography {#bibliography}
 
-<a id="orga93b30a"></a>Afzali-Far, Behrouz. 2016. “Vibrations and Dynamic Isotropy in Hexapods-Analytical Studies.” Lund University.
+<a id="org28bc5f9"></a>Afzali-Far, Behrouz. 2016. “Vibrations and Dynamic Isotropy in Hexapods-Analytical Studies.” Lund University.

content/phdthesis/babakhani12_activ_dampin_vibrat_high_precis_motion_system.md

@@ -1,14 +1,16 @@
 +++
 title = "Active damping of vibrations in high-precision motion systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
+ref_author = "Babakhani, B."
+ref_year = 2012
 +++
 
 Tags
-: [Active Damping]({{<relref "active_damping.md#" >}})
+: [Active Damping]({{< relref "active_damping.md" >}})
 
 Reference
-: ([Babakhani 2012](#org0b93bb2))
+: (<a href="#citeproc_bib_item_1">Babakhani 2012</a>)
 
 Author(s)
 : Babakhani, B.
@@ -17,7 +19,8 @@ Year
 : 2012
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org0b93bb2"></a>Babakhani, Bayan. 2012. “Active Damping of Vibrations in High-Precision Motion Systems.” University of Twente. <https://doi.org/10.3990/1.9789036534642>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Babakhani, Bayan. 2012. “Active Damping of Vibrations in High-Precision Motion Systems.” University of Twente. doi:<a href="https://doi.org/10.3990/1.9789036534642">10.3990/1.9789036534642</a>.</div>
+</div>

content/phdthesis/bishop02_devel_precis_point_contr_vibrat.md

@@ -0,0 +1,25 @@
++++
+title = "Development of precision pointing controllers with and without vibration suppression for the NPS precision pointing hexapod"
+author = ["Thomas Dehaeze"]
+draft = true
+ref_author = "Bishop Jr, R. M."
+ref_year = 2002
++++
+
+Tags
+:
+
+
+Reference
+: ([Bishop Jr 2002](#org19f0b30))
+
+Author(s)
+: Bishop Jr, R. M.
+
+Year
+: 2002
+
+
+## Bibliography {#bibliography}
+
+<a id="org19f0b30"></a>Bishop Jr, Ronald M. 2002. “Development of Precision Pointing Controllers with and without Vibration Suppression for the NPS Precision Pointing Hexapod.” Naval Postgraduate School, Monterey, California.

content/phdthesis/hanieh03_activ_stewar.md

@@ -0,0 +1,26 @@
++++
+title = "Active isolation and damping of vibrations via stewart platform"
+author = ["Dehaeze Thomas"]
+draft = true
+ref_author = "Hanieh, A. A."
+ref_year = 2003
++++
+
+Tags
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Active Damping]({{< relref "active_damping.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Hanieh 2003</a>)
+
+Author(s)
+: Hanieh, A. A.
+
+Year
+: 2003
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Hanieh, Ahmed Abu. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Université Libre de Bruxelles, Brussels, Belgium.</div>
+</div>

content/phdthesis/jabben07_mechat.md

@@ -1,11 +1,16 @@
 +++
 title = "Mechatronic design of a magnetically suspended rotating platform"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
+ref_author = "Jabben, L."
+ref_year = 2007
 +++
 
 Tags
-: [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})
+: [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Jabben 2007</a>)
 
 Author
 : Jabben, L.
@@ -13,9 +18,6 @@ Author
 Year
 : 2007
 
-DOI
-:
-
 
 ## Dynamic Error Budgeting {#dynamic-error-budgeting}
 
@@ -41,16 +43,15 @@ This approach allows frequency dependent error budgeting, which is why it is ref
 #### Ground vibrations {#ground-vibrations}
 
 
-#### Electronic Noise {#electronic-noise}
+#### [Electronic Noise]({{< relref "electronic_noise.md" >}}) {#electronic-noise--electronic-noise-dot-md}
 
-**Thermal Noise** (or Johson noise).
+**Thermal Noise** (or Johnson noise).
 This noise can be modeled as a voltage source in series with the system impedance.
 The noise source has a PSD given by:
 \\[ S\_T(f) = 4 k T \text{Re}(Z(f)) \ [V^2/Hz] \\]
-with \\(k = 1.38 \cdot 10^{-23} \,[J/K]\\) the Boltzmann's constant, \\(T\\) the temperature [K] and \\(Z(f)\\) the frequency dependent impedance of the system.
+with \\(k = 1.38 \cdot 10^{-23} \\,[J/K]\\) the Boltzmann's constant, \\(T\\) the temperature [K] and \\(Z(f)\\) the frequency dependent impedance of the system.
 
 <div class="exampl">
-  <div></div>
 
 A kilo Ohm resistor at 20 degree Celsius will show a thermal noise of \\(0.13 \mu V\\) from zero up to one kHz.
 
@@ -60,12 +61,11 @@ A kilo Ohm resistor at 20 degree Celsius will show a thermal noise of \\(0.13 \m
 Seen with junctions in a transistor.
 It has a white spectral density:
 \\[ S\_S = 2 q\_e i\_{dc} \ [A^2/Hz] \\]
-with \\(q\_e\\) the electronic charge (\\(1.6 \cdot 10^{-19}\, [C]\\)), \\(i\_{dc}\\) the average current [A].
+with \\(q\_e\\) the electronic charge (\\(1.6 \cdot 10^{-19}\\, [C]\\)), \\(i\_{dc}\\) the average current [A].
 
 <div class="exampl">
-  <div></div>
 
-An averable current of 1 A will introduce noise with a STD of \\(10 \cdot 10^{-9}\,[A]\\) from zero up to one kHz.
+A current of 1 A will introduce noise with a STD of \\(10 \cdot 10^{-9}\\,[A]\\) from zero up to one kHz.
 
 </div>
 
@@ -98,24 +98,23 @@ The corresponding PSD is white up to the Nyquist frequency:
 with \\(f\_N\\) the Nyquist frequency [Hz].
 
 <div class="exampl">
-  <div></div>
 
 Let's take the example of a 16 bit ADC which has an electronic noise with a SNR of 80dB.
 Let's suppose the ADC is used to measure a position over a range of 1 mm.
 
--   ADC quantization noise: it has 16 bots over the 1 mm range.
+-   ADC quantization noise: it has 16 bits over the 1 mm range.
-    The standard diviation from the quantization is:
+    The standard deviation from the quantization is:
-    \\[ \sigma\_{ADq} = \frac{1 \cdot 10^6/2^16}{\sqrt{12}} = 4.4\,[nm] \\]
+    \\[ \sigma\_{ADq} = \frac{1 \cdot 10^6/2^{16}}{\sqrt{12}} = 4.4\\,[nm] \\]
--   ADC electronic noise: the RMS value of a sine that covers to full range is \\(\frac{0.5}{\sqrt{2}} = 0.354\,[mm]\\).
+-   ADC electronic noise: the RMS value of a sine that covers to full range is \\(\frac{0.5}{\sqrt{2}} = 0.354\\,[mm]\\).
     With a SNR of 80dB, the electronic noise from the ADC becomes:
-    \\[ \sigma\_{ADn} = 35\,[nm] \\]
+    \\[ \sigma\_{ADn} = 35\\,[nm] \\]
 
-Let's suppose the ADC is used to measure a sensor with an electronic noise having a standard deviation of \\(\sigma\_{sn} = 17\,[nm]\\).
+Let's suppose the ADC is used to measure a sensor with an electronic noise having a standard deviation of \\(\sigma\_{sn} = 17\\,[nm]\\).
 
 The PSD of this digitalized sensor noise is:
-\\[ \sigma\_s = \sqrt{\sigma\_{sn}^2 + \sigma\_{ADq}^2 + \sigma\_{ADn}^2} = 39\,[nm]\\]
+\\[ \sigma\_s = \sqrt{\sigma\_{sn}^2 + \sigma\_{ADq}^2 + \sigma\_{ADn}^2} = 39\\,[nm]\\]
 from which the PSD of the total sensor noise \\(S\_s\\) is calculated:
-\\[ S\_s = \frac{\sigma\_s^2}{f\_N} = 1.55\,[nm^2/Hz] \\]
+\\[ S\_s = \frac{\sigma\_s^2}{f\_N} = 1.55\\,[nm^2/Hz] \\]
 with \\(f\_N\\) is the Nyquist frequency of 1kHz.
 
 </div>
@@ -130,9 +129,8 @@ To have a pressure difference, the body must have a certain minimum dimension, d
 For a body of typical dimensions of 100mm, only frequencies above 800 Hz have a significant disturbance contribution.
 
 <div class="exampl">
-  <div></div>
 
-Consider a cube with a rib size of 100 mm located in a room with a sound level of 80dB, distributed between one and ten kHz, then the force disturbance PSD equal \\(2.2 \cdot 10^{-2}\,[N^2/Hz]\\)
+Consider a cube with a rib size of 100 mm located in a room with a sound level of 80dB, distributed between one and ten kHz, then the force disturbance PSD equal \\(2.2 \cdot 10^{-2}\\,[N^2/Hz]\\)
 
 </div>
 
@@ -161,21 +159,21 @@ Three factors influence the performance:
 The DEB helps identifying which disturbance is the limiting factor, and it should be investigated if the controller can deal with this disturbance before re-designing the plant.
 
 The modelling of disturbance as stochastic variables, is by excellence suitable for the optimal stochastic control framework.
-In Figure [1](#orgbf22b5e), the generalized plant maps the disturbances to the performance channels.
+In [Figure 1](#figure--fig:jabben07-general-plant), the generalized plant maps the disturbances to the performance channels.
 By minimizing the \\(\mathcal{H}\_2\\) system norm of the generalized plant, the variance of the performance channels is minimized.
 
-<a id="orgbf22b5e"></a>
+<a id="figure--fig:jabben07-general-plant"></a>
 
-{{< figure src="/ox-hugo/jabben07_general_plant.png" caption="Figure 1: Control system with the generalized plant \\(G\\). The performance channels are stacked in \\(z\\), while the controller input is denoted with \\(y\\)" >}}
+{{< figure src="/ox-hugo/jabben07_general_plant.png" caption="<span class=\"figure-number\">Figure 1: </span>Control system with the generalized plant \\(G\\). The performance channels are stacked in \\(z\\), while the controller input is denoted with \\(y\\)" >}}
 
 
 #### Using Weighting Filters for Disturbance Modelling {#using-weighting-filters-for-disturbance-modelling}
 
-Since disturbances are generally not white, the system of Figure [1](#orgbf22b5e) needs to be augmented with so called **disturbance weighting filters**.
+Since disturbances are generally not white, the system of [Figure 1](#figure--fig:jabben07-general-plant) needs to be augmented with so called **disturbance weighting filters**.
 
 A disturbance weighting filter gives the disturbance PSD when white noise as input is applied.
 
-This is illustrated in Figure [2](#org27e9aeb) where a vector of white noise time signals \\(\underbar{w}(t)\\) is filtered through a weighting filter to obtain the colored physical disturbances \\(w(t)\\) with the desired PSD \\(S\_w\\) .
+This is illustrated in [Figure 2](#figure--fig:jabben07-weighting-functions) where a vector of white noise time signals \\(\underbar{w}(t)\\) is filtered through a weighting filter to obtain the colored physical disturbances \\(w(t)\\) with the desired PSD \\(S\_w\\) .
 
 The generalized plant framework also allows to include **weighting filters for the performance channels**.
 This is useful for three reasons:
@@ -184,9 +182,9 @@ This is useful for three reasons:
 -   some performance channels may be of more importance than others
 -   by using dynamic weighting filters, one can emphasize the performance in a certain frequency range
 
-<a id="org27e9aeb"></a>
+<a id="figure--fig:jabben07-weighting-functions"></a>
 
-{{< figure src="/ox-hugo/jabben07_weighting_functions.png" caption="Figure 2: Control system with the generalized plant \\(G\\) and weighting functions" >}}
+{{< figure src="/ox-hugo/jabben07_weighting_functions.png" caption="<span class=\"figure-number\">Figure 2: </span>Control system with the generalized plant \\(G\\) and weighting functions" >}}
 
 The weighting filters should be stable transfer functions.
 
@@ -207,13 +205,13 @@ By making the \\(\mathcal{H}\_2\\) norm of \\(V\_h\\) equal to the RMS-value of
 IF only the output \\(y\\) are considered in the performance channel \\(z\\), the resulting optimal controller might result in very large actuator signals.
 So, to obtain feasible controllers, the performance channel is a combination of controller output \\(u\\) and system output \\(y\\).
 By choosing suitable weighting filters for \\(y\\) and \\(u\\), the performance can be optimized while keeping the controller effort limited:
-\\[ \\|z\\|\_{rms}^2 = \left\\| \begin{bmatrix} y \\ \alpha u \end{bmatrix} \right\\|\_{rms}^2 = \\|y\\|\_{rms}^2 + \alpha^2 \\|u\\|\_{rms}^2 \\]
+\\[ \\|z\\|\_{rms}^2 = \left\\| \begin{bmatrix} y \\\ \alpha u \end{bmatrix} \right\\|\_{rms}^2 = \\|y\\|\_{rms}^2 + \alpha^2 \\|u\\|\_{rms}^2 \\]
 
-By calculation \\(\mathcal{H}\_2\\) optimal controllers for increasing \\(\alpha\\) and plotting the performance \\(\\|y\\|\\) vs the controller effort \\(\\|u\\|\\), the curve as depicted in Figure [3](#org5ae58f0) is obtained.
+By calculation \\(\mathcal{H}\_2\\) optimal controllers for increasing \\(\alpha\\) and plotting the performance \\(\\|y\\|\\) vs the controller effort \\(\\|u\\|\\), the curve as depicted in [Figure 3](#figure--fig:jabben07-pareto-curve-H2) is obtained.
 
-<a id="org5ae58f0"></a>
+<a id="figure--fig:jabben07-pareto-curve-H2"></a>
 
-{{< figure src="/ox-hugo/jabben07_pareto_curve_H2.png" caption="Figure 3: An illustration of a Pareto curve. Each point of the curve represents the performance obtained with an optimal controller. The curve is obtained by varying \\(\alpha\\) and calculating an \\(\mathcal{H}\_2\\) optimal controller for each \\(\alpha\\)." >}}
+{{< figure src="/ox-hugo/jabben07_pareto_curve_H2.png" caption="<span class=\"figure-number\">Figure 3: </span>An illustration of a Pareto curve. Each point of the curve represents the performance obtained with an optimal controller. The curve is obtained by varying \\(\alpha\\) and calculating an \\(\mathcal{H}\_2\\) optimal controller for each \\(\alpha\\)." >}}
 
 
 ## Conclusion {#conclusion}

content/phdthesis/li01_simul_fault_vibrat_isolat_point.md

@@ -1,14 +1,16 @@
 +++
 title = "Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
+ref_author = "Li, X."
+ref_year = 2001
 +++
 
 Tags
-: [Stewart Platforms]({{<relref "stewart_platforms.md#" >}}), [Vibration Isolation]({{<relref "vibration_isolation.md#" >}}), [Cubic Architecture]({{<relref "cubic_architecture.md#" >}}), [Flexible Joints]({{<relref "flexible_joints.md#" >}}), [Multivariable Control]({{<relref "multivariable_control.md#" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Cubic Architecture]({{< relref "cubic_architecture.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}}), [Multivariable Control]({{< relref "multivariable_control.md" >}})
 
 Reference
-: ([Li 2001](#org7277b25))
+: (<a href="#citeproc_bib_item_1">Li 2001</a>)
 
 Author(s)
 : Li, X.
@@ -22,17 +24,17 @@ Year
 
 ### Flexure Jointed Hexapods {#flexure-jointed-hexapods}
 
-A general flexible jointed hexapod is shown in Figure [1](#org858f898).
+A general flexible jointed hexapod is shown in [Figure 1](#figure--fig:li01-flexure-hexapod-model).
 
-<a id="org858f898"></a>
+<a id="figure--fig:li01-flexure-hexapod-model"></a>
 
-{{< figure src="/ox-hugo/li01_flexure_hexapod_model.png" caption="Figure 1: A flexure jointed hexapod. {P} is a cartesian coordinate frame located at, and rigidly attached to the payload's center of mass. {B} is the frame attached to the base, and {U} is a universal inertial frame of reference" >}}
+{{< figure src="/ox-hugo/li01_flexure_hexapod_model.png" caption="<span class=\"figure-number\">Figure 1: </span>A flexure jointed hexapod. {P} is a cartesian coordinate frame located at, and rigidly attached to the payload's center of mass. {B} is the frame attached to the base, and {U} is a universal inertial frame of reference" >}}
 
-Flexure jointed hexapods have been developed to meet two needs illustrated in Figure [2](#orgda07839).
+Flexure jointed hexapods have been developed to meet two needs illustrated in [Figure 2](#figure--fig:li01-quet-dirty-box).
 
-<a id="orgda07839"></a>
+<a id="figure--fig:li01-quet-dirty-box"></a>
 
-{{< figure src="/ox-hugo/li01_quet_dirty_box.png" caption="Figure 2: (left) Vibration machinery must be isolated from a precision bus. (right) A precision paylaod must be manipulated in the presence of base vibrations and/or exogenous forces." >}}
+{{< figure src="/ox-hugo/li01_quet_dirty_box.png" caption="<span class=\"figure-number\">Figure 2: </span>(left) Vibration machinery must be isolated from a precision bus. (right) A precision paylaod must be manipulated in the presence of base vibrations and/or exogenous forces." >}}
 
 Since only small movements are considered in flexure jointed hexapod, the Jacobian matrix, which relates changes in the Cartesian pose to changes in the strut lengths, can be considered constant.
 Thus a static kinematic decoupling algorithm can be implemented for both vibration isolation and pointed controls on flexible jointed hexapods.
@@ -41,14 +43,14 @@ On the other hand, the flexures add some complexity to the hexapod dynamics.
 Although the flexure joints do eliminate friction and backlash, they add spring dynamics and severely limit the workspace.
 Moreover, base and/or payload vibrations become significant contributors to the motion.
 
-The University of Wyoming hexapods (example in Figure [3](#orgccc775c)) are:
+The University of Wyoming hexapods (example in [Figure 3](#figure--fig:li01-stewart-platform)) are:
 
 -   Cubic (mutually orthogonal)
 -   Flexure Jointed
 
-<a id="orgccc775c"></a>
+<a id="figure--fig:li01-stewart-platform"></a>
 
-{{< figure src="/ox-hugo/li01_stewart_platform.png" caption="Figure 3: Flexure jointed Stewart platform used for analysis and control" >}}
+{{< figure src="/ox-hugo/li01_stewart_platform.png" caption="<span class=\"figure-number\">Figure 3: </span>Flexure jointed Stewart platform used for analysis and control" >}}
 
 The objectives of the hexapods are:
 
@@ -79,13 +81,13 @@ p\_x & p\_y & p\_z & \theta\_x & \theta\_y & \theta\_z
 
 \begin{equation}
 J = \begin{bmatrix}
-{}^B\hat{u}\_1^T & [({}^B\_PR^P p\_1) \times {}^B\hat{u}\_1]^T \\\\\\
+{}^B\hat{u}\_1^T & [({}^B\_PR^P p\_1) \times {}^B\hat{u}\_1]^T \\\\
-\vdots & \vdots \\\\\\
+\vdots & \vdots \\\\
 {}^B\hat{u}\_6^T & [({}^B\_PR^P p\_6) \times {}^B\hat{u}\_6]^T
 \end{bmatrix}
 \end{equation}
 
-where (see Figure [1](#org858f898)) \\(p\_i\\) denotes the payload attachment point of strut \\(i\\), the prescripts denote the frame of reference, and \\(\hat{u}\_i\\) denotes a unit vector along strut \\(i\\).
+where (see [Figure 1](#figure--fig:li01-flexure-hexapod-model)) \\(p\_i\\) denotes the payload attachment point of strut \\(i\\), the prescripts denote the frame of reference, and \\(\hat{u}\_i\\) denotes a unit vector along strut \\(i\\).
 To make the dynamic model as simple as possible, the origin of {P} is located at the payload's center of mass.
 Thus all \\({}^Pp\_i\\) are found with respect to the center of mass.
 
@@ -94,43 +96,95 @@ Thus all \\({}^Pp\_i\\) are found with respect to the center of mass.
 
 The dynamics of a flexure jointed hexapod can be written in joint space:
 
-\begin{equation}
+\begin{equation} \label{eq:hexapod\_eq\_motion}
 \begin{split}
-& \left( J^{-T} {}^B\_PR^P M\_x {}^B\_PR^T J^{-1} + M\_s \right) \ddot{l} + B \dot{l} + K (l - l\_r) = \\\\\\
+& \left( J^{-T} \cdot {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR^T \cdot J^{-1} + M\_s \right) \ddot{l} + B \dot{l} + K (l - l\_r) = \\\\
-&\quad f\_m - \left( M\_s + J^{-T} {}^B\_PR^P M\_x {}^U\_PR^T J\_c J\_b^{-1} \right) \ddot{q}\_u + J^{-T} {}^U\_BR\_T(\mathcal{F}\_e + \mathcal{G} + \mathcal{C})
+&\quad f\_m - \left( M\_s + J^{-T} \cdot {}^B\_PR \cdot {}^PM\_x \cdot {}^U\_PR^T \cdot J\_c \cdot J\_b^{-1} \right) \ddot{q}\_u + J^{-T} \cdot {}^U\_BR^T(\mathcal{F}\_e + \mathcal{G} + \mathcal{C})
 \end{split}
 \end{equation}
 
+where:
 
-### Test {#test}
+-   \\({}^PM\_x\\) is the 6x6 mass/inertia matrix of the payload, found with respect to the payload frame {P}, whose origin is at the hexapod payload's center of mass
+-   \\({}^U\_BR\\) is the 6x6 rotation matrix from the base frame {B} to the inertial frame of reference {U} (it consists of two identical 3x3 rotation matrices forming a block diagonal 6x6 matrix).
+    Similarly, \\({}^B\_PR\\) is the rotation matrix from the payload frame to the base frame, and \\({}^U\_PR = {}^U\_BR {}^B\_PR\\)
+-   \\(J\\) is the 6x6 Jacobian matrix relating payload cartesian movements to strut length changes
+-   \\(M\_s\\) is a diagonal 6x6 matrix containing the moving mass of each strut
+-   \\(l\\) is the 6x1 vector of strut lengths
+-   \\(B\\) and \\(K\\) are 6x6 diagonal matrices containing the damping and stiffness, respectively, of each strut
+-   \\(l\_r\\) is the constant vector of relaxed strut lengths
+-   \\(f\_m\\) is the vector of strut motor force
+-   \\(J\_c\\) and \\(J\_b\\) are 6x6 Jacobian matrices capturing base motion
+-   \\(\ddot{q}\_u\\) is a 6x1 vector of base acceleration along each strut
+-   \\(\mathcal{F}\_r\\) is a vector of payload exogenous generalized forces
+-   \\(\mathcal{C}\\) is a vector containing all the Coriolis and centripetal terms
+-   \\(\mathcal{G}\\) is a vector containing all gravity terms
 
-**Jacobian Analysis**:
-\\[ \delta \mathcal{L} = J \delta \mathcal{X} \\]
-The origin of \\(\\{P\\}\\) is taken as the center of mass of the payload.
 
-**Decoupling**:
+#### Decoupling {#decoupling}
-If we refine the (force) inputs and (displacement) outputs as shown in Figure [4](#org7721136) or in Figure [5](#orgdc42940), we obtain a decoupled plant provided that:
+
+Two decoupling algorithms are proposed by combining static input-output transformations with hexapod geometric design.
+
+Define a new input and a new output:
+
+\begin{equation}
+u\_1 = J^T f\_m, \quad y = J^{-1} (l - l\_r)
+\end{equation}
+
+Equation \eqref{eq:hexapod\_eq\_motion} can be rewritten as:
+
+\begin{equation} \label{eq:hexapod\_eq\_motion\_decoup\_1}
+\begin{split}
+& \left( {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR^T + J^T \cdot M\_s \cdot J \right) \cdot \ddot{y} + J^T \cdot B J \dot{y} + J^T \cdot K \cdot J y = \\\\
+&\quad u\_1 - \left( J^T \cdot M\_s + {}^B\_PR \cdot {}^PM\_x \cdot {}^U\_PR^T \cdot J\_c \cdot J\_b^{-1} \right) \ddot{q}\_u + {}^U\_BR^T\mathcal{F}\_e
+\end{split}
+\end{equation}
+
+If the hexapod is designed such that the payload mass/inertia matrix written in the base frame (\\(^BM\_x = {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR\_T\\)) and \\(J^T J\\) are diagonal, the dynamics from \\(u\_1\\) to \\(y\\) are decoupled ([Figure 4](#figure--fig:li01-decoupling-conf)).
+
+<a id="figure--fig:li01-decoupling-conf"></a>
+
+{{< figure src="/ox-hugo/li01_decoupling_conf.png" caption="<span class=\"figure-number\">Figure 4: </span>Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
+
+Alternatively, a new set of inputs and outputs can be defined:
+
+\begin{equation}
+u\_2 = J^{-1} f\_m, \quad y = J^{-1} (l - l\_r)
+\end{equation}
+
+And another decoupled plant is found ([Figure 5](#figure--fig:li01-decoupling-conf-bis)):
+
+\begin{equation} \label{eq:hexapod\_eq\_motion\_decoup\_2}
+\begin{split}
+& \left( J^{-1} \cdot J^{-T} \cdot {}^BM\_x + M\_s \right) \cdot \ddot{y} + B \dot{y} + K y = \\\\
+&\quad u\_2 - J^{-1} \cdot J^{-T} \left( J^T \cdot M\_s + {}^B\_PR \cdot {}^PM\_x \cdot {}^U\_PR^T \cdot J\_c \cdot J\_b^{-1} \right) \ddot{q}\_u + {}^U\_BR^T\mathcal{F}\_e
+\end{split}
+\end{equation}
+
+<a id="figure--fig:li01-decoupling-conf-bis"></a>
+
+{{< figure src="/ox-hugo/li01_decoupling_conf_bis.png" caption="<span class=\"figure-number\">Figure 5: </span>Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
+
+<div class="important">
+
+These decoupling algorithms have two constraints:
 
 1.  the payload mass/inertia matrix must be diagonal (the CoM is coincident with the origin of frame \\(\\{P\\}\\))
 2.  the geometry of the hexapod and the attachment of the payload to the hexapod must be carefully chosen
 
-> For instance, if the hexapod has a mutually orthogonal geometry (cubic configuration), the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts.
+For instance, if the hexapod has a mutually orthogonal geometry (cubic configuration), the payload's center of mass must coincide with the center of the cube formed by the orthogonal struts.
 
-<a id="org7721136"></a>
+</div>
-
-{{< figure src="/ox-hugo/li01_decoupling_conf.png" caption="Figure 4: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
-
-<a id="orgdc42940"></a>
-
-{{< figure src="/ox-hugo/li01_decoupling_conf_bis.png" caption="Figure 5: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
 
 
 ## Simultaneous Vibration Isolation and Pointing Control {#simultaneous-vibration-isolation-and-pointing-control}
 
-Basic idea:
+Many applications require simultaneous vibration isolation and precision pointing.
 
--   acceleration feedback is used to provide high-frequency vibration isolation
+The basic idea to achieve such objective is to use:
--   cartesian pointing feedback can be used to provide low-frequency pointing
+
+-   acceleration feedback to provide high-frequency vibration isolation
+-   cartesian pointing feedback to provide low-frequency pointing
 
 The compensation is divided in frequency because:
 
@@ -139,132 +193,188 @@ The compensation is divided in frequency because:
 
 The control bandwidth is divided as follows:
 
--   low-frequency disturbances as attenuated and tracking is accomplished by feedback from low bandwidth pointing sensors
+-   low-frequency disturbances are attenuated and tracking is accomplished by feedback from low bandwidth pointing sensors
 -   mid-frequency disturbances are attenuated by feedback from band-pass sensors like accelerometer or load cells
 -   high-frequency disturbances are attenuated by passive isolation techniques
 
 
 ### Vibration Isolation {#vibration-isolation}
 
-The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [6](#org0dd19dc).
+The system is decoupled into six independent SISO subsystems using the architecture shown in [Figure 6](#figure--fig:li01-vibration-isolation-control).
 
-<a id="org0dd19dc"></a>
+<a id="figure--fig:li01-vibration-isolation-control"></a>
 
-{{< figure src="/ox-hugo/li01_vibration_isolation_control.png" caption="Figure 6: Figure caption" >}}
+{{< figure src="/ox-hugo/li01_vibration_isolation_control.png" caption="<span class=\"figure-number\">Figure 6: </span>Vibration isolation control strategy" >}}
 
-One of the subsystem plant transfer function is shown in Figure [6](#org0dd19dc)
+One of the subsystem plant transfer function is shown in [Figure 6](#figure--fig:li01-vibration-isolation-control)
 
-<a id="org6a21353"></a>
+<a id="figure--fig:li01-vibration-isolation-control"></a>
 
-{{< figure src="/ox-hugo/li01_vibration_control_plant.png" caption="Figure 7: Plant transfer function of one of the SISO subsystem for Vibration Control" >}}
+{{< figure src="/ox-hugo/li01_vibration_control_plant.png" caption="<span class=\"figure-number\">Figure 7: </span>Plant transfer function of one of the SISO subsystem for Vibration Control" >}}
 
 Each compensator is designed using simple loop-shaping techniques.
+A typical compensator consists of the following elements:
 
-The unity control bandwidth of the isolation loop is designed to be from **5Hz to 50Hz**.
+-   first order lag-lead filter to provide adequate phase margin a the low frequency crossover
+-   a second order lag-lead filter to increase the gain between crossovers and provide adequate phase margin at the high frequency crossover
+-   a second order notch filter to cancel the mode at 150Hz
+-   a second order low pass filter to provide steep roll-off and gain stabilize the plant at high frequency
+-   a first order high pass filter to eliminate DC signals
 
-> Despite a reasonably good match between the modeled and the measured transfer functions, the model based decoupling algorithm does not produce the expected decoupling.
+The unity control bandwidth of the isolation loop is designed to be from **5Hz to 50Hz**, so the vibration isolation loop works as a band-pass filter.
-> Only about 20 dB separation is achieve between the diagonal and off-diagonal responses.
+
+<div class="important">
+
+Despite a reasonably good match between the modeled and the measured transfer functions, the model based decoupling algorithm does not produce the expected decoupling.
+Only about 20 dB separation is achieve between the diagonal and off-diagonal responses.
+
+</div>
+
+<div class="note">
+
+Severe phase delay exists in the actual transfer function.
+This is due to the limited sample frequency and sensor bandwidth limitation.
+
+The zero at around 130Hz is non-minimum phase which limits the control bandwidth.
+The reason is not explained.
+
+</div>
 
 
-### Pointing Control {#pointing-control}
+### Pointing Control Techniques {#pointing-control-techniques}
 
-A block diagram of the pointing control system is shown in Figure [8](#orgb338488).
+A block diagram of the pointing control system is shown in [Figure 8](#figure--fig:li01-pointing-control).
 
-<a id="orgb338488"></a>
+<a id="figure--fig:li01-pointing-control"></a>
 
-{{< figure src="/ox-hugo/li01_pointing_control.png" caption="Figure 8: Figure caption" >}}
+{{< figure src="/ox-hugo/li01_pointing_control.png" caption="<span class=\"figure-number\">Figure 8: </span>Figure caption" >}}
 
 The plant is decoupled into two independent SISO subsystems.
-The compensators are design with inverse-dynamics methods.
+The decoupling matrix consists of the columns of \\(J\\) corresponding to the pointing DoFs.
+
+[Figure 9](#figure--fig:li01-transfer-function-angle) shows the measured transfer function of the \\(\theta\_x\\) axis.
+
+<a id="figure--fig:li01-transfer-function-angle"></a>
+
+{{< figure src="/ox-hugo/li01_transfer_function_angle.png" caption="<span class=\"figure-number\">Figure 9: </span>Experimentally measured plant transfer function of \\(\theta\_x/\theta\_{x\_d}\\)" >}}
+
+A typical compensator consists of the following elements:
+
+-   a first order low pass filter to increase the low frequency loop gain and provide a slope of -20dB/decade for the magnitude curve at the crossover
+-   two complex zeros with high \\(Q\\) to provide adequate phase margin at the crossover
+-   a pole after the zeros to decrease the excess gain caused by these zeros
+-   a second order notch filter to cancel the mode at 150Hz
+-   a second order low pass filter to provide steep roll off and gain stabilize the plant at high frequency
 
 The unity control bandwidth of the pointing loop is designed to be from **0Hz to 20Hz**.
 
-A feedforward control is added as shown in Figure [9](#orgb372596).
+A feedforward control is added as shown in [Figure 10](#figure--fig:li01-feedforward-control).
+\\(C\_f\\) is the feedforward compensator which is a 2x2 diagonal matrix.
+Ideally, the feedforward compensator is an invert of the plant dynamics.
 
-<a id="orgb372596"></a>
+<a id="figure--fig:li01-feedforward-control"></a>
 
-{{< figure src="/ox-hugo/li01_feedforward_control.png" caption="Figure 9: Feedforward control" >}}
+{{< figure src="/ox-hugo/li01_feedforward_control.png" caption="<span class=\"figure-number\">Figure 10: </span>Feedforward control" >}}
 
 
 ### Simultaneous Control {#simultaneous-control}
 
 The simultaneous vibration isolation and pointing control is approached in two ways:
 
-1.  design and implement the vibration isolation control first, identify the pointing plant when the isolation loops are closed, then implement the pointing compensators
+1.  **Closing the vibration isolation loop first**: Design and implement the vibration isolation control first, identify the pointing plant when the isolation loops are closed, then implement the pointing compensators.
-2.  the reverse design order
+2.  **Closing the pointing loop first**: Reverse order.
 
-Figure [10](#orgbafcf4b) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
+[Figure 11](#figure--fig:li01-parallel-control) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
 
-<a id="orgbafcf4b"></a>
+<a id="figure--fig:li01-parallel-control"></a>
 
-{{< figure src="/ox-hugo/li01_parallel_control.png" caption="Figure 10: A parallel scheme" >}}
+{{< figure src="/ox-hugo/li01_parallel_control.png" caption="<span class=\"figure-number\">Figure 11: </span>A parallel scheme" >}}
 
-The transfer function matrix for the pointing loop after the vibration isolation is closed is still decoupled. The same happens when closing the pointing loop first and looking at the transfer function matrix of the vibration isolation.
+<div class="important">
 
-The effect of the isolation loop on the pointing loop is large around the natural frequency of the plant as shown in Figure [11](#org2a20ab8).
+The transfer function matrix for the pointing loop after the vibration isolation is closed is still decoupled.
+The same happens when closing the pointing loop first and looking at the transfer function matrix of the vibration isolation.
 
-<a id="org2a20ab8"></a>
+However, the interaction between loops may affect the transfer functions of the **first** closed loop, and thus affect its relative stability.
 
-{{< figure src="/ox-hugo/li01_effect_isolation_loop_closed.png" caption="Figure 11: \\(\theta\_x/\theta\_{x\_d}\\) transfer function with the isolation loop closed (simulation)" >}}
+</div>
-
-The effect of pointing control on the isolation plant has not much effect.
-
-> The interaction between loops may affect the transfer functions of the **first** closed loop, and thus affect its relative stability.
 
 The dynamic interaction effect:
 
--   only happens in the unity bandwidth of the loop transmission of the first closed loop.
+-   Only happens in the unity bandwidth of the loop transmission of the first closed loop.
--   affect the closed loop transmission of the loop first closed (see Figures [12](#orgc137ea3) and [13](#orgc06274a))
+-   Affect the closed loop transmission of the loop first closed (see [Figure 12](#figure--fig:li01-closed-loop-pointing) and [Figure 13](#figure--fig:li01-closed-loop-vibration))
 
-As shown in Figure [12](#orgc137ea3), the peak resonance of the pointing loop increase after the isolation loop is closed.
+As shown in [Figure 12](#figure--fig:li01-closed-loop-pointing), the peak resonance of the pointing loop increase after the isolation loop is closed.
 The resonances happen at both crossovers of the isolation loop (15Hz and 50Hz) and they may show of loss of robustness.
 
-<a id="orgc137ea3"></a>
+<a id="figure--fig:li01-closed-loop-pointing"></a>
 
-{{< figure src="/ox-hugo/li01_closed_loop_pointing.png" caption="Figure 12: Closed-loop transfer functions \\(\theta\_y/\theta\_{y\_d}\\) of the pointing loop before and after the vibration isolation loop is closed" >}}
+{{< figure src="/ox-hugo/li01_closed_loop_pointing.png" caption="<span class=\"figure-number\">Figure 12: </span>Closed-loop transfer functions \\(\theta\_y/\theta\_{y\_d}\\) of the pointing loop before and after the vibration isolation loop is closed" >}}
 
-The same happens when first closing the vibration isolation loop and after the pointing loop (Figure [13](#orgc06274a)).
+The same happens when first closing the vibration isolation loop and after the pointing loop ([Figure 13](#figure--fig:li01-closed-loop-vibration)).
 The first peak resonance of the vibration isolation loop at 15Hz is increased when closing the pointing loop.
 
-<a id="orgc06274a"></a>
+<a id="figure--fig:li01-closed-loop-vibration"></a>
 
-{{< figure src="/ox-hugo/li01_closed_loop_vibration.png" caption="Figure 13: Closed-loop transfer functions of the vibration isolation loop before and after the pointing control loop is closed" >}}
+{{< figure src="/ox-hugo/li01_closed_loop_vibration.png" caption="<span class=\"figure-number\">Figure 13: </span>Closed-loop transfer functions of the vibration isolation loop before and after the pointing control loop is closed" >}}
 
-> The isolation loop adds a second resonance peak at its high-frequency crossover in the pointing closed-loop transfer function, which may cause instability.
+<div class="important">
-> Thus, it is recommended to design and implement the isolation control system first, and then identify the pointing plant with the isolation loop closed.
+
+From the analysis above, it is hard to say which loop has more significant affect on the other loop, but the isolation loop adds a second resonance peak at its high frequency crossover in the pointing closed loop transfer function, which may cause instability.
+Thus, it is recommended to design and implement the isolation control system first, and then identify the pointing plant with the isolation loop closed.
+
+</div>
 
 
 ### Experimental results {#experimental-results}
 
-Two hexapods are stacked (Figure [14](#org2a11277)):
+Two hexapods are stacked ([Figure 14](#figure--fig:li01-test-bench)):
 
 -   the bottom hexapod is used to generate disturbances matching candidate applications
 -   the top hexapod provide simultaneous vibration isolation and pointing control
 
-<a id="org2a11277"></a>
+<a id="figure--fig:li01-test-bench"></a>
 
-{{< figure src="/ox-hugo/li01_test_bench.png" caption="Figure 14: Stacked Hexapods" >}}
+{{< figure src="/ox-hugo/li01_test_bench.png" caption="<span class=\"figure-number\">Figure 14: </span>Stacked Hexapods" >}}
 
-Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [15](#org5933a45).
+First, the vibration isolation and pointing controls were implemented separately.
+Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in [Figure 15](#figure--fig:li01-vibration-isolation-control-results).
 
-<a id="org5933a45"></a>
+<a id="figure--fig:li01-vibration-isolation-control-results"></a>
 
-{{< figure src="/ox-hugo/li01_vibration_isolation_control_results.png" caption="Figure 15: Vibration isolation control: open-loop (solid) vs. closed-loop (dashed)" >}}
+{{< figure src="/ox-hugo/li01_vibration_isolation_control_results.png" caption="<span class=\"figure-number\">Figure 15: </span>Vibration isolation control: open-loop (solid) vs. closed-loop (dashed)" >}}
 
 The simultaneous control is of dual use:
 
 -   it provide simultaneous pointing and isolation control
 -   it can also be used to expand the bandwidth of the isolation control to low frequencies because the pointing loops suppress pointing errors due to both base vibrations and tracking
 
-The results of simultaneous control is shown in Figure [16](#org996a848) where the bandwidth of the isolation control is expanded to very low frequency.
+The results of simultaneous control is shown in [Figure 16](#figure--fig:li01-simultaneous-control-results) where the bandwidth of the isolation control is expanded to very low frequency.
 
-<a id="org996a848"></a>
+<a id="figure--fig:li01-simultaneous-control-results"></a>
 
-{{< figure src="/ox-hugo/li01_simultaneous_control_results.png" caption="Figure 16: Simultaneous control: open-loop (solid) vs. closed-loop (dashed)" >}}
+{{< figure src="/ox-hugo/li01_simultaneous_control_results.png" caption="<span class=\"figure-number\">Figure 16: </span>Simultaneous control: open-loop (solid) vs. closed-loop (dashed)" >}}
+
+
+### Summary and Conclusion {#summary-and-conclusion}
+
+<div class="sum">
+
+A parallel control scheme is proposed in this chapters.
+This scheme is suitable for simultaneous vibration isolation and pointing control.
+Part of this scheme involves closing one loop first, then re-identifying and designing the new control before closed the other loop.
+
+An investigation into the interaction between loops shows that the order of closing loops is not important.
+However, only two channels need to be re-designed or adjusted for the pointing loop if the isolation loop is closed first.
+Experiments show that this scheme takes advantage of the bandwidths of both pointing and vibration sensors, and provides vibration isolation and pointing controls over a broad band.
+
+</div>
 
 
 ## Future research areas {#future-research-areas}
 
+<div class="sum">
+
 Proposed future research areas include:
 
 -   **Include base dynamics in the control**:
@@ -286,8 +396,11 @@ Proposed future research areas include:
     -   **LVDT** to provide differential position of the hexapod payload with respect to the base
     -   **Geophones** to provide payload and base velocity information
 
+</div>
 
 
 ## Bibliography {#bibliography}
 
-<a id="org7277b25"></a>Li, Xiaochun. 2001. “Simultaneous, Fault-Tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” University of Wyoming.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Li, Xiaochun. 2001. “Simultaneous, Fault-Tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” University of Wyoming.</div>
+</div>

content/phdthesis/monkhorst04_dynam_error_budget.md

@@ -1,14 +1,16 @@
 +++
 title = "Dynamic error budgeting, a design approach"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
+ref_author = "Monkhorst, W."
+ref_year = 2004
 +++
 
 Tags
-: [Dynamic Error Budgeting]({{<relref "dynamic_error_budgeting.md#" >}})
+: [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting.md" >}})
 
 Reference
-: ([Monkhorst 2004](#org0da5be0))
+: (<a href="#citeproc_bib_item_1">Monkhorst 2004</a>)
 
 Author(s)
 : Monkhorst, W.
@@ -19,6 +21,11 @@ Year
 
 ## Introduction {#introduction}
 
+The performance of a mechatronic system is generally defined by the error made, which is caused by the disturbances \\(d\\) that act on the system.
+In order to study how the disturbances \\(d\\) propagates to the error, frequency dependent models of the disturbances and subsystems must be used.
+Disturbances (which are stochastic) are modeled with their power spectral densities.
+The new design approach will be referred to as _Dynamic Error Budgeting_, where "dynamic" refers to the use of the frequency dependent models.
+
 Challenge definition of this thesis:
 
 > Develop a tool which enables the designer to account for stochastic disturbances during the design of a mechatronics system.
@@ -38,21 +45,26 @@ Develop tools should enable the designer to:
 
 Main motivations are:
 
--   Cutting costs in the design phase
+-   **Cutting costs in the design phase**: if the error is not simulated during the design phase, the final performance level can only be found when a costly prototype is build and the performance can be measured physically. If the performance level is not met, the designer has to find out what component or disturbance causes the output to exceed the error budget and then redesign the system. If the error could be simulated beforehand however, changes can be made when the system is still in the design phase, cutting down the costs of the system.
--   Speeding up the design process
+-   **Speeding up the design process**: It can give a quick indication if a concept is feasible or not.
--   Enhancing design insight
+    Several concepts can be analyzed in a short period of time and the most promising concept can be chosen, speeding up the design process.
+-   **Enhancing design insight**: If the performance specifications is not met, the designer wants to know which component or what system property is limiting the performance most.
 
 
 ### DEB design process {#deb-design-process}
 
+The DEB design process can be summarized as follows: choose a system concept and simulate the output error.
+If the total error is meets the performance specifications, the design is satisfying.
+If the error exceeds the specified budget, the designer has to change the system such that the specifications is met.
+
 Step by step, the process is as follows:
 
--   design a concept system
+-   Design a concept system.
--   model the concept system, such that the closed loop transfer functions can be determined
+-   Model the concept system, such that the closed loop transfer functions can be determined.
 -   Identify all significant disturbances.
     Model them with their _Power Spectral Density_
 -   Define the performance outputs of the system and simulate the output error.
-    Using the theory of _propagation_, the contribution of each disturbance to the output error can be analyzed and the critical disturbance can be pointed out
+    Using the theory of _propagation_, the contribution of each disturbance to the output error can be analyzed and the critical disturbance can be pointed out.
 -   Make changes to the system that are expected to improve the performance level, and simulate the output error again.
     Iterate until the error budget is meet.
 
@@ -61,16 +73,15 @@ Step by step, the process is as follows:
 
 The assumptions when applying DEB are:
 
--   the system can be accurately described with a **linear time invariant model**.
+-   The system can be accurately described with a **linear time invariant model**.
     This is usually the case as much effort is put in to make systems have a linear behavior and because feedback loops have a " linearizing" effect on the closed loop behavior.
--   the disturbances action on the system must be **stationary** (their statistical properties are not allowed to change over time).
+-   The disturbances action on the system must be **stationary** (their statistical properties are not allowed to change over time).
--   the disturbances are **uncorrelated** with each other.
+-   The disturbances are **uncorrelated** with each other.
     This is more difficult to satisfy for MIMO systems and the designer must make sure that the separate disturbances all originate from separate independent sources.
--   the disturbance signals are modeled by their **Power Spectral Density**.
+-   The disturbance signals are modeled by their **Power Spectral Density**.
     This implies that only stochastic disturbances are allowed.
-    Deterministic components like sinusoidal and DC signals are infinite peaks in their PSD and should not be used.
     For the deterministic part, other techniques can be used to determine their influence to the error.
--   the calculation method makes no assumption on the distribution of the distribution functions of the disturbances.
+-   The calculation method makes no assumption on the distribution of the distribution functions of the disturbances.
     In practice, many disturbances will have a normal like distribution.
 
 
@@ -95,38 +106,38 @@ Find a controller \\(C\_{\mathcal{H}\_2}\\) which minimizes the \\(\mathcal{H}\_
 
 In order to synthesize an \\(\mathcal{H}\_2\\) controller that will minimize the output error, the total system including disturbances needs to be modeled as a system with zero mean white noise inputs.
 
-This is done by using weighting filter \\(V\_w\\), of which the output signal has a PSD \\(S\_w(f)\\) when the input is zero mean white noise (Figure [1](#org4676e24)).
+This is done by using weighting filter \\(V\_w\\), of which the output signal has a PSD \\(S\_w(f)\\) when the input is zero mean white noise ([Figure 1](#figure--fig:monkhorst04-weighting-filter)).
 
-<a id="org4676e24"></a>
+<a id="figure--fig:monkhorst04-weighting-filter"></a>
 
-{{< figure src="/ox-hugo/monkhorst04_weighting_filter.png" caption="Figure 1: The use of a weighting filter \\(V\_w(f)\,[SI]\\) to give the weighted signal \\(\bar{w}(t)\\) a certain PSD \\(S\_w(f)\\)." >}}
+{{< figure src="/ox-hugo/monkhorst04_weighting_filter.png" caption="<span class=\"figure-number\">Figure 1: </span>The use of a weighting filter \\(V\_w(f)\\,[SI]\\) to give the weighted signal \\(\bar{w}(t)\\) a certain PSD \\(S\_w(f)\\)." >}}
 
 The white noise input \\(w(t)\\) is dimensionless, and when the weighting filter has units [SI], the resulting weighted signal \\(\bar{w}(t)\\) has units [SI].
 The PSD \\(S\_w(f)\\) of the weighted signal is:
 \\[ |S\_w(f)| = V\_w(j 2 \pi f) V\_w^T(-j 2 \pi f) \\]
 
 Given \\(S\_w(f)\\), \\(V\_w(f)\\) can be obtained using a technique called _spectral factorization_.
-However, this can be avoided if the modelling of the disturbances is directly done in terms of weighting filters.
+However, this can be avoided if the modeling of the disturbances is directly done in terms of weighting filters.
 
-Output weighting filters can also be used to scale different outputs relative to each other (Figure [2](#org7706a36)).
+Output weighting filters can also be used to scale different outputs relative to each other ([Figure 2](#figure--fig:monkhorst04-general-weighted-plant)).
 
-<a id="org7706a36"></a>
+<a id="figure--fig:monkhorst04-general-weighted-plant"></a>
 
-{{< figure src="/ox-hugo/monkhorst04_general_weighted_plant.png" caption="Figure 2: The open loop system \\(\bar{G}\\) in series with the diagonal input weightin filter \\(V\_w\\) and diagonal output scaling iflter \\(W\_z\\) defining the generalized plant \\(G\\)" >}}
+{{< figure src="/ox-hugo/monkhorst04_general_weighted_plant.png" caption="<span class=\"figure-number\">Figure 2: </span>The open loop system \\(\bar{G}\\) in series with the diagonal input weightin filter \\(V\_w\\) and diagonal output scaling iflter \\(W\_z\\) defining the generalized plant \\(G\\)" >}}
 
 
 #### Output scaling and the Pareto curve {#output-scaling-and-the-pareto-curve}
 
-In this research, the outputs of the closed loop system (Figure [3](#org8166dc2)) are:
+In this research, the outputs of the closed loop system ([Figure 3](#figure--fig:monkhorst04-closed-loop-H2)) are:
 
 -   the performance (error) signal \\(e\\)
 -   the controller output \\(u\\)
 
 In this way, the designer can analyze how much control effort is used to achieve the performance level at the performance output.
 
-<a id="org8166dc2"></a>
+<a id="figure--fig:monkhorst04-closed-loop-H2"></a>
 
-{{< figure src="/ox-hugo/monkhorst04_closed_loop_H2.png" caption="Figure 3: The closed loop system with weighting filters included. The system has \\(n\\) disturbance inputs and two outputs: the error \\(e\\) and the control signal \\(u\\). The \\(\mathcal{H}\_2\\) minimized the \\(\mathcal{H}\_2\\) norm of this system." >}}
+{{< figure src="/ox-hugo/monkhorst04_closed_loop_H2.png" caption="<span class=\"figure-number\">Figure 3: </span>The closed loop system with weighting filters included. The system has \\(n\\) disturbance inputs and two outputs: the error \\(e\\) and the control signal \\(u\\). The \\(\mathcal{H}\_2\\) minimized the \\(\mathcal{H}\_2\\) norm of this system." >}}
 
 The resulting problem is a multi-objective control problem: while constraining the variance of the controller output \\(u\\), the variance of the performance channel should be minimized.
 This problem can be solved by scaling the controller output \\(u\\) with a factor \\(\alpha\\) during the \\(\mathcal{H}\_2\\) synthesis.
@@ -148,7 +159,8 @@ When an \\(\mathcal{H}\_2\\) controller is synthesized for a particular system,
 Drawbacks however are, that no robustness guarantees can be given and that the order of the \\(\mathcal{H}\_2\\) controller will generally be too high for implementation.
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="org0da5be0"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Monkhorst, Wouter. 2004. “Dynamic Error Budgeting, a Design Approach.” Delft University.</div>
+</div>

content/phdthesis/poel10_explor_activ_hard_mount_vibrat.md

@@ -1,14 +1,16 @@
 +++
 title = "An exploration of active hard mount vibration isolation for precision equipment"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = true
+ref_author = "van der Poel, G. W."
+ref_year = 2010
 +++
 
 Tags
-: [Vibration Isolation](vibration_isolation.md)
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
 
 Reference
-: ([Poel 2010](#orgf254685))
+: (<a href="#citeproc_bib_item_1">Van der Poel 2010</a>)
 
 Author(s)
 : van der Poel, G. W.
@@ -17,7 +19,8 @@ Year
 : 2010
 
 
-
 ## Bibliography {#bibliography}
 
-<a id="orgf254685"></a>Poel, Gerrit Wijnand van der. 2010. “An Exploration of Active Hard Mount Vibration Isolation for Precision Equipment.” University of Twente. <https://doi.org/10.3990/1.9789036530163>.
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Poel, Gerrit Wijnand van der. 2010. “An Exploration of Active Hard Mount Vibration Isolation for Precision Equipment.” University of Twente. doi:<a href="https://doi.org/10.3990/1.9789036530163">10.3990/1.9789036530163</a>.</div>
+</div>

content/phdthesis/treichel17_model_robus_adapt_track_contr.md

@@ -0,0 +1,25 @@
++++
+title = "Modeling and robust adaptive tracking control of a planar precision positioning system"
+author = ["Thomas Dehaeze"]
+draft = true
+ref_author = "Treichel, K."
+ref_year = 2017
++++
+
+Tags
+:
+
+
+Reference
+: ([Treichel 2017](#org35de13e))
+
+Author(s)
+: Treichel, K.
+
+Year
+: 2017
+
+
+## Bibliography {#bibliography}
+
+<a id="org35de13e"></a>Treichel, Kai. 2017. “Modeling and Robust Adaptive Tracking Control of a Planar Precision Positioning System.” Ilmenau University of Technology.

content/phdthesis/verbaan15_robus.md

@@ -0,0 +1,443 @@
++++
+title = "Robust mass damper design for bandwidth increase of motion stages"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (<a href="#citeproc_bib_item_1">Verbaan 2015</a>)
+
+Author(s)
+: Verbaan, C.
+
+Year
+: 2015
+
+> This thesis addresses the challenge to increase the modal damping of the bandwidth limiting resonances of motions stages.
+> This modal damping increase is realized by adding passive elements, called robust tuned mass dampers, at specific stage locations.
+>
+> [...]
+>
+> The damper parameters that have to be determined are mass, stiffness, and damping.
+> The optimal parameters are obtained by executing optimization algorithm.
+>
+> The first motion stage design is optimized based on an open-loop criterion for modal damping increase between 1 and 4kHz.
+> Experimental validation shows that a suppression factor of over 24dB is obtained.
+
+
+## Robust Mass Damper and broad banded damping {#robust-mass-damper-and-broad-banded-damping}
+
+> In high tech motion systems, the finite stiffness of mechanical components results in natural frequencies which limit the bandwidth of the control system.
+> This is usually counteracted by increasing the controller complexity by adding notch filters.
+> The height of the non-rigid body modes in the frequency response function and the amount of damping significantly affect the achievable bandwidth.
+> This chapter described a method to add damping to the flexible behavior of a motion stage, by using robust mass dampers which are mass-spring-damper systems with an **over-critical** damping value.
+> This high damping results in robust dynamic behavior with respect to stiffness and damping variations for both the motion stage and the damper mechanisms.
+> The main result is a significant increase in modal damping over a broad band of resonance frequencies.
+
+
+### Tuned mass damper {#tuned-mass-damper}
+
+The effectiveness of the TMD is related to the mass ratio between \\(m\\) and \\(M\\).
+To obtain a substantial suppression factor in combination with a relatively small increase in mass, the mass ratio is usually determined to be approximately 5 to 10% of the main structural mass.
+The undamped natural frequency of the TMD has to be tuned close to the targeted natural frequency of the main structure.
+
+A drawback of the TMD is the relatively **large sensitivity of the suppression factor for variations in stiffness and damping values**.
+This sensitivity also holds for natural frequency variations of the main structure.
+
+<a id="figure--fig:verbaan15-tmd-principle"></a>
+
+{{< figure src="/ox-hugo/verbaan15_tmd_principle.png" caption="<span class=\"figure-number\">Figure 1: </span>TMD principle" >}}
+
+
+### Damper design and validation {#damper-design-and-validation}
+
+This damper is designed and tested to prove that it is possible to create dampers with over-critical damping values and with natural frequencies that are high enough to be useful.
+The spring and damper are assumed to behave linearly.
+In addition, the vibration amplitudes of high-tech positioning tables are small, which allows for assuming linear system theory.
+These small vibration amplitudes lead to small damper strokes.
+Therefore **flexures** can be used to provide for the guidance of the moving mass.
+The dimensions of the flexures determine the spring stiffness and therefore the natural frequency of the TMD.
+An additional advantage of flexures is the lack of hysteresis, which **enables the damper to work even if the damper strokes are very small**.
+
+The dampers are intended to act purely in z-direction.
+The natural frequency in this direction is determined at 1250Hz and the natural frequency in the other directions should be as high as possible.
+
+<a id="figure--fig:verbaan15-tmd-modes"></a>
+
+{{< figure src="/ox-hugo/verbaan15_tmd_modes.png" caption="<span class=\"figure-number\">Figure 2: </span>Natural frequency of the TMD. First natural frequency at 1250Hz and the second at 8100Hz." >}}
+
+The second challenge is to create a damping mechanism with a high damping coefficient in a relatively small volume.
+The damper is designed to be **passive**.
+This guarantees stability of the damper system itself and preserves from increasing complexity.
+As damping concept, a **viscous fuild damper** is chosen due to the following properties:
+
+-   the linear time independent behavior
+-   the ability to create an extremely large damping constant in a small volume
+-   separation of stiffness and damping
+-   the supreme damping properties of fuilds with respect to other damping materials
+
+The guild applied is Rocol Kilopoise 0868 and is chosen based on the extremely high viscosity of 220 Pas.
+
+In order to measure the damping the measurement bench shown in [3](#figure--fig:verbaan15-tmd-mech-system) is used.
+The measured FRF are shown in [4](#figure--fig:verbaan15-obtained-damping-bench).
+The measurement clearly shows that the damper mechanism is over-critically damped.
+
+<a id="figure--fig:verbaan15-tmd-mech-system"></a>
+
+{{< figure src="/ox-hugo/verbaan15_tmd_mech_system.png" caption="<span class=\"figure-number\">Figure 3: </span>Damper test setup to measure the damping characteristics" >}}
+
+<a id="figure--fig:verbaan15-obtained-damping-bench"></a>
+
+{{< figure src="/ox-hugo/verbaan15_obtained_damping_bench.png" caption="<span class=\"figure-number\">Figure 4: </span>Obtained damping results" >}}
+
+
+## Linear viscoelastic characterisation of an ultra-high viscosity fluid {#linear-viscoelastic-characterisation-of-an-ultra-high-viscosity-fluid}
+
+> This chapter presents the use of a state of the art damper for high precision motion stages as a sliding plate rheometer for measuring linear viscoelastic properties in the frequency range of 10Hz to 10kHz.
+> This design is flexure based to minimize parasitic nonlinear forces.
+> Design and the damping mechanism are elaborated and a model is presented that describes the dynamic behavior.
+
+The damper shown in [5](#figure--fig:verbaan15-damper-parts) can be used as a sliding plate rheometer to measure the linear viscoelastic properties of ultra-high viscosity fluids in the frequency range 10Hz to 10kHz.
+
+<a id="figure--fig:verbaan15-damper-parts"></a>
+
+{{< figure src="/ox-hugo/verbaan15_damper_parts.png" caption="<span class=\"figure-number\">Figure 5: </span>Damper parts" >}}
+
+The full damper assembly consists of a mass, mounted on two springs and a damper in parallel configuration.
+The mass can make small strokes in the x-direction and is fixed in all other directions.
+The spring is a double leaf spring guide.
+The space between the lead springs is used to accommodate for the damping mechanism.
+
+<a id="figure--fig:verbaan15-tmd-slot-fin-parts"></a>
+
+{{< figure src="/ox-hugo/verbaan15_tmd_slot_fin_parts.png" caption="<span class=\"figure-number\">Figure 6: </span>Exploded view of the damper parts" >}}
+
+A high-viscosity fluid is applied to create a velocity dependent force.
+For this purpose, the sliding plate principle is used which induces a **shear flow**: the fluid is placed between two slot plates and a fin is positioned between these two plates ([7](#figure--fig:verbaan15single-double-fin)).
+A **flexible encapsulation** is used to hold the fluid between find and slot part.
+
+To study different damping values with the same fluid, two damper designs with different geometries are used (see [7](#figure--fig:verbaan15single-double-fin)).
+
+<a id="figure--fig:verbaan15single-double-fin"></a>
+
+{{< figure src="/ox-hugo/verbaan15single_double_fin.png" caption="<span class=\"figure-number\">Figure 7: </span>Cross-sectional views of the two different damping mechanims. The single fin (left) and double fin (right)." >}}
+
+To excite the damper mass, a voice coil is mounted to the hardware.
+The damper position is measured with a laser vibrometer.
+
+A sliding plate damper for high frequencies introduces side effects:
+
+1.  geometry related effects
+2.  frequency dependent effects
+
+A first geometrical effect is due to the **finite length of the plates**.
+The ratio length/gap here is more than 100 which makes this effect negligible.
+A second geometrical effect is due to the difficulty to get the **plates parallel to each other**, especially with the normal forces acting on the moving fin, induced by the flow.
+This design counteracts this problem in two-ways: the damper part is **symmetric**, which means that the fin normal forces cancel each other.
+In addition, the double leaf spring mechanism has a **very high lateral stiffness**, which minimizes lateral displacements.
+A third geometrical effect is pumping of the fluid, which appears in the case of closed ends and introduces a flow opposite to the fin velocity, and therefore introduces a parasitic damping force.
+This problem is avoided by letting the gaps' ends open.
+The **fin is shorted than the slot** to maintain the same damping area over the damper stroke.
+
+These effects all arise at low frequencies, at which the flow can be assumed homogeneous.
+The ratio between inertial and viscous effects determines up to which frequency the flow can be assumed homogeneous:
+
+\begin{equation}
+t\_c = \frac{10 \rho h^2}{\eta}
+\end{equation}
+
+in which \\(\rho\\) describes the fluid density in \\(kg/m^3\\), \\(\eta\\) the dynamic viscosity in \\(Pa s\\) and \\(h\\) the gap width in \\(m\\).
+Dimensions are provided in [1](#table--tab:single-fin-parameters).
+This estimate results in a frequency above 100kHz.
+It shows that high fluid viscosities and small gap widths enable high frequencies without losing homogeneous flow conditions.
+
+<a id="table--tab:single-fin-parameters"></a>
+<div class="table-caption">
+  <span class="table-number"><a href="#table--tab:single-fin-parameters">Table 1</a>:</span>
+  Parameters for the single fin design
+</div>
+
+| Dimension      | Value [mm] |
+|----------------|------------|
+| Length \\(l\\) | 16         |
+| Width \\(w\\)  | 8.5        |
+| Gap \\(h\\)    | 0.12       |
+
+**Conclusion**:
+A design of a sliding plate damper that can be used to characterize fluid behavior of high viscosity fluids in the frequency range between 10Hz and 10kHz.
+The drawbacks of standard sliding plate devices are taken care off by the mechanical design.
+The flexure mechanism very precisely determines the position of the fin with respect to the slot part.
+A three mode Maxwell model can accurately describe the behavior.
+
+
+## Damping optimization of a complex motion stage {#damping-optimization-of-a-complex-motion-stage}
+
+
+### Stage and damper dynamic models {#stage-and-damper-dynamic-models}
+
+This chapter presents the results of a robust mass damper implementation on a complex motion stage with realistic natural frequencies to increase the modal damping of flexible modes.
+A design approach is presented which results in parameter values for the dampers to improve the modal damping over a specified frequency range.
+
+[8](#figure--fig:verbaan15-stage-undamped) shows a collocated FRF of the stage's corner.
+The goal is to increase the modal damping of modes 7, 9, 10/11 and 13.
+
+<a id="figure--fig:verbaan15-stage-undamped"></a>
+
+{{< figure src="/ox-hugo/verbaan15_stage_undamped.png" caption="<span class=\"figure-number\">Figure 8: </span>FRF at the stage corner in the z-direction, undamped" >}}
+
+The transfer function \\(T\_i(s)\\) is defined as the contribution of the a single mode \\(i\\) in an input/output transfer function:
+
+\begin{equation}
+T\_i(s) = \frac{\phi\_i^{\text{act}} \phi\_i^{\text{sen}}}{s^2 + 2 \xi \omega\_i s + \omega\_i^2} = \frac{1}{m\_i s^2 + c\_i s + k\_i}
+\end{equation}
+
+With \\(\phi\_i^{\text{act}}\\) and \\(\phi\_i^{\text{sen}}\\) the modal factors of the actuator and sensor.
+
+From this equation, it appears that the modal mass of a mode in a certain transfer function equals:
+
+\begin{equation}
+m\_i = \frac{1}{\phi\_i^{\text{act}} \phi\_i^{\text{sen}}}
+\end{equation}
+
+This equation shows that a certain mode's modal mass depends on the locations of the actuator and sensor.
+Since a TMD can be seen as a local control loop, the actuator and sensor location are equal.
+This results in the following equation for the apparent modal mass for mode \\(i\\) at the TMD location:
+
+\begin{equation}
+m\_i = \frac{}{(\phi\_i^{\text{TMD}})^2}
+\end{equation}
+
+It is known from literature that the efficiency of a TMD depends on the **mass ratio** of the TMD and the mode that has to be damped.
+It follows that the efficiency of a TMD to damp a certain resonance depends on the position of the damper on the stage in a quadratic sense.
+The TMD has to be located at the maximum displacement of the mode(s) to be damped.
+
+The damper configuration consists of an inertial mass \\(m\\), a transnational flexible guide designed as a double leaf spring mechanism with total stiffness \\(c\\) and a part that creates the damping force with damping constant \\(d\\) (model shown in [9](#figure--fig:verbaan15-maxwell-fluid-model)).
+The velocity dependent damper force is the result of two parameters:
+
+-   the fluid's mechanical properties
+-   the damper geometry
+
+The fluid model is presented in [10](#figure--fig:verbaan15-fluid-lve-model).
+This figure shows the viscous and elastic properties of the fluid as a function of the frequency.
+The damper principle is chosen to be a parallel plate damper based on the shear principle with the viscous fluid in between the two parallel plates.
+In case of a velocity difference between these plates, a velocity gradient is created in the fluid causing a specific force per unit of area, which, multiplied by the effective area submerged in the fluid, leads to a damping force.
+
+The damping can be expressed with a geometrical damping factor (GDF) in meters:
+
+\begin{equation}
+\text{GDF} = \frac{A}{h} = \frac{2 n l w}{h}
+\end{equation}
+
+with \\(A\\) the total area of the damper fins, \\(n\\) is the number of fins, \\(l\\) is the fin length, \\(w\\) is the fin width and \\(h\\) is the effective gap width in which the fluid is applied.
+
+This GDF, combined with the fluid properties in Pas and Pa, lead to a spring stiffness in N/m and a damping constant in N/(m/s).
+
+In general, larger suppression factors can be obtained with larger TMD masses.
+In the example, the modal mass is 3.5kg and the damper mass is 110g (useful inertial mass of 65g).
+
+<a id="figure--fig:verbaan15-maxwell-fluid-model"></a>
+
+{{< figure src="/ox-hugo/verbaan15_maxwell_fluid_model.png" caption="<span class=\"figure-number\">Figure 9: </span>Damper model with multi-mode Maxwell fluid model included" >}}
+
+<a id="figure--fig:verbaan15-fluid-lve-model"></a>
+
+{{< figure src="/ox-hugo/verbaan15_fluid_lve_model.png" caption="<span class=\"figure-number\">Figure 10: </span>Storage and loss modulus of the 3 Maxwell mode LVE fluid model" >}}
+
+
+### TMD and RMD optimisation {#tmd-and-rmd-optimisation}
+
+An algorithm is used to optimize the damping and is used in two cases:
+
+-   a small banded optimisation which includes a single resonance.
+    This results in a **tuned mass damper** optimal design
+-   a broad banded optimization which includes a range of resonances.
+    This results in a **robust mass damper** optimal design
+
+The algorithm is first used to calculate the optimal parameters to suppress a **single** resonance frequency.
+The result is shown in [11](#figure--fig:verbaan15-tmd-optimization) and shows **Tuned Mass Damper** behavior.
+
+For this single frequency, stiffness and damping values can be calculated by hand.
+
+<a id="figure--fig:verbaan15-tmd-optimization"></a>
+
+{{< figure src="/ox-hugo/verbaan15_tmd_optimization.png" caption="<span class=\"figure-number\">Figure 11: </span>Result of the optimization procedure. The cost function is specified between 1kHz and 2kHz. This implies that the first mode is suppressed by the damper." >}}
+
+To obtain broad banded damping, the cost function is redefined between 1 and 4kHz.
+[12](#figure--fig:verbaan15-broadbanded-damping-results) presents the resulting bode diagram.
+
+<a id="figure--fig:verbaan15-broadbanded-damping-results"></a>
+
+{{< figure src="/ox-hugo/verbaan15_broadbanded_damping_results.png" caption="<span class=\"figure-number\">Figure 12: </span>Result of the optimization procedure with the cost function specified between 1 and 4kHz. The result is a range of resonances that are suppressed by the dampers." >}}
+
+Results of optimizations for increasing damper mass, in the range from 10 to 250g per damper are shown in [13](#figure--fig:verbaan15-results-fct-mass).
+
+<a id="figure--fig:verbaan15-results-fct-mass"></a>
+
+{{< figure src="/ox-hugo/verbaan15_results_fct_mass.png" caption="<span class=\"figure-number\">Figure 13: </span>Optimal damper parameters as a function of the damper mass. The upper graph shows the suppression factor in dB, the second graph shows the natural frequency of the damper in Hz and the lower graph shows the geometrical damping factor in m." >}}
+
+
+### Damper Design and Validation {#damper-design-and-validation}
+
+A damper mechanism is design which contains the following properties:
+
+-   a moving mass \\(m\_d = 65\\,g\\)
+-   a mounting mass \\(m\_m = 45\\,g\\)
+-   a natural frequency \\(\omega\_0 = 1270\\,Hz\\)
+-   other natural frequencies as high as possible
+-   a geometrical damping factor of 14.3m
+-   an encapsulation to contain the fluid
+
+[14](#figure--fig:verbaan15-RMD-mechanical-parts) shows an exploded view of the RMD design.
+The mechanism part is monolithically designed and consists of:
+
+1.  a mounting side
+2.  leaf spring pair
+3.  the damper side
+
+The fluid is surrounded by a flexible encapsulation, which prevents it from running out.
+
+<a id="figure--fig:verbaan15-RMD-mechanical-parts"></a>
+
+{{< figure src="/ox-hugo/verbaan15_RMD_mechanical_parts.png" caption="<span class=\"figure-number\">Figure 14: </span>Exploded view of the robust mass damper design with different parts indicated" >}}
+
+<a id="figure--fig:verbaan15-RMD-design-modes"></a>
+
+{{< figure src="/ox-hugo/verbaan15_RMD_design_modes.png" caption="<span class=\"figure-number\">Figure 15: </span>Four lowest natural frequencies and corresponding mode shapes of the RMD while mounted to a stage corner" >}}
+
+<a id="figure--fig:verbaan15-tmd-side-front-views"></a>
+
+{{< figure src="/ox-hugo/verbaan15_tmd_side_front_views.png" caption="<span class=\"figure-number\">Figure 16: </span>A side view and a front view of the fin and slot parts" >}}
+
+| Dimension   | Value | Unit |
+|-------------|-------|------|
+| Length fin  | 17    | mm   |
+| Height fins | 4     | mm   |
+| Gap width   | 50    | um   |
+| GDF         | 14    | m    |
+
+<a id="figure--fig:verbaan15-damped-undamped-frf"></a>
+
+{{< figure src="/ox-hugo/verbaan15_damped_undamped_frf.png" caption="<span class=\"figure-number\">Figure 17: </span>Measured undamped and damped FRF" >}}
+
+
+### Conclusion {#conclusion}
+
+This chapter shows an approach to add damping to a range of resonances of a motion stage by adding robust mass dampers.
+Analysis is performed to calculate the damping increase beforehand, and experiments are conducted to validate the behavior of both the damper and the stage with dampers added.
+
+The broadbanded solution shows a resonance suppression of at least 24.3dB between 1kHz and 4kHz.
+The overall mass increase is less than 2%.
+
+The robustness, as one of the most important properties of the RMD, is proven: the suppression factor is well predictable despite different errors and estimations:
+
+-   stage model errors (the natural frequencies resulting from the FEM are an overestimation of the real frequencies)
+-   fluid model errors
+-   a simplified 1DoF model is applied as a damper model
+-   production tolerances for the dampers
+
+Tuned mass dampers are well known in literature.
+The equations are proven to calculate the optimal suppression factor, natural frequency and damping ratio.
+In these equations, the damper behavior is assumed to be purely viscous.
+We shows that larger suppression factors are possible by using visco-elastic fluids as damping medium.
+Although this effect is relatively small for single resonance suppression, it is larger for broadbanded suppression.
+The damper benefits from the frequency dependent stiffness of the fluid.
+
+
+## Conclusion {#conclusion}
+
+In this thesis, the opportunities to increase the performance of high-tech motion systems are investigated by increasing the modal damping of non-rigid body resonances by introducing robust mass dampers (RMD), which provides damping over a broad frequency band.
+A combination of techniques is applied to improve the performance of motion stages in a systematical way, including mechanical design, dynamic modeling, material characterization and optimization procedures.
+Theoretical improvement factors are calculated and experimental validation is provided to support the theory.
+The main conclusions of the previous chapters are summarized and listed by subject.
+
+
+### Robust Mass Dampers {#robust-mass-dampers}
+
+Robust mass dampers have proven to be able to provide **broad banded damping**.
+In addition, **robust behavior** is proven in case of parameter variations of both the motion stage and/or the parameters of the RMDs.
+This property explicitly underlines the suitability of RMDs to improve the behavior of motion stages that are operated in closed-loop conditions: parameter sensitive designs will result in a performance decrease and might eventually lead to destabilization of the closed-loop system.
+
+The RMDs in this thesis are **passive and stand-alone devices**.
+Advantages of these types of devices are
+
+1.  the stabilizing behavior due to the principle of energy dissipation.
+2.  The stand-alone property implies that no connection between any structural part and the motion stage is created, and no signal or power cables are needed which prevents the introduction of disturbance forces.
+3.  The damper design by application of LVE behavior enables larger suppression factors than purely viscous fluid behavior.
+
+At least in case of motion stages with a relatively large length-height ratio it appears that an overall mass contribution by the RMDs of 2 % of the stage mass is sufficient to improve the stage performance significantly.
+This is proven by experiments.
+
+
+### Influence on stage dynamics {#influence-on-stage-dynamics}
+
+The relatively high modal damping of the RMDs prevents for visible effects in the rigid body mass line of the frequency response functions.
+In other directions, the natural frequencies of the RMDs can be designed above 6 kHz for dampers of 65 g.
+This is usually high enough to prevent for detrimental properties in the direction of motion
+
+
+### RMD locations {#rmd-locations}
+
+The **location of an RMD on the mechanical stage is a significant factor in the performance increase factor**.
+The effectiveness of the RMD to improve the modal damping factor scales quadratically with the stage displacement at the damper location.
+Therefore, if the limiting natural frequencies are determined, **the locations with large displacements for the corresponding mode shapes have to be found**.
+In case of more than one resonance this might be a weighted criterion for the different modes.
+This approach is applicable for both open- loop and closed-loop performance criteria.
+
+
+### The fluid model {#the-fluid-model}
+
+A **linear visco-elastic fluid model** is derived from measurements and applied in the optimization formulations.
+The results show that the model quality is good enough to predict the system’s damped behavior quite accurately.
+
+
+### Open-loop modal damping improvement {#open-loop-modal-damping-improvement}
+
+The principle of **broad banded damping** is well applicable for practical cases: the intended damping range was 1-4 kHz.
+In addition, a damping increase is visible up to 6 kHz.
+This frequency range abundantly covers the range in which performance limiting flexibilities usually arise in motion stage designs.
+An optimization criterion in terms of resonance suppression is applied and works well: this criterion inherently only optimizes the visible resonances at the actuator and sensor location.
+The choice which resonances should be suppressed, therefore, is specified in the cost function by the frequency response function.
+Robustness of the solution and broad banded effect in practical cases is proven by the experimental validation.
+The calculated suppression factor compares well to the measured ones.
+The suppression factor amounts approximately 24 dB between 1 and 4 kHz, which indicates a modal damping increase factor of 16.
+
+
+### Closed-loop performance increase {#closed-loop-performance-increase}
+
+The principle of closed-loop performance increase is formulated in an optimization formulation which accurately estimates the bandwidth improvement factor.
+The optimization formulation is non-convex, however, a hybrid optimization procedure is able to solve this specific problem in a limited amount of time.
+In addition to the improvements in the intended control loops, other control loops often benefit from the damping increase.
+
+
+### Advantages in analysis {#advantages-in-analysis}
+
+A more general observation regarding the analyses method is presented.
+The approach with separate RMDs is an efficient approach which contains two large advantages: It enables to continue with the current applied mechanical design approach for high natural frequencies and increase the modal damping afterwards.
+This enables to still apply the materials with high specific stiffness and low damping.
+
+In the analysis phase the advantages are enormous:
+
+1.  Undamped natural frequencies and mode shapes can be calculated and are valid for the low damped stage’s mechanical design.
+    These algorithms are very efficient and large models can be solved.
+2.  State space models can be created which contain the complexity of the FEM model and can be validated by calculating the responses by means of superposition of the undamped modes in the FEM software.
+3.  RMDs can be added at specific locations.
+    This results in non-proportional damping and complex mode shapes, which are correctly calculated by the state space model.
+4.  This enables to apply optimization algorithms and compare different RMDs very quickly.
+
+The complete model including dampers can be solved in FEM, however, this approach contains serious drawbacks:
+
+1.  The mode shapes change from real normal modes to complex modes due to the damping at specific locations.
+    This implies that complex solvers have to be applied.
+    These solvers are much more time consuming than the solvers for real natural modes.
+2.  The frequency response functions can be calculated using fully harmonic solvers.
+    This results in the most accurate solution because the model is not truncated as in case of a state space model with a limited number of modes.
+    However, this algorithm solves the complete model for every frequency point in the frequency response function and, therefore, this approach is extremely time-consuming.
+3.  Therefore, in this approach the ability to implement different RMD parameters and execute optimization algorithms practically vanishes due to the limitations listed above.
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Verbaan, C.A.M. 2015. “Robust mass damper design for bandwidth increase of motion stages.” Mechanical Engineering; Technische Universiteit Eindhoven.</div>
+</div>

content/phdthesis/wang07_dynam_model_exper_ident_activ.md

@@ -0,0 +1,25 @@
++++
+title = "Dynamic modeling, experimental identification, and active vibration control design of a smart parallel manipulator."
+author = ["Thomas Dehaeze"]
+draft = true
+ref_author = "Wang, X."
+ref_year = 2007
++++
+
+Tags
+:
+
+
+Reference
+: ([Wang 2007](#orgdaa802c))
+
+Author(s)
+: Wang, X.
+
+Year
+: 2007
+
+
+## Bibliography {#bibliography}
+
+<a id="orgdaa802c"></a>Wang, Xiaoyun. 2007. “Dynamic Modeling, Experimental Identification, and Active Vibration Control Design of a Smart Parallel Manipulator.” University of Toronto.

content/phdthesis/zuo04_elemen_system_desig_activ_passiv_vibrat_isolat.md

@@ -0,0 +1,78 @@
++++
+title = "Element and system design for active and passive vibration isolation"
+author = ["Dehaeze Thomas"]
+draft = false
+ref_author = "Zuo, L."
+ref_year = 2004
++++
+
+Tags
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Eddy Current Damping]({{< relref "eddy_current_damping.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Zuo 2004</a>)
+
+Author(s)
+: Zuo, L.
+
+Year
+: 2004
+
+> Vibration isolation systems can have various system architectures.
+> When we configure an active isolation system, we can use compliant actuators (such as voice coils) or stiff actuators (such as PZT stacks).
+> We also need to consider how to **combine the active actuation with passive elements**: we can place the actuator in parallel or in series with the passive elements.
+> Most of the isolation systems fall into the category of soft active mounts, in which a compliant actuator is placed in parallel with a spring.
+> A second category is **hard active mounts**, in which the **payload mass is directly mounted to a stiff actuator**.
+> Soft active mounts generally have advantages for better passive performance; hard active mounts are favored for payload disturbance rejection, but combination with passive stages is required due to the lack of isolation performance out of the control bandwidth.
+> Beard, von Flotow and Schubert proposed another type of hard mount, wherein **a stiff PZT actuator is placed in series with a spring** stiffer than the top passive stage.
+> They found that coupling from flexible modes is much smaller than in soft active mounts in the load (force) feedback.
+> Note that reaction force actuators can also work with soft mounts or hard mounts.
+
+
+## Passive Vibration Isolation {#passive-vibration-isolation}
+
+
+### The Role of damping and its practical constructions {#the-role-of-damping-and-its-practical-constructions}
+
+
+#### Viscous damping {#viscous-damping}
+
+
+#### Eddy-current damper {#eddy-current-damper}
+
+<a id="figure--fig:zuo04-eddy-current-magnets"></a>
+
+{{< figure src="/ox-hugo/zuo04_eddy_current_magnets.png" caption="<span class=\"figure-number\">Figure 1: </span>(left) Magnetic field and conductor plates assemblies, (right) magnet arrays" >}}
+
+<a id="figure--fig:zuo04-eddy-current-setup"></a>
+
+{{< figure src="/ox-hugo/zuo04_eddy_current_setup.png" caption="<span class=\"figure-number\">Figure 2: </span>Single DoF system damped by eddy current damper" >}}
+
+
+## Elements and configurations for active vibration systems {#elements-and-configurations-for-active-vibration-systems}
+
+
+### System architectures {#system-architectures}
+
+<a id="figure--fig:zuo04-piezo-spring-series"></a>
+
+{{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="<span class=\"figure-number\">Figure 3: </span>PZT actuator and spring in series" >}}
+
+<a id="figure--fig:zuo04-voice-coil-spring-parallel"></a>
+
+{{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="<span class=\"figure-number\">Figure 4: </span>Voice coil actuator and spring in parallel" >}}
+
+<a id="figure--fig:zuo04-piezo-plant"></a>
+
+{{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="<span class=\"figure-number\">Figure 5: </span>Transmission from PZT voltage to geophone output" >}}
+
+<a id="figure--fig:zuo04-voice-coil-plant"></a>
+
+{{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="<span class=\"figure-number\">Figure 6: </span>Transmission from voice coil voltage to geophone output" >}}
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Zuo, Lei. 2004. “Element and System Design for Active and Passive Vibration Isolation.” Massachusetts Institute of Technology.</div>
+</div>

content/posts/test.md

@@ -1,6 +1,6 @@
 +++
 title = "First Blog Post"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 date = 2021-04-23T00:00:00+02:00
 tags = ["hugo", "org"]
 categories = ["emacs", "test"]
@@ -17,7 +17,7 @@ This is a test for a blog post.
 
 You can make words **bold**, _italic_, <span class="underline">underlined</span>, `verbatim` and `code`, and, if you must, ~~strike-through~~.
 
-Here is some inline code Matlab code: `[K,CL,gamma] = mixsyn(G,W1,[],W3);`.
+Here is some inline code Matlab code: <span class="inline-src language-matlab" data-lang="matlab">`[K,CL,gamma] = mixsyn(G,W1,[],W3);`</span>.
 
 
 ### Links to Footnotes {#links-to-footnotes}
@@ -89,15 +89,15 @@ Unumbered equation:
 
 Using the `equation` environment in Eq. \eqref{eq:numbered}.
 
-\begin{equation}
+\begin{equation} \label{eq:numbered}
-  F(s) = \int\_0^\infty f(t) e^{-st} dt \label{eq:numbered}
+  F(s) = \int\_0^\infty f(t) e^{-st} dt
 \end{equation}
 
-Using the `align` environment Equations \eqref{eq:align_1} and \eqref{eq:align_2}.
+Using the `align` environment Equations \eqref{eq:align\_1} and \eqref{eq:align\_2}.
 
 \begin{align}
-  \mathcal{F}(a) &= \frac{1}{2\pi i}\oint\_\gamma \frac{f(z)}{z - a}\,dz \label{eq:align\_1} \\\\\\
+  \mathcal{F}(a) &= \frac{1}{2\pi i}\oint\_\gamma \frac{f(z)}{z - a}\\,dz \label{eq:align\_1} \\\\
-  \int\_D (\nabla\cdot \mathcal{F})\,dV &=\int\_{\partial D}\mathcal{F}\cdot n\, dS \label{eq:align\_2}
+  \int\_D (\nabla\cdot \mathcal{F})\\,dV &=\int\_{\partial D}\mathcal{F}\cdot n\\, dS \label{eq:align\_2}
 \end{align}
 
 
@@ -105,13 +105,15 @@ Using the `align` environment Equations \eqref{eq:align_1} and \eqref{eq:align_2
 
 Below is a verse.
 
-<p class="verse">
+<div class="verse">
+
 Great clouds overhead<br />
 Tiny black birds rise and fall<br />
 Snow covers Emacs<br />
 <br />
 &nbsp;&nbsp;&nbsp;---AlexSchroeder<br />
-</p>
+
+</div>
 
 Below is a quote.
 
@@ -127,7 +129,6 @@ Below is a quote.
 An aside block can be used as shown below.
 
 <aside>
-  <aside></aside>
 
 This is a note about the text using the `aside` environment.
 This can be as long as wanted