Update Content - 2025-07-18

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

.gitignore

@@ -1,2 +1,4 @@
 nohup.out
-
+resources/
+public/
+static/ltximg/

config.toml

@@ -26,11 +26,11 @@ changefreq = "weekly"
 priority = 0.5
 filename = "sitemap.xml"
 
-[[menu.main]]
-name = "Home"
-weight = 10
-identifier = "home"
-url = "/"
+# [[menu.main]]
+# name = "Home"
+# weight = 10
+# identifier = "home"
+# url = "/"
 
 [[menu.main]]
 name = "Zettels"
@@ -44,6 +44,12 @@ weight = 50
 identifier = "bibliography"
 url = "/bibliography/"
 
+[[menu.main]]
+name = "Dotfiles"
+weight = 60
+identifier = "dotfiles"
+url = "https://dotfiles.tdehaeze.xyz/"
+
 [[menu.main]]
 name = "Search"
 weight = 70
@@ -106,8 +112,6 @@ uglyURLs = false
 enable = true
 jquery = '<script src="https://cdn.jsdelivr.net/npm/jquery@3.2.1/dist/jquery.min.js" integrity="sha256-hwg4gsxgFZhOsEEamdOYGBf13FyQuiTwlAQgxVSNgt4=" crossorigin="anonymous"></script>'
 slideout = '<script src="https://cdn.jsdelivr.net/npm/slideout@1.0.1/dist/slideout.min.js" integrity="sha256-t+zJ/g8/KXIJMjSVQdnibt4dlaDxc9zXr/9oNPeWqdg=" crossorigin="anonymous"></script>'
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-fancyboxCSS = '<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/@fancyapps/fancybox@3.1.20/dist/jquery.fancybox.min.css" integrity="sha256-7TyXnr2YU040zfSP+rEcz29ggW4j56/ujTPwjMzyqFY=" crossorigin="anonymous">'
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 timeagoLocalesJS = '<script src="https://cdn.jsdelivr.net/npm/timeago.js@3.0.2/dist/timeago.locales.min.js" integrity="sha256-ZwofwC1Lf/faQCzN7nZtfijVV6hSwxjQMwXL4gn9qU8=" crossorigin="anonymous"></script>'
 
@@ -117,21 +121,9 @@ enable = false
 hint = 30
 warn = 180
 
-[params.gitment]          # Gitment is a comment system based on GitHub issues. see https://github.com/imsun/gitment
-owner = ""              # Your GitHub ID
-repo = ""               # The repo to store comments
-clientId = ""           # Your client ID
-clientSecret = ""       # Your client secret
-
-[params.utterances]       # https://utteranc.es/
-owner = ""              # Your GitHub ID
-repo = ""               # The repo to store comments
-
-[params.gitalk]           # Gitalk is a comment system based on GitHub issues. see https://github.com/gitalk/gitalk
-owner = ""              # Your GitHub ID
-repo = ""               # The repo to store comments
-clientId = ""           # Your client ID
-clientSecret = ""       # Your client secret
+# [params.utterances]       # https://utteranc.es/
+# repo = "tdehaeze/brain-dump-comments"
+# theme = "boxy-light"
 
 [params.valine]
 enable = false

content/article/abir16_optim_estim_real_time_dynam.md

@@ -0,0 +1,23 @@
++++
+title = "Optimized estimator for real-time dynamic displacement measurement using accelerometers"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: ([Abir et al. 2016](#org1dabfe9))
+
+Author(s)
+: Abir, J., Longo, S., Morantz, P., & Shore, P.
+
+Year
+: 2016
+
+
+## Bibliography {#bibliography}
+
+<a id="org1dabfe9"></a>Abir, Jonathan, Stefano Longo, Paul Morantz, and Paul Shore. 2016. “Optimized Estimator for Real-Time Dynamic Displacement Measurement Using Accelerometers.” _Mechatronics_ 39 (nil):1–11. <https://doi.org/10.1016/j.mechatronics.2016.07.003>.

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
-: <sup id="279b5558de3a8131b329a9ba1a99e4f8"><a class="reference-link" href="#alkhatib03_activ_struc_vibrat_contr" title="Rabih Alkhatib \&amp; Golnaraghi, Active Structural Vibration Control: a Review, {The Shock and Vibration Digest}, v(5), 367-383 (2003).">(Rabih Alkhatib \& Golnaraghi, 2003)</a></sup>
+: (<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](#orgb7a9ee5).
+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="orgb7a9ee5"></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="org352d1a3"></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](#org352d1a3), 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:
@@ -224,5 +224,9 @@ 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
-<a class="bibtex-entry" id="alkhatib03_activ_struc_vibrat_contr">Alkhatib, R., & Golnaraghi, M. F., *Active structural vibration control: a review*, The Shock and Vibration Digest, *35(5)*, 367–383 (2003).  http://dx.doi.org/10.1177/05831024030355002</a> [↩](#279b5558de3a8131b329a9ba1a99e4f8)
+
+## 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>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
-: <sup id="5b41da575e27e6e86f1a1410a0170836"><a class="reference-link" href="#bibel92_guidel_h" title="Bibel \&amp; Malyevac, Guidelines for the selection of weighting functions for  H-infinity control, NAVAL SURFACE WARFARE CENTER DAHLGREN DIV VA, (1992).">(Bibel \& Malyevac, 1992)</a></sup>
+: (<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="org5999225"></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](#org5999225), 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)\\\\\\
-e(s) &= S(s) r(s) - S(s) d(s) - S(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)\\\\
 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
--   **Disturbance rejection**: \\(S=0\\) => large gains
+-   **Command following**: \\(S=0\\) and \\(T=1\\) =&gt; 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="org4e0009c"></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](#org4e0009c)): \\(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](#org4e0009c)): \\(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](#orgdd8fae0)).
+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="orgdd8fae0"></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](#org0d13a20)).
+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="org0d13a20"></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](#org45b0983).
+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="org45b0983"></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}
@@ -181,5 +175,9 @@ 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
-<a class="bibtex-entry" id="bibel92_guidel_h">Bibel, J. E., & Malyevac, D. S., *Guidelines for the selection of weighting functions for h-infinity control* (1992).</a> [↩](#5b41da575e27e6e86f1a1410a0170836)
+
+## 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>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

@@ -1,14 +1,15 @@
 +++
 title = "Control of spacecraft and aircraft"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-: [HAC-HAC]({{< relref "hac_hac" >}})
+:
+
 
 Reference
-: <sup id="4970865a21830fff7b1daeec187bfa68"><a class="reference-link" href="#bryson93_contr_spacec_aircr" title="Bryson, Control of Spacecraft and Aircraft, Princeton university press Princeton, New Jersey (1993).">(Bryson, 1993)</a></sup>
+: (<a href="#citeproc_bib_item_1">Bryson 1993</a>)
 
 Author(s)
 : Bryson, A. E.
@@ -19,6 +20,8 @@ Year
 
 ## 9.2.3 Roll-Off Filters {#9-dot-2-dot-3-roll-off-filters}
 
+[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.
 > This reduces the possibility of destabilizing the unmodelled higher frequency dynamics ("**spillover**").
@@ -35,17 +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 {#9-dot-5-dot-2-low-authority-control-high-authority-control}
+## 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="orgdde3e8f"></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
-<a class="bibtex-entry" id="bryson93_contr_spacec_aircr">Bryson, A. E., *Control of spacecraft and aircraft* (1993), : Princeton university press Princeton, New Jersey.</a> [↩](#4970865a21830fff7b1daeec187bfa68)
+
+## 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>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"]
-draft = false
+author = ["Dehaeze Thomas"]
+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
-: <sup id="6a014e3a2ee3e41d20bd0644654c56f0"><a class="reference-link" href="#butler11_posit_contr_lithog_equip" title="Hans Butler, Position Control in Lithographic Equipment, {IEEE Control Systems}, v(5), 28-47 (2011).">(Hans Butler, 2011)</a></sup>
+: (<a href="#citeproc_bib_item_1">Butler 2011</a>)
 
 Author(s)
 : Butler, H.
@@ -16,5 +16,9 @@ Author(s)
 Year
 : 2011
 
-# Bibliography
-<a class="bibtex-entry" id="butler11_posit_contr_lithog_equip">Butler, H., *Position control in lithographic equipment*, IEEE Control Systems, *31(5)*, 28–47 (2011).  http://dx.doi.org/10.1109/mcs.2011.941882</a> [↩](#6a014e3a2ee3e41d20bd0644654c56f0)
+
+## 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>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

@@ -1,19 +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
-: <sup id="ba05ff213f8e5963d91559d95becfbdb"><a class="reference-link" href="#chen00_ident_decoup_contr_flexur_joint_hexap" title="Yixin Chen \&amp; McInroy, Identification and Decoupling Control of Flexure Jointed  Hexapods, nil, in in: {Proceedings 2000 ICRA. Millennium Conference. IEEE
-                      International Conference on Robotics and Automation. Symposia
-                      Proceedings (Cat. No.00CH37065)}, edited by (2000)">(Yixin Chen \& McInroy, 2000)</a></sup>
+: (<a href="#citeproc_bib_item_1">Chen and McInroy 2000</a>)
 
 Author(s)
-: Chen, Y., & McInroy, J.
+: Chen, Y., &amp; McInroy, J.
 
 Year
 : 2000
@@ -33,7 +31,7 @@ Year
 
 ## Introduction {#introduction}
 
-Typical decoupling algorithm 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
@@ -45,12 +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 <sup id="5da427f78c552aa92cd64c2a6df961f1"><a class="reference-link" href="#mcinroy99_dynam" title="McInroy, Dynamic modeling of flexure jointed hexapods for control  purposes, nil, in in: {Proceedings of the 1999 IEEE International Conference on
-                  Control Applications (Cat. No.99CH36328)}, edited by (1999)">(McInroy, 1999)</a></sup> ([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="org81e0a96"></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:
 
@@ -59,9 +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}} + \\\\\\
-  & {}^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}} - \\\\\\
+  & \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 \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}
 
@@ -82,7 +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}
 
@@ -102,7 +99,10 @@ where
 
 ## Experimental Results {#experimental-results}
 
-# Bibliography
-<a class="bibtex-entry" id="chen00_ident_decoup_contr_flexur_joint_hexap">Chen, Y., & McInroy, J., *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) (pp. ) (2000). : .</a> [↩](#ba05ff213f8e5963d91559d95becfbdb)
 
-<a class="bibtex-entry" id="mcinroy99_dynam">McInroy, J., *Dynamic modeling of flexure jointed hexapods for control purposes*, In , Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) (pp. ) (1999). : .</a> [↩](#5da427f78c552aa92cd64c2a6df961f1)
+## 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>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>
+  <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

@@ -0,0 +1,23 @@
++++
+title = "Decoupled control of flexure-jointed hexapods using estimated joint-space mass-inertia matrix"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+: [Decoupled Control]({{<relref "decoupled_control.md#" >}})
+
+Reference
+: ([Chen and McInroy 2004](#org1a36c5c))
+
+Author(s)
+: Chen, Y., & McInroy, J.
+
+Year
+: 2004
+
+
+
+## Bibliography {#bibliography}
+
+<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/chesne16_enhan_dampin_flexib_struc_using_force_feedb.md

@@ -0,0 +1,91 @@
++++
+title = "Enhanced damping of flexible structures using force feedback"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Active Damping]({{< relref "active_damping" >}}), [Integral Force Feedback]({{< relref "integral_force_feedback" >}})
+
+Reference
+: ([Chesné, Milhomem, and Collette 2016](#org2953ca1))
+
+Author(s)
+: Simon Chesné, Milhomem, A., & Collette, C.
+
+Year
+: 2016
+
+One problem of Integral Force Feedback (IFF) is that the achievable damping decreases at high frequency.
+A modification of the IFF is proposed in order to significantly increase the damping of **a** selected mode.
+
+The test system is shown in Figure [1](#org9c0dbe3).
+
+Classical IFF corresponds to:
+
+\begin{equation}
+H(s) = \frac{g}{s}
+\end{equation}
+
+<a id="org9c0dbe3"></a>
+
+{{< figure src="/ox-hugo/chesne16_2dof_system.png" caption="Figure 1: Two DoF system representing a flexible structuer controlled by an active mount" >}}
+
+The proposed controller, called **alpha controller** is:
+
+\begin{equation}
+H(s) = g \frac{s + \alpha}{s^2}
+\end{equation}
+
+where \\(\alpha\\) is a parameter.
+
+A new pair of pole/zero has been introduced.
+The new pole is located at \\(s = 0\\) and the zeros at \\(s = -\alpha\\).
+
+For \\(\omega > \alpha\\) the controller is essentially an integrator.
+For \\(\omega < \alpha\\) the controller is a double integrator.
+
+Depending on the chosen \\(\alpha\\) we obtain different root locus as shown in Figure [2](#org08e7f67).
+There is an optimal gain \\(\alpha^\star\\) at which the attainable damping of the flexible mode is maximized.
+
+<a id="org08e7f67"></a>
+
+{{< figure src="/ox-hugo/chesne16_root_locus_alpha.png" caption="Figure 2: Root locus with the alpha controller for different values of \\(\alpha\\)" >}}
+
+The obtained transmissibility is shown without controller, for classical IFF and for \\(\alpha\\) controller in Figure [3](#org2c2d3d7).
+
+Using the \\(\alpha\\) controller, the compliance is however degraded a lot.
+
+<a id="org2c2d3d7"></a>
+
+{{< figure src="/ox-hugo/chesne16_transmissibility.png" caption="Figure 3: Transmissibility \\(x\_1/x\_0\\)" >}}
+
+In order to recover the compliance at low frequency, high pass filters can be added to the controller.
+
+\begin{equation}
+H(s) = g \frac{s + \alpha}{(s + \beta)^2}
+\end{equation}
+
+The condition for stability found here is:
+
+\begin{equation}
+\alpha \ge \beta/2
+\end{equation}
+
+<div class="sum">
+  <div></div>
+
+The active damping of flexible structures with collocated force sensor/actuator pairs have been reviewed in this Note.
+In the first part of the Note, two limitations of the integral force feedback (IFF) have been discussed, which are the limited damping of flexible modes and the loss of compliance.
+By slightly modifying the controller, it has been shown that the active damping of a target mode can be significantly increased.
+Analytical formulas of the optimal parameters have been derived.
+In the second part, the loss of compliance inherent to IFF has been addressed.
+It has been shown that, when a high-pass filter is inserted into the IFF controller, the compliance at low frequency can be recovered but the unconditional stability is lost.
+On the other side, with the new proposed control law, the stability is always guaranteed even when using a high-pass filter.
+
+</div>
+
+
+## Bibliography {#bibliography}
+
+<a id="org2953ca1"></a>Chesné, Simon, Ariston Milhomem, and Christophe Collette. 2016. “Enhanced Damping of Flexible Structures Using Force Feedback.” _Journal of Guidance, Control, and Dynamics_ 39 (7):1654–58. <https://doi.org/10.2514/1.g001620>.

content/article/claeyssen07_amplif_piezoel_actuat.md

@@ -1,21 +1,41 @@
 +++
 title = "Amplified piezoelectric actuators: static & dynamic applications"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
 +++
 
 Tags
-:
-
+: [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}})
 
 Reference
-: <sup id="5decd2b31c4a9842b80c58b56f96590a"><a class="reference-link" href="#claeyssen07_amplif_piezoel_actuat" title="Frank Claeyssen, Le Letty, Barillot, \&amp; Sosnicki, Amplified Piezoelectric Actuators: Static \&amp; Dynamic  Applications, {Ferroelectrics}, v(1), 3-14 (2007).">(Frank Claeyssen {\it et al.}, 2007)</a></sup>
+: (<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
 
-# Bibliography
-<a class="bibtex-entry" id="claeyssen07_amplif_piezoel_actuat">Claeyssen, F., Letty, R. L., Barillot, F., & Sosnicki, O., *Amplified piezoelectric actuators: static \& dynamic applications*, Ferroelectrics, *351(1)*, 3–14 (2007).  http://dx.doi.org/10.1080/00150190701351865</a> [↩](#5decd2b31c4a9842b80c58b56f96590a)
+The amplified piezo actuator APA is an external leveraged actuator based on a shell used both for the ceramic **pre stress** and for the ceramic **motion magnification**.
+
+It is based on low voltage multilayer piezoelectric ceramics (PZT type).
+In static conditions, their free strain \\(S\_p\\) is typically 0.1% when driven at 150 V.
+
+The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
+The flatter is the actuator, the higher is the amplification.
+
+Piezoceramics can bear large compressive stress but they can not bear tensile forces with a good reliability.
+The usual way to solve this limitation consists in prestressing the ceramics by maintaining a compressive stress.
+This introduces another force limit: if the internal dynamic forces are above the prestress, the actuator is endangered because of the ceramic goes in tensile stress and also the ceramic stack looses contact with the shell interface.
+
+For many APA actuators, the amplitude of maximal applicable external force is close to half the actuator blocked force.
+
+The maximum dynamic force achievable by the actuator is determined by the prestress.
+The prestress design allows a peak force equal to half the blocked force.
+
+
+## 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>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
-: <sup id="2d69d483f210ca387ca8061596ec27ea"><a class="reference-link" href="#collette11_review_activ_vibrat_isolat_strat" title="Christophe Collette, Stef Janssens \&amp; Kurt Artoos, Review of Active Vibration Isolation Strategies, {Recent Patents on Mechanical Engineeringe}, v(3), 212-219 (2011).">(Christophe Collette {\it et al.}, 2011)</a></sup>
+: (<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
@@ -22,12 +22,11 @@ Year
 
 ### Passive Isolation Tradeoffs {#passive-isolation-tradeoffs}
 
-<div class="cbox">
-  <div></div>
+1DoF Equations:
 
-\\[ X(s) = \underbrace{\frac{cs + k}{ms^2 + cs + k}}\_{T\_{wx}(s)} W(s) + \underbrace{\frac{1}{ms^2 + cs + k}}\_{T\_{Fx}(s)} F(s) \\]
-
-</div>
+\begin{equation}
+\boxed{X(s) = \underbrace{\frac{cs + k}{ms^2 + cs + k}}\_{T\_{wx}(s)} W(s) + \underbrace{\frac{1}{ms^2 + cs + k}}\_{T\_{Fx}(s)} F(s)}
+\end{equation}
 
 -   \\(T\_{wx}(s)\\) is called the **transmissibility** of the isolator. It characterize the way seismic vibrations \\(w\\) are transmitted to the equipment.
 -   \\(T\_{Fx}(s)\\) is called the **compliance**. It characterize the capacity of disturbing forces \\(F\\) to create motion \\(x\\) of the equipment.
@@ -52,7 +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>
 
@@ -71,9 +70,13 @@ The general expression of the force delivered by the actuator is \\(f = g\_a \dd
 
 ## Conclusions {#conclusions}
 
-<a id="org4270456"></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
-<a class="bibtex-entry" id="collette11_review_activ_vibrat_isolat_strat">Collette, C., Janssens, S., & Artoos, K., *Review of active vibration isolation strategies*, Recent Patents on Mechanical Engineeringe, *4(3)*, 212–219 (2011).  http://dx.doi.org/10.2174/2212797611104030212</a> [↩](#2d69d483f210ca387ca8061596ec27ea)
+
+## 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>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

@@ -1,18 +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
-: <sup id="1223611da2f9b157af97503a4fec7631"><a class="reference-link" href="#collette14_vibrat" title="Collette \&amp; Matichard, Vibration control of flexible structures using fusion of  inertial sensors and hyper-stable actuator-sensor pairs, in in: {International Conference on Noise and Vibration Engineering
-                      (ISMA2014)}, edited by (2014)">(Collette \& Matichard, 2014)</a></sup>
+: (<a href="#citeproc_bib_item_1">Collette and Matichard 2014</a>)
 
 Author(s)
-: Collette, C., & Matichard, F.
+: Collette, C., &amp; Matichard, F.
 
 Year
 : 2014
@@ -20,7 +19,7 @@ Year
 
 ## Introduction {#introduction}
 
-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
@@ -29,7 +28,7 @@ Sensor fusion is used  to combine the benefits of different types of sensors:
 
 ## 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:
 >
@@ -39,24 +38,24 @@ 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>
 
 | Sensors          | Advantages                       | Disadvantages                         |
 |------------------|----------------------------------|---------------------------------------|
-| Relative motion  | Servo-position                   | No isolation from gorund motion       |
+| Relative motion  | Servo-position                   | No isolation from ground motion       |
 | Force sensors    | Improve isolation                | Increase compliance                   |
 | Inertial sensors | Improve isolation and compliance | AC couple and noisy at high frequency |
 
 
 ## 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>
 
@@ -100,5 +99,9 @@ Three types of sensors have been considered for the high frequency part of the f
 -   The fusion with an **accelerometre** is used to increase the loop gain. However, as the accelerometer is not dual with the actuator, there is no guaranty stability when the isolation stage is mounted on a flexible support.
 -   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
-<a class="bibtex-entry" id="collette14_vibrat">Collette, C., & Matichard, F., *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) (pp. ) (2014). : .</a> [↩](#1223611da2f9b157af97503a4fec7631)
+
+## 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>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

@@ -1,22 +1,22 @@
 +++
 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
-: <sup id="7772841a8f05142ec30f0f6daae20932"><a class="reference-link" href="#collette15_sensor_fusion_method_high_perfor" title="Collette \&amp; Matichard, Sensor Fusion Methods for High Performance Active Vibration  Isolation Systems, {Journal of Sound and Vibration}, v(nil), 1-21 (2015).">(Collette \& Matichard, 2015)</a></sup>
+: (<a href="#citeproc_bib_item_1">Collette and Matichard 2015</a>)
 
 Author(s)
-: Collette, C., & Matichard, F.
+: Collette, C., &amp; Matichard, F.
 
 Year
 : 2015
 
-In order to have good stability margins, it is common practice to collocate sensors and actuators. This ensures alternating poles and zeros along the imaginary axis. Then, each phase lag introduced by the poles is compensed by phase leag introduced by the zeroes. This guarantees stability and such system is referred to as **hyperstable**.
+In order to have good stability margins, it is common practice to collocate sensors and actuators. This ensures alternating poles and zeros along the imaginary axis. Then, each phase lag introduced by the poles is compensated by phase lead introduced by the zeroes. This guarantees stability and such system is referred to as **hyperstable**.
 
 In this paper, we study and compare different sensor fusion methods combining inertial sensors at low frequency with sensors adding stability at high frequency.
 The stability margins of the controller can be significantly increased with no or little effect on the low-frequency active isolation, provided that the two following conditions are fulfilled:
@@ -24,5 +24,9 @@ The stability margins of the controller can be significantly increased with no o
 -   the high frequency sensor and the actuator are dual
 -   there exists a bandwidth where we can superimpose the open loop transfer functions obtained with the two sensors.
 
-# Bibliography
-<a class="bibtex-entry" id="collette15_sensor_fusion_method_high_perfor">Collette, C., & Matichard, F., *Sensor fusion methods for high performance active vibration isolation systems*, Journal of Sound and Vibration, *342(nil)*, 1–21 (2015).  http://dx.doi.org/10.1016/j.jsv.2015.01.006</a> [↩](#7772841a8f05142ec30f0f6daae20932)
+
+## 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>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

@@ -1,37 +1,41 @@
 +++
 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
-: <sup id="ad17e03f0fbbcc1a070557d7b5a0e1e1"><a class="reference-link" href="#dasgupta00_stewar_platf_manip" title="Bhaskar Dasgupta \&amp; Mruthyunjaya, The Stewart Platform Manipulator: a Review, {Mechanism and Machine Theory}, v(1), 15-40 (2000).">(Bhaskar Dasgupta \& Mruthyunjaya, 2000)</a></sup>
+: (<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>
 
 |              | **Advantages**            | **Disadvantages**     |
 |--------------|---------------------------|-----------------------|
-| **Serial**   | Manoeuverability          | Poor precision        |
+| **Serial**   | Maneuverability           | Poor precision        |
 |              | Large workspace           | Bends under high load |
 |              |                           | Vibrate at high speed |
 | **Parallel** | High stiffness            | Small workspace       |
 |              | Good dynamic performances |                       |
 |              | Precise positioning       |                       |
 
-The generalized Stewart platforms consists of two rigid bodies (referred to as the base and the platoform) connected through six extensible legs, each with sherical joints at both ends.
+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
-<a class="bibtex-entry" id="dasgupta00_stewar_platf_manip">Dasgupta, B., & Mruthyunjaya, T., *The stewart platform manipulator: a review*, Mechanism and Machine Theory, *35(1)*, 15–40 (2000).  http://dx.doi.org/10.1016/s0094-114x(99)00006-3</a> [↩](#ad17e03f0fbbcc1a070557d7b5a0e1e1)
+
+## 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>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
 +++
 
@@ -9,22 +9,26 @@ Tags
 
 
 Reference
-: <sup id="8ce53b8a612ce8ae3eb616cd1ed05630"><a class="reference-link" href="#devasia07_survey_contr_issues_nanop" title="Devasia, Eleftheriou, Moheimani \&amp; SO Reza, A Survey of Control Issues in Nanopositioning, {IEEE Transactions on Control Systems Technology}, v(5), 802--823 (2007).">(Devasia {\it et al.}, 2007)</a></sup>
+: (<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: 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="org103305d"></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
-<a class="bibtex-entry" id="devasia07_survey_contr_issues_nanop">Devasia, S., Eleftheriou, E., & Moheimani, S. R., *A survey of control issues in nanopositioning*, IEEE Transactions on Control Systems Technology, *15(5)*, 802–823 (2007). </a> [↩](#8ce53b8a612ce8ae3eb616cd1ed05630)
+
+## 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>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
-: <sup id="c823f68dd2a72b9667a61b3c046b4731"><a class="reference-link" href="#fleming10_nanop_system_with_force_feedb" title="Fleming, Nanopositioning System With Force Feedback for  High-Performance Tracking and Vibration Control, {IEEE/ASME Transactions on Mechatronics}, v(3), 433-447 (2010).">(Fleming, 2010)</a></sup>
+: (<a href="#citeproc_bib_item_1">Fleming 2010</a>)
 
 Author(s)
 : Fleming, A.
@@ -16,7 +16,8 @@ Author(s)
 Year
 : 2010
 
-Summary:
+
+## Summary {#summary}
 
 -   The noise generated by a piezoelectric force sensor is much less than a capacitive sensor
 -   Dynamical model of a piezoelectric stack actuator and piezoelectric force sensor
@@ -30,9 +31,9 @@ Summary:
 
 ## Model of a multi-layer monolithic piezoelectric stack actuator {#model-of-a-multi-layer-monolithic-piezoelectric-stack-actuator}
 
-<a id="org3f4c96b"></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
@@ -77,7 +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} \\]
@@ -112,11 +113,16 @@ As piezoelectric sensors have a capacitive source impedance, the sensor noise de
 The current noise density of a general purpose LM833 FET-input op-amp is \\(0.5\ pA/\sqrt{\text{Hz}}\\).
 The capacitance of a piezoelectric stack is typically between \\(1 \mu F\\) and \\(100 \mu F\\).
 
-# Bibliography
-<a class="bibtex-entry" id="fleming10_nanop_system_with_force_feedb">Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010).  http://dx.doi.org/10.1109/tmech.2009.2028422</a> [↩](#c823f68dd2a72b9667a61b3c046b4731)
+
+## Tested feedback control strategies {#tested-feedback-control-strategies}
+
+<a id="figure--fig:fleming10-fb-control-strats"></a>
+
+{{< 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" >}}
 
 
-## Backlinks {#backlinks}
+## Bibliography {#bibliography}
 
--   [Actuators]({{< relref "actuators" >}})
--   [Force Sensors]({{< relref "force_sensors" >}})
+<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"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
@@ -9,8 +9,7 @@ Tags
 
 
 Reference
-: <sup id="a1cc9b70316a7dda2f652efd146caf84"><a class="reference-link" href="#fleming12_estim" title="Andrew Fleming, Estimating the resolution of nanopositioning systems from  frequency domain data, nil, in in: {2012 IEEE International Conference on Robotics and
-                      Automation}, edited by (2012)">(Andrew Fleming, 2012)</a></sup>
+: (<a href="#citeproc_bib_item_1">Fleming 2012</a>)
 
 Author(s)
 : Fleming, A. J.
@@ -18,5 +17,9 @@ Author(s)
 Year
 : 2012
 
-# Bibliography
-<a class="bibtex-entry" id="fleming12_estim">Fleming, A. J., *Estimating the resolution of nanopositioning systems from frequency domain data*, In , 2012 IEEE International Conference on Robotics and Automation (pp. ) (2012). : .</a> [↩](#a1cc9b70316a7dda2f652efd146caf84)
+
+## 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>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
-: <sup id="3fb5b61524290e36d639a4fac65703d0"><a class="reference-link" href="#fleming13_review_nanom_resol_posit_sensor" title="Andrew Fleming, A Review of Nanometer Resolution Position Sensors:  Operation and Performance, {Sensors and Actuators A: Physical}, v(nil), 106-126 (2013).">(Andrew Fleming, 2013)</a></sup>
+: (<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="org6e00657"></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="org076fb4b"></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](#org92eeb72)).
+There is usually a trade-off between bandwidth and resolution ([Figure 3](#figure--fig:tradeoff-res-bandwidth)).
 
-<a id="org92eeb72"></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).
@@ -166,25 +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    |
-| Piezoresistive | \\(1-500\,\mu m\\)               | 5 ppm   | 0.5 nm     | >100 kHz | 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    |
-| 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 |
-| Interferometer | Meters                           |         | 0.5 nm     | >100kHz  | 1 ppm FSR |
-| Encoder        | Meters                           |         | 6 nm       | >100kHz  | 5 ppm FSR |
-
-# Bibliography
-<a class="bibtex-entry" id="fleming13_review_nanom_resol_posit_sensor">Fleming, A. J., *A review of nanometer resolution position sensors: operation and performance*, Sensors and Actuators A: Physical, *190(nil)*, 106–126 (2013).  http://dx.doi.org/10.1016/j.sna.2012.10.016</a> [↩](#3fb5b61524290e36d639a4fac65703d0)
+| Sensor Type    | Range                              | DNR     | Resolution | Max. BW     | Accuracy  |
+|----------------|------------------------------------|---------|------------|-------------|-----------|
+| 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     | &gt;100 kHz | 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    |
+| 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 |
+| Interferometer | Meters                             |         | 0.5 nm     | &gt;100kHz  | 1 ppm FSR |
+| Encoder        | Meters                             |         | 6 nm       | &gt;100kHz  | 5 ppm FSR |
 
 
-## Backlinks {#backlinks}
+## Bibliography {#bibliography}
 
--   [Position Sensors]({{< relref "position_sensors" >}})
+<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

@@ -0,0 +1,25 @@
++++
+title = "Low-order damping and tracking control for scanning probe systems"
+author = ["Dehaeze Thomas"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (<a href="#citeproc_bib_item_1">Fleming, Teo, and Leang 2015</a>)
+
+Author(s)
+: Fleming, A. J., Teo, Y. R., &amp; Leang, K. K.
+
+Year
+: 2015
+
+
+## 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>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

@@ -1,22 +0,0 @@
-+++
-title = "Studies on stewart platform manipulator: a review"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}})
-
-Reference
-: <sup id="cc10fe9545c7c381cc2b610e8f91a071"><a class="reference-link" href="#furqan17_studies_stewar_platf_manip" title="Mohd Furqan, Mohd Suhaib \&amp; Nazeer Ahmad, Studies on Stewart Platform Manipulator: a Review, {Journal of Mechanical Science and Technology}, v(9), 4459-4470 (2017).">(Mohd Furqan {\it et al.}, 2017)</a></sup>
-
-Author(s)
-: Furqan, M., Suhaib, M., & Ahmad, N.
-
-Year
-: 2017
-
-Lots of references.
-
-# Bibliography
-<a class="bibtex-entry" id="furqan17_studies_stewar_platf_manip">Furqan, M., Suhaib, M., & Ahmad, N., *Studies on stewart platform manipulator: a review*, Journal of Mechanical Science and Technology, *31(9)*, 4459–4470 (2017).  http://dx.doi.org/10.1007/s12206-017-0846-1</a> [↩](#cc10fe9545c7c381cc2b610e8f91a071)

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
-: <sup id="bedab298599c84f60236313ebaad2714"><a class="reference-link" href="#furutani04_nanom_cuttin_machin_using_stewar" title="Katsushi Furutani, Michio Suzuki \&amp; Ryusei Kudoh, Nanometre-Cutting Machine Using a Stewart-Platform Parallel  Mechanism, {Measurement Science and Technology}, v(2), 467-474 (2004).">(Katsushi Furutani {\it et al.}, 2004)</a></sup>
+: (<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
@@ -34,5 +34,9 @@ Possible sources of error:
 To minimize the errors, a calibration is done between the required leg length and the wanted platform pose.
 Then, it is fitted with 4th order polynomial and included in the control architecture.
 
-# Bibliography
-<a class="bibtex-entry" id="furutani04_nanom_cuttin_machin_using_stewar">Furutani, K., Suzuki, M., & Kudoh, R., *Nanometre-cutting machine using a stewart-platform parallel mechanism*, Measurement Science and Technology, *15(2)*, 467–474 (2004).  http://dx.doi.org/10.1088/0957-0233/15/2/022</a> [↩](#bedab298599c84f60236313ebaad2714)
+
+## 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>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"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
-: [Position Sensors]({{< relref "position_sensors" >}})
+: [Position Sensors]({{< relref "position_sensors.md" >}})
 
 Reference
-: <sup id="b820b918ced36901ea0ad4bf653202c6"><a class="reference-link" href="#gao15_measur_techn_precis_posit" title="Gao, Kim, Bosse, Haitjema, , Chen, Lu, Knapp, Weckenmann, , Estler \&amp; Kunzmann, Measurement Technologies for Precision Positioning, {CIRP Annals}, v(2), 773-796 (2015).">(Gao {\it et al.}, 2015)</a></sup>
+: (<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., …
@@ -16,5 +16,9 @@ Author(s)
 Year
 : 2015
 
-# Bibliography
-<a class="bibtex-entry" id="gao15_measur_techn_precis_posit">Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …, *Measurement technologies for precision positioning*, CIRP Annals, *64(2)*, 773–796 (2015).  http://dx.doi.org/10.1016/j.cirp.2015.05.009</a> [↩](#b820b918ced36901ea0ad4bf653202c6)
+
+## 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>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

@@ -1,15 +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
-: <sup id="07f63c751c1d9fcfe628178688f7ec24"><a class="reference-link" href="#garg07_implem_chall_multiv_contr" title="Sanjay Garg, Implementation Challenges for Multivariable Control: What  you did not learn in school!, nil, in in: {AIAA Guidance, Navigation and Control Conference and
-                      Exhibit}, edited by (2007)">(Sanjay Garg, 2007)</a></sup>
+: (<a href="#citeproc_bib_item_1">Garg 2007</a>)
 
 Author(s)
 : Garg, S.
@@ -35,5 +34,9 @@ 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
-<a class="bibtex-entry" id="garg07_implem_chall_multiv_contr">Garg, S., *Implementation challenges for multivariable control: what you did not learn in school!*, In , AIAA Guidance, Navigation and Control Conference and Exhibit (pp. ) (2007). : .</a> [↩](#07f63c751c1d9fcfe628178688f7ec24)
+
+## 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>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/garrido12_centr_multiv_contr_by_simpl_decoup.md

@@ -0,0 +1,118 @@
++++
+title = "Centralized Multivariable Control By Simplified Decoupling"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Decoupled Control](decoupled_control.md)
+
+Reference
+: ([Garrido, Vázquez, and Morilla 2012](#org32a9ef5))
+
+Author(s)
+: Garrido, J., Francisco V\\'azquez, & Morilla, F.
+
+Year
+: 2012
+
+
+## Introduction {#introduction}
+
+Most decoupling approaches use the conventional decoupling scheme in Figure [1](#org265d382) with:
+
+-   \\(G(s)\\) the process matrix
+-   \\(D(s)\\) the decoupler matrix
+-   \\(C(s)\\) the diagonal control matrix
+
+The design of the decoupler is obtained from:
+
+\begin{equation}
+D(s) = G^{-1} (s) \cdot Q(s)
+\end{equation}
+
+where \\(Q(s)\\) is the desired apparent process which is a diagonal matrix.
+
+The main problem of this methodology is the fact that the complexity of the decoupler elements increases for high dimensional MIMO processes, which may require model reductions.
+
+An alternative decoupling methods, called _inverted decoupling_, maintains very simple apparent processes and decoupler element independently of the system size.
+However, inverted decoupling cannot be applied to processes with multivariable [Right Half Plane Zeros](right_half_plane_zeros.md).
+
+<a id="org265d382"></a>
+
+{{< figure src="/ox-hugo/garrido12_decoupling_control_system.png" caption="Figure 1: Block diagram of a decoupling control system" >}}
+
+This work focuses on one of the most extended forms of conventional decoupling called simplified decoupling, in  which \\(n\\) elements of the decoupler are set to unity.
+When the system has two inputs and two outputs (TITO), the simplified decoupling \\(G(s)\\) is given by:
+
+\begin{equation}
+D(s) = \begin{bmatrix}
+1 & -g\_{12}(s)/g\_{11}(s) \\\\\\
+-g\_{21}(s)/g\_{22}(s) & 1
+\end{bmatrix}
+\end{equation}
+
+And the decoupled apparent process \\(Q(s)\\) is given by:
+
+\begin{equation}
+Q(s) = G(s) \cdot D(s) = \begin{bmatrix}
+g\_{11}(s) - \frac{g\_{21}(s g\_{12}(s))}{g\_{22}(s)} & 0 \\\\\\
+0 & g\_{22}(s) - \frac{g\_{21}(s)g\_{12}(s)}{g\_{11}(s)}
+\end{bmatrix}
+\end{equation}
+
+In cases where the system is larger than 2x2, the decoupler elements set to unity are always the diagonal ones as found using:
+
+\begin{equation}
+D(s) = G(s)^{-1} (\text{diag}(G(s)^{-1}))^{-1}
+\end{equation}
+
+In this work, a simplified decoupling strategy is proposed for stable processes with possibly RHP zeros and time delays.
+
+
+## Methodology {#methodology}
+
+Assuming that the process \\(G(s)\\) may have RHP zeros and time delays, but does not have any unstable poles, the decoupler matrix \\(D(s)\\) is obtained as follows (one of many possible configurations):
+
+\begin{equation}
+D(s) = \begin{bmatrix}
+1 & \frac{\text{adj}G\_{12}}{\text{adj}G\_{22}} & \dots & \frac{\text{adj}G\_{1n}}{\text{adj}\_{nn}} \\\\\\
+\frac{\text{adj}G\_{21}}{\text{adj}G\_{11}} & 1 & \dots & \frac{\text{adj}G\_{2n}}{\text{adj}\_{nn}} \\\\\\
+\vdots & \vdots & \ddots & \vdots \\\\\\
+\frac{\text{adj}G\_{n1}}{\text{adj}G\_{11}} & \frac{\text{adj}G\_{n2}}{\text{adj}G\_{22}} & \dots & 1
+\end{bmatrix}
+\end{equation}
+
+And the decoupled apparent plant is:
+
+\begin{equation}
+A(s) = \begin{bmatrix}
+\frac{|G|}{\text{adj}G\_{11}} & 0 & \dots & 0 \\\\\\
+0 & \frac{|G|}{\text{adj}G\_{22}} & \dots & 0 \\\\\\
+\vdots & \vdots & \ddots & \vdots \\\\\\
+0 & 0 & \dots & \frac{|G|}{\text{adj}G\_{nn}}
+\end{bmatrix}
+\end{equation}
+
+where \\(|G(s)|\\) is the determinant of \\(G(s)\\), \\(\text{adj}G(s)\\) is the adjugate matrix of \\(G(s)\\), that is, the transpose of the cofactor matrix of \\(G(s)\\).
+
+The proposed general simplified decoupling control is performed in three steps:
+
+1.  select a configuration: select the \\(n\\) elements of \\(D(s)\\) to be set to unity, one for each column
+2.  Compose the decoupler elements of \\(D(s)\\)
+3.  Design the \\(n\\) controllers of the diagonal control \\(C(s)\\) for the decoupled processes
+
+The realizability requirement for the decoupler is that all of its elements must be proper, causal and stable.
+For processes with time delays, non-minimum phase zeros or different relative degrees, direct calculation of the decoupler element can lead to elements with RHP poles or negative relative degrees.
+
+Several advice for the proper chose of the configuration are given in the paper.
+
+
+## Design and practical considerations {#design-and-practical-considerations}
+
+It is usually necessary to approximate the expressions of \\(|G(s)|\\) and \\(\text{adj}G(s)\\) as it usually give non-rational expressions.
+
+
+## Bibliography {#bibliography}
+
+<a id="org32a9ef5"></a>Garrido, Juan, Francisco Vázquez, and Fernando Morilla. 2012. “Centralized Multivariable Control by Simplified Decoupling.” _Journal of Process Control_ 22 (6):1044–62. <https://doi.org/10.1016/j.jprocont.2012.04.008>.

content/article/geng95_intel_contr_system_multip_degree.md

@@ -1,24 +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
-: <sup id="76af0f5c88615842fa91864c8618fb58"><a class="reference-link" href="#geng95_intel_contr_system_multip_degree" title="Jason Geng, George Pan, Leonard Haynes, , Ben Wada \&amp; John Garba, An Intelligent Control System for Multiple  Degree-Of-Freedom Vibration Isolation, {Journal of Intelligent Material Systems and Structures}, v(6), 787-800 (1995).">(Jason Geng {\it et al.}, 1995)</a></sup>
+: (<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="org9d6018b"></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
-<a class="bibtex-entry" id="geng95_intel_contr_system_multip_degree">Geng, Z. J., Pan, G. G., Haynes, L. S., Wada, B. K., & Garba, J. A., *An intelligent control system for multiple degree-of-freedom vibration isolation*, Journal of Intelligent Material Systems and Structures, *6(6)*, 787–800 (1995).  http://dx.doi.org/10.1177/1045389x9500600607</a> [↩](#76af0f5c88615842fa91864c8618fb58)
+
+## 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>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

@@ -1,20 +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
-: <sup id="10e535e895bdcd6b921bff33ef68cd81"><a class="reference-link" href="#hanieh03_activ_stewar" title="Hanieh, Active isolation and damping of vibrations via Stewart  platform (2003).">(Hanieh, 2003)</a></sup>
-
-Author(s)
-: Hanieh, A. A.
-
-Year
-: 2003
-
-# Bibliography
-<a class="bibtex-entry" id="hanieh03_activ_stewar">Hanieh, A. A., *Active isolation and damping of vibrations via stewart platform* (2003). Universit{\'e} Libre de Bruxelles, Brussels, Belgium.</a> [↩](#10e535e895bdcd6b921bff33ef68cd81)

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
-: <sup id="f9698a1741fe7492aa9b7b42c7724670"><a class="reference-link" href="#hauge04_sensor_contr_space_based_six" title="Hauge \&amp; Campbell, Sensors and Control of a Space-Based Six-Axis Vibration  Isolation System, {Journal of Sound and Vibration}, v(3-5), 913-931 (2004).">(Hauge \& Campbell, 2004)</a></sup>
+: (<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="org342e642"></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](#org342e642)):
+**Stewart platform** ([Figure 1](#figure--fig:hauge04-stewart-platform)):
 
 -   Low corner frequency
 -   Large actuator stroke (\\(\pm5mm\\))
--   Sensors in each strut (Figure [2](#orge1d3dcd)):
+-   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="orge1d3dcd"></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="org5bf1a1a"></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
--   Sensitivity weighted LQG controller (SWLQG) => address robustness in flexible dynamic systems
+-   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) =&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**:
@@ -136,9 +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="org52ac01d"></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
-<a class="bibtex-entry" id="hauge04_sensor_contr_space_based_six">Hauge, G., & Campbell, M., *Sensors and control of a space-based six-axis vibration isolation system*, Journal of Sound and Vibration, *269(3-5)*, 913–931 (2004).  http://dx.doi.org/10.1016/s0022-460x(03)00206-2</a> [↩](#f9698a1741fe7492aa9b7b42c7724670)
+
+## 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>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/heertjes11_minim_cross_talk_high_precis.md

@@ -0,0 +1,34 @@
++++
+title = "Minimizing cross-talk in high-precision motion systems using data-based dynamic decoupling"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Decoupled Control](decoupled_control.md)
+
+Reference
+: ([Heertjes and Engelen 2011](#org76c1202))
+
+Author(s)
+: Heertjes, M., & Engelen, A. v.
+
+Year
+: 2011
+
+> In the field of high-precision motion control, a static decoupling control design is generally used to command motion in the directions of an orthogonal basis.
+> Around the center-of-gravity of the system it then usually suffices to apply single-input single-output control in each of these directions separately.
+> Among the advantages are robust stability and performance through straightforward control designs and loop shaping techniques.
+>
+> If the static decoupling part does not fully achieve desired decoupling of the underlying MIMO motion system, a multi-variable controller can be sought to replace the SISO controller part.
+> A more natural approach would therefore be to replace the MIMO static decoupling part by a dynamic part and leave the SISO controller part intact.
+
+<!--quoteend-->
+
+> The aim of the paper is to minimize directly the cross-talk outputs via data-based optimization.
+> The criterion to be optimized consists solely of time-domain signals taken from a performance-relevant time interval.
+
+
+## Bibliography {#bibliography}
+
+<a id="org76c1202"></a>Heertjes, Marcel, and Arjan van Engelen. 2011. “Minimizing Cross-Talk in High-Precision Motion Systems Using Data-Based Dynamic Decoupling.” _Control Engineering Practice_ 19 (12):1423–32. <https://doi.org/10.1016/j.conengprac.2011.07.016>.

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
-: <sup id="66ab0e7602a1dedda963d7da60533b0d"><a class="reference-link" href="#holler12_instr_x_ray_nano_imagin" title="Holler, Raabe, Diaz, Guizar-Sicairos, , Quitmann, Menzel \&amp; Bunk, An Instrument for 3d X-Ray Nano-Imaging, {Review of Scientific Instruments}, v(7), 073703 (2012).">(Holler {\it et al.}, 2012)</a></sup>
+: (<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="org16e51fb"></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.
@@ -38,5 +38,9 @@ Obtain position stability of 10nm (standard deviation).
     The interferometer is positionned on top of a translation stage. The PSD information is used to close the loop so that the interferometer follows the displacement of the metrology sphere.
 -   **Feedback Loop**: Using the signals from the 2 interferometers, the loop is closed to compensate low frequency vibrations and thermal drifts.
 
-# Bibliography
-<a class="bibtex-entry" id="holler12_instr_x_ray_nano_imagin">Holler, M., Raabe, J., Diaz, A., Guizar-Sicairos, M., Quitmann, C., Menzel, A., & Bunk, O., *An instrument for 3d x-ray nano-imaging*, Review of Scientific Instruments, *83(7)*, 073703 (2012).  http://dx.doi.org/10.1063/1.4737624</a> [↩](#66ab0e7602a1dedda963d7da60533b0d)
+
+## 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>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

@@ -1,20 +1,24 @@
 +++
 title = "Active damping based on decoupled collocated control"
-author = ["Thomas Dehaeze"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
-: [Active Damping]({{< relref "active_damping" >}})
+: [Active Damping]({{< relref "active_damping.md" >}})
 
 Reference
-: <sup id="cc7836a555fe4dbae791e17008c29bfd"><a class="reference-link" href="#holterman05_activ_dampin_based_decoup_colloc_contr" title="Holterman \&amp; deVries, Active Damping Based on Decoupled Collocated Control, {IEEE/ASME Transactions on Mechatronics}, v(2), 135-145 (2005).">(Holterman \& deVries, 2005)</a></sup>
+: (<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
-<a class="bibtex-entry" id="holterman05_activ_dampin_based_decoup_colloc_contr">Holterman, J., & deVries, T., *Active damping based on decoupled collocated control*, IEEE/ASME Transactions on Mechatronics, *10(2)*, 135–145 (2005).  http://dx.doi.org/10.1109/tmech.2005.844702</a> [↩](#cc7836a555fe4dbae791e17008c29bfd)
+
+## 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>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
-: <sup id="aad53368e29e8a519e2f63857044fa46"><a class="reference-link" href="#ito16_compar_class_high_precis_actuat" title="Shingo Ito \&amp; Georg Schitter, Comparison and Classification of High-Precision Actuators  Based on Stiffness Influencing Vibration Isolation, {IEEE/ASME Transactions on Mechatronics}, v(2), 1169-1178 (2016).">(Shingo Ito \& Georg Schitter, 2016)</a></sup>
+: (<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="orgffb6d7f"></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="org658b9e0"></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}
@@ -66,10 +66,9 @@ The stiffness requirement for low-stiffness actuators can be rephrased in the fr
 In practice, this is difficult to achieve with piezoelectric actuators as their first resonant frequency \\(\omega\_r\\) is **too close to other resonant frequencies to ensure close-loop stability**.
 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
-<a class="bibtex-entry" id="ito16_compar_class_high_precis_actuat">Ito, S., & Schitter, G., *Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation*, IEEE/ASME Transactions on Mechatronics, *21(2)*, 1169–1178 (2016).  http://dx.doi.org/10.1109/tmech.2015.2478658</a> [↩](#aad53368e29e8a519e2f63857044fa46)
 
+## Bibliography {#bibliography}
 
-## Backlinks {#backlinks}
-
--   [Actuators]({{< relref "actuators" >}})
+<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/ito16_flexur_desig_precis_posit_using.md

@@ -0,0 +1,23 @@
++++
+title = "Flexure design for precision positioning using low-stiffness actuators"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: ([Ito et al. 2016](#orgf0a77de))
+
+Author(s)
+: Ito, S., Cigarini, F., Unger, S., & Schitter, G.
+
+Year
+: 2016
+
+
+## Bibliography {#bibliography}
+
+<a id="orgf0a77de"></a>Ito, Shingo, Francesco Cigarini, Severin Unger, and Georg Schitter. 2016. “Flexure Design for Precision Positioning Using Low-Stiffness Actuators.” _IFAC-PapersOnLine_ 49 (21):200–205. <https://doi.org/10.1016/j.ifacol.2016.10.548>.

content/article/jiao18_dynam_model_exper_analy_stewar.md

@@ -1,20 +1,24 @@
 +++
 title = "Dynamic modeling and experimental analyses of stewart platform with flexible hinges"
-author = ["Thomas Dehaeze"]
-draft = false
+author = ["Dehaeze Thomas"]
+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
-: <sup id="ee917739f88877d6c2758c1c36565deb"><a class="reference-link" href="#jiao18_dynam_model_exper_analy_stewar" title="Jian Jiao, Ying Wu, Kaiping Yu \&amp; Rui Zhao, Dynamic Modeling and Experimental Analyses of Stewart  Platform With Flexible Hinges, {Journal of Vibration and Control}, v(1), 151-171 (2018).">(Jian Jiao {\it et al.}, 2018)</a></sup>
+: (<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
-<a class="bibtex-entry" id="jiao18_dynam_model_exper_analy_stewar">Jiao, J., Wu, Y., Yu, K., & Zhao, R., *Dynamic modeling and experimental analyses of stewart platform with flexible hinges*, Journal of Vibration and Control, *25(1)*, 151–171 (2018).  http://dx.doi.org/10.1177/1077546318772474</a> [↩](#ee917739f88877d6c2758c1c36565deb)
+
+## 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>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

@@ -0,0 +1,22 @@
++++
+title = "Robust control and H-Infinity optimization - Tutorial paper"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+: [H Infinity Control]({{<relref "h_infinity_control.md#" >}}), [Weighting Functions]({{<relref "weighting_functions.md#" >}})
+
+Reference
+: ([Kwakernaak 1993](#orgb190420))
+
+Author(s)
+: Kwakernaak, H.
+
+Year
+: 1993
+
+
+## Bibliography {#bibliography}
+
+<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/legnani12_new_isotr_decoup_paral_manip.md

@@ -1,18 +1,17 @@
 +++
 title = "A new isotropic and decoupled 6-dof parallel manipulator"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 draft = false
-GHissueID = 1
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}})
 
 Reference
-: <sup id="17295cbc2858c65ecc60d51b450233e3"><a class="reference-link" href="#legnani12_new_isotr_decoup_paral_manip" title="Legnani, Fassi, Giberti, Cinquemani, \&amp; Tosi, A New Isotropic and Decoupled 6-dof Parallel Manipulator, {Mechanism and Machine Theory}, v(nil), 64-81 (2012).">(Legnani {\it et al.}, 2012)</a></sup>
+: (<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
@@ -23,13 +22,17 @@ Year
 
 Example of generated isotropic manipulator (not decoupled).
 
-<a id="org9b13cfd"></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="org958618e"></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
-<a class="bibtex-entry" id="legnani12_new_isotr_decoup_paral_manip">Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., & Tosi, D., *A new isotropic and decoupled 6-dof parallel manipulator*, Mechanism and Machine Theory, *58(nil)*, 64–81 (2012).  http://dx.doi.org/10.1016/j.mechmachtheory.2012.07.008</a> [↩](#17295cbc2858c65ecc60d51b450233e3)
+
+## 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>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_fault_vibrat_isolat_point.md

@@ -8,7 +8,7 @@ Tags
 : [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Cubic Architecture]({{< relref "cubic_architecture" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}), [Multivariable Control]({{< relref "multivariable_control" >}})
 
 Reference
-: <sup id="f885df380638b868e509fbbf75912d1e"><a class="reference-link" href="#li01_simul_fault_vibrat_isolat_point" title="Li, Simultaneous, Fault-tolerant Vibration Isolation and  Pointing Control of Flexure Jointed Hexapods (2001).">(Li, 2001)</a></sup>
+: ([Li 2001](#orgb27ac3b))
 
 Author(s)
 : Li, X.
@@ -24,7 +24,7 @@ Year
 -   Cubic (mutually orthogonal)
 -   Flexure Joints => eliminate friction and backlash but add complexity to the dynamics
 
-<a id="org24b3ba4"></a>
+<a id="org4770c80"></a>
 
 {{< figure src="/ox-hugo/li01_stewart_platform.png" caption="Figure 1: Flexure jointed Stewart platform used for analysis and control" >}}
 
@@ -38,18 +38,18 @@ Year
 The origin of \\(\\{P\\}\\) is taken as the center of mass of the payload.
 
 **Decoupling**:
-If we refine the (force) inputs and (displacement) outputs as shown in Figure [2](#org5d5e02c) or in Figure [3](#org0c14c06), we obtain a decoupled plant provided that:
+If we refine the (force) inputs and (displacement) outputs as shown in Figure [2](#org63bb176) or in Figure [3](#orgd88dae0), we obtain a decoupled plant provided that:
 
 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.
 
-<a id="org5d5e02c"></a>
+<a id="org63bb176"></a>
 
 {{< figure src="/ox-hugo/li01_decoupling_conf.png" caption="Figure 2: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
 
-<a id="org0c14c06"></a>
+<a id="orgd88dae0"></a>
 
 {{< figure src="/ox-hugo/li01_decoupling_conf_bis.png" caption="Figure 3: Decoupling the dynamics of the Stewart Platform using the Jacobians" >}}
 
@@ -75,15 +75,15 @@ The control bandwidth is divided as follows:
 
 ### Vibration Isolation {#vibration-isolation}
 
-The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [4](#orgf519833).
+The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [4](#org51e3a97).
 
-<a id="orgf519833"></a>
+<a id="org51e3a97"></a>
 
 {{< figure src="/ox-hugo/li01_vibration_isolation_control.png" caption="Figure 4: Figure caption" >}}
 
-One of the subsystem plant transfer function is shown in Figure [4](#orgf519833)
+One of the subsystem plant transfer function is shown in Figure [4](#org51e3a97)
 
-<a id="orgef0f6ef"></a>
+<a id="org9c55360"></a>
 
 {{< figure src="/ox-hugo/li01_vibration_control_plant.png" caption="Figure 5: Plant transfer function of one of the SISO subsystem for Vibration Control" >}}
 
@@ -97,9 +97,9 @@ The unity control bandwidth of the isolation loop is designed to be from **5Hz t
 
 ### Pointing Control {#pointing-control}
 
-A block diagram of the pointing control system is shown in Figure [6](#org1c5bf82).
+A block diagram of the pointing control system is shown in Figure [6](#org5fb43ce).
 
-<a id="org1c5bf82"></a>
+<a id="org5fb43ce"></a>
 
 {{< figure src="/ox-hugo/li01_pointing_control.png" caption="Figure 6: Figure caption" >}}
 
@@ -108,9 +108,9 @@ The compensators are design with inverse-dynamics methods.
 
 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 [7](#org700dd8b).
+A feedforward control is added as shown in Figure [7](#orgea70803).
 
-<a id="org700dd8b"></a>
+<a id="orgea70803"></a>
 
 {{< figure src="/ox-hugo/li01_feedforward_control.png" caption="Figure 7: Feedforward control" >}}
 
@@ -122,17 +122,17 @@ The simultaneous vibration isolation and pointing control is approached in two w
 1.  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
 
-Figure [8](#orga79e625) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
+Figure [8](#orgc0af645) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
 
-<a id="orga79e625"></a>
+<a id="orgc0af645"></a>
 
 {{< figure src="/ox-hugo/li01_parallel_control.png" caption="Figure 8: 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.
 
-The effect of the isolation loop on the pointing loop is large around the natural frequency of the plant as shown in Figure [9](#orgbd95400).
+The effect of the isolation loop on the pointing loop is large around the natural frequency of the plant as shown in Figure [9](#orgdfaf4bf).
 
-<a id="orgbd95400"></a>
+<a id="orgdfaf4bf"></a>
 
 {{< figure src="/ox-hugo/li01_effect_isolation_loop_closed.png" caption="Figure 9: \\(\theta\_x/\theta\_{x\_d}\\) transfer function with the isolation loop closed (simulation)" >}}
 
@@ -143,19 +143,19 @@ The effect of pointing control on the isolation plant has not much effect.
 The dynamic interaction effect:
 
 -   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 [10](#org191e7e3) and [11](#org28140a0))
+-   affect the closed loop transmission of the loop first closed (see Figures [10](#orge4bfb77) and [11](#org2bba93e))
 
-As shown in Figure [10](#org191e7e3), the peak resonance of the pointing loop increase after the isolation loop is closed.
+As shown in Figure [10](#orge4bfb77), 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="org191e7e3"></a>
+<a id="orge4bfb77"></a>
 
 {{< figure src="/ox-hugo/li01_closed_loop_pointing.png" caption="Figure 10: 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 [11](#org28140a0)).
+The same happens when first closing the vibration isolation loop and after the pointing loop (Figure [11](#org2bba93e)).
 The first peak resonance of the vibration isolation loop at 15Hz is increased when closing the pointing loop.
 
-<a id="org28140a0"></a>
+<a id="org2bba93e"></a>
 
 {{< figure src="/ox-hugo/li01_closed_loop_vibration.png" caption="Figure 11: Closed-loop transfer functions of the vibration isolation loop before and after the pointing control loop is closed" >}}
 
@@ -165,18 +165,18 @@ The first peak resonance of the vibration isolation loop at 15Hz is increased wh
 
 ### Experimental results {#experimental-results}
 
-Two hexapods are stacked (Figure [12](#orgb11b2c6)):
+Two hexapods are stacked (Figure [12](#orgd81de76)):
 
 -   the bottom hexapod is used to generate disturbances matching candidate applications
 -   the top hexapod provide simultaneous vibration isolation and pointing control
 
-<a id="orgb11b2c6"></a>
+<a id="orgd81de76"></a>
 
 {{< figure src="/ox-hugo/li01_test_bench.png" caption="Figure 12: Stacked Hexapods" >}}
 
-Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [13](#orgdd443cd).
+Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [13](#orgd54b851).
 
-<a id="orgdd443cd"></a>
+<a id="orgd54b851"></a>
 
 {{< figure src="/ox-hugo/li01_vibration_isolation_control_results.png" caption="Figure 13: Vibration isolation control: open-loop (solid) vs. closed-loop (dashed)" >}}
 
@@ -185,9 +185,9 @@ 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 [14](#org64f7223) where the bandwidth of the isolation control is expanded to very low frequency.
+The results of simultaneous control is shown in Figure [14](#orgb3f240b) where the bandwidth of the isolation control is expanded to very low frequency.
 
-<a id="org64f7223"></a>
+<a id="orgb3f240b"></a>
 
 {{< figure src="/ox-hugo/li01_simultaneous_control_results.png" caption="Figure 14: Simultaneous control: open-loop (solid) vs. closed-loop (dashed)" >}}
 
@@ -215,5 +215,8 @@ 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
 
-# Bibliography
-<a class="bibtex-entry" id="li01_simul_fault_vibrat_isolat_point">Li, X., *Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods* (2001). University of Wyoming.</a> [↩](#f885df380638b868e509fbbf75912d1e)
+
+
+## Bibliography {#bibliography}
+
+<a id="orgb27ac3b"></a>Li, Xiaochun. 2001. “Simultaneous, Fault-Tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods.” University of Wyoming.

content/article/li01_simul_vibrat_isolat_point_contr.md

@@ -1,23 +1,26 @@
 +++
 title = "Simultaneous vibration isolation and pointing control of flexure jointed hexapods"
-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
-: <sup id="e3df2691f750617c3995644d056d553a"><a class="reference-link" href="#li01_simul_vibrat_isolat_point_contr" title="Xiaochun Li, Jerry Hamann \&amp; John McInroy, Simultaneous Vibration Isolation and Pointing Control of  Flexure Jointed Hexapods, nil, in in: {Smart Structures and Materials 2001: Smart Structures and
-                      Integrated Systems}, edited by (2001)">(Xiaochun Li {\it et al.}, 2001)</a></sup>
+: (<a href="#citeproc_bib_item_1">Li, Hamann, and McInroy 2001</a>)
 
 Author(s)
-: Li, X., Hamann, J. C., & McInroy, J. E.
+: 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
-<a class="bibtex-entry" id="li01_simul_vibrat_isolat_point_contr">Li, X., Hamann, J. C., & McInroy, J. E., *Simultaneous vibration isolation and pointing control of flexure jointed hexapods*, In , Smart Structures and Materials 2001: Smart Structures and Integrated Systems (pp. ) (2001). : .</a> [↩](#e3df2691f750617c3995644d056d553a)
+
+## 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"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
@@ -9,13 +9,17 @@ Tags
 
 
 Reference
-: <sup id="3ab8ef7353729de315618a708ece8379"><a class="reference-link" href="#lin06_distur_atten_precis_hexap_point" title="Haomin Lin \&amp; John McInroy, Disturbance Attenuation in Precise Hexapod Pointing Using  Positive Force Feedback, {Control Engineering Practice}, v(11), 1377-1386 (2006).">(Haomin Lin \& John McInroy, 2006)</a></sup>
+: (<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
-<a class="bibtex-entry" id="lin06_distur_atten_precis_hexap_point">Lin, H., & McInroy, J. E., *Disturbance attenuation in precise hexapod pointing using positive force feedback*, Control Engineering Practice, *14(11)*, 1377–1386 (2006).  http://dx.doi.org/10.1016/j.conengprac.2005.10.002</a> [↩](#3ab8ef7353729de315618a708ece8379)
+
+## 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>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/mcinroy00_desig_contr_flexur_joint_hexap.md

@@ -1,7 +1,7 @@
 +++
 title = "Design and control of flexure jointed hexapods"
-author = ["Thomas Dehaeze"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
@@ -9,13 +9,17 @@ Tags
 
 
 Reference
-: <sup id="f6d310236552ee92579cf0673a2ca695"><a href="#mcinroy00_desig_contr_flexur_joint_hexap" title="McInroy \&amp; Hamann, Design and Control of Flexure Jointed Hexapods, {IEEE Transactions on Robotics and Automation}, v(4), 372-381 (2000).">(McInroy \& Hamann, 2000)</a></sup>
+: (<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
-<a id="mcinroy00_desig_contr_flexur_joint_hexap"></a>McInroy, J., & Hamann, J., *Design and control of flexure jointed hexapods*, IEEE Transactions on Robotics and Automation, *16(4)*, 372–381 (2000).  http://dx.doi.org/10.1109/70.864229 [↩](#f6d310236552ee92579cf0673a2ca695)
+
+## 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>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
-: <sup id="8bfe2d2dce902a584fa016e86a899044"><a class="reference-link" href="#mcinroy02_model_desig_flexur_joint_stewar" title="McInroy, Modeling and Design of Flexure Jointed Stewart Platforms  for Control Purposes, {IEEE/ASME Transactions on Mechatronics}, v(1), 95-99 (2002).">(McInroy, 2002)</a></sup>
+: (<a href="#citeproc_bib_item_2">McInroy 2002</a>)
 
 Author(s)
 : McInroy, J.
@@ -17,8 +17,7 @@ Author(s)
 Year
 : 2002
 
-This short paper is very similar to <sup id="5da427f78c552aa92cd64c2a6df961f1"><a class="reference-link" href="#mcinroy99_dynam" title="McInroy, Dynamic modeling of flexure jointed hexapods for control  purposes, nil, in in: {Proceedings of the 1999 IEEE International Conference on
-                  Control Applications (Cat. No.99CH36328)}, edited by (1999)">(McInroy, 1999)</a></sup>.
+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.
 
@@ -37,15 +36,15 @@ This short paper is very similar to <sup id="5da427f78c552aa92cd64c2a6df961f1"><
 
 ## Flexure Jointed Hexapod Dynamics {#flexure-jointed-hexapod-dynamics}
 
-<a id="org1e5260a"></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](#org1e5260a)).
+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](#org1e5260a) 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
@@ -79,10 +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}
 
@@ -108,7 +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:
@@ -116,12 +115,11 @@ 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\\\\\\
-  & - 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}
+\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}
+\end{equation}
 
 Joint (\\(l\\)) and Cartesian (\\(\mathcal{X}\\)) terms are still mixed.
 In the next section, a connection between the two will be found to complete the formulation
@@ -134,21 +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="orgbd4aaf0"></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](#orgbd4aaf0) 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](#orgbd4aaf0) (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 \\\\\\
-  m\_s \Delta \ddot{y} + \frac{k\_r}{l^2} \Delta y \\\\\\
+  -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{z} + \frac{k\_r}{l^2} \Delta z
 \end{bmatrix}
 \end{equation}
@@ -159,16 +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} A\_x \cos \omega t \\ A\_y \cos \omega t \\  A\_z \cos \omega t \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}
 \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 + \frac{k\_r}{l^2} \Big) A\_y \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\_z \cos \omega t
   \end{bmatrix}
 \end{equation}
@@ -190,24 +188,32 @@ The first part depends on the mechanical terms and the frequency of the movement
   x\_{\text{gain}\_\omega} = \frac{|-m\_s \omega^2 + k|}{|-m\_s \omega^2 + \frac{k\_r}{l^2}|}
 \end{equation}
 
-> In order to get dominance at low frequencies, the hexapod must be designed so that:
->
-> \begin{equation}
->   \frac{k\_r}{l^2} \ll k \label{eq:cond\_stiff}
-> \end{equation}
+<div class="important">
+
+In order to get dominance at low frequencies, the hexapod must be designed so that:
+
+\begin{equation}
+  \frac{k\_r}{l^2} \ll k \label{eq:cond\_stiff}
+\end{equation}
+
+</div>
 
 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 \\]
 
-> 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:
->
-> \begin{equation}
->   \text{control bandwidth} \ll \sqrt{\frac{k\_r}{m\_s l^2}} \label{eq:cond\_bandwidth}
-> \end{equation}
+<div class="important">
+
+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:
+
+\begin{equation}
+  \text{control bandwidth} \ll \sqrt{\frac{k\_r}{m\_s l^2}} \label{eq:cond\_bandwidth}
+\end{equation}
+
+</div>
 
 The control bandwidth can be increase for hexapods that are designed so that \\(x\_{\text{gain}\_\omega} \gg 1\\) for \\(\omega \ll \sqrt{k/m\_s}\\).
 This can be achieve, for instance, by adding damping.
@@ -217,12 +223,52 @@ In this case, it is reasonable to use:
   \text{control bandwidth} \ll \sqrt{\frac{k}{m\_s}}
 \end{equation}
 
-> 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 class="important">
+
+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}
 
-# Bibliography
-<a class="bibtex-entry" id="mcinroy02_model_desig_flexur_joint_stewar">McInroy, J., *Modeling and design of flexure jointed stewart platforms for control purposes*, IEEE/ASME Transactions on Mechatronics, *7(1)*, 95–99 (2002).  http://dx.doi.org/10.1109/3516.990892</a> [↩](#8bfe2d2dce902a584fa016e86a899044)
+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\\).
 
-<a class="bibtex-entry" id="mcinroy99_dynam">McInroy, J., *Dynamic modeling of flexure jointed hexapods for control purposes*, In , Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) (pp. ) (1999). : .</a> [↩](#5da427f78c552aa92cd64c2a6df961f1)
+This section will derive this implicit relationship.
+Let denote:
+
+-   \\(\mathcal{X}\_B\\) the pose of {B} with respect to {U}
+-   \\({}^B\mathcal{X}\_P\\) the pose of {P} with respect to {B}
+-   \\({}^Uq\_i = {}^U\_BR {}^Bq\_i + {}^UP\_{BORG}\\) the position of the ith base attachment point, expressed in the universal frame {U}
+-   \\(P\_{BORG}\\) the position of the origin of frame {B}
+
+Note that although \\({}^Bq\_i\\) is fixed, \\({}^Uq\_i\\) varies due to base motion.
+
+Differentiating twice and converting derivatives of rotation matrices into angular velocity cross products yields:
+
+\begin{equation}
+  {}^U\dot{q}\_i = \omega\_B \times {}^U\_BR {}^Bq\_i + \underbrace{{}^U\_BR {}^B\dot{q}\_i}\_{= 0} + v\_B
+\end{equation}
+
+\begin{equation}
+  {}^U\ddot{q}\_i = \dot{\omega}\_B \times {}^U\_BR {}^Bq\_i + \omega\_B \times \omega\_B \times {}^U\_BR {}^Bq\_i + \dot{v}\_B
+\end{equation}
+
+where:
+
+-   \\(\omega\_B\\) denotes the angular velocity of {B} with respect to {U}
+-   \\(v\_B = {}^U\dot{P}\_{BORG}\\) denotes the linear velocity of the origin of {B} with respect to {U}
+
+By using the vector triple identity \\(a \cdot (b \times c) = b \cdot (c \times a)\\) and putting the equation in a matrix form:
+
+\begin{equation}
+  {}^U \hat{u}\_i^T {}^U\ddot{q}\_i = \left[ {}^U\hat{u}\_i^T \left( {}^U\_BR {}^Bq\_i \times {}^U\hat{u}\_i \right)^T \right] \ddot{\mathcal{X}}\_B + {}^U\hat{u}\_i^T \left( \omega\_B \times \left[ \omega\_B \times {}^U\_BR {}^Bq\_i \right] \right)
+\end{equation}
+
+
+## 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>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 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

@@ -1,15 +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
-: <sup id="5da427f78c552aa92cd64c2a6df961f1"><a class="reference-link" href="#mcinroy99_dynam" title="McInroy, Dynamic modeling of flexure jointed hexapods for control  purposes, nil, in in: {Proceedings of the 1999 IEEE International Conference on
-                      Control Applications (Cat. No.99CH36328)}, edited by (1999)">(McInroy, 1999)</a></sup>
+: (<a href="#citeproc_bib_item_1">McInroy 1999</a>)
 
 Author(s)
 : McInroy, J.
@@ -17,7 +16,7 @@ Author(s)
 Year
 : 1999
 
-This conference paper has been further published in a journal as a short note <sup id="8bfe2d2dce902a584fa016e86a899044"><a class="reference-link" href="#mcinroy02_model_desig_flexur_joint_stewar" title="McInroy, Modeling and Design of Flexure Jointed Stewart Platforms  for Control Purposes, {IEEE/ASME Transactions on Mechatronics}, v(1), 95-99 (2002).">(McInroy, 2002)</a></sup>.
+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}
@@ -39,22 +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="orgb4329bb"></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](#org4a04030).
+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="org4a04030"></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>:
-  Definition of quantities on Figure <a href="#org4a04030">2</a>
+  <span class="table-number"><a href="#table--tab:mcinroy99-strut-model">Table 1</a>:</span>
+  Definition of quantities on <a href="#org1f8da5d">2</a>
 </div>
 
 | **Symbol**                   | **Meaning**                                |
@@ -71,11 +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 <sup id="8bfe2d2dce902a584fa016e86a899044"><a class="reference-link" href="#mcinroy02_model_desig_flexur_joint_stewar" title="McInroy, Modeling and Design of Flexure Jointed Stewart Platforms  for Control Purposes, {IEEE/ASME Transactions on Mechatronics}, v(1), 95-99 (2002).">(McInroy, 2002)</a></sup>).
+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](#org4a04030) (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
@@ -106,10 +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}
 
@@ -135,7 +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:
@@ -143,11 +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\\\\\\
-  & - 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)
+  & {}^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)
 \end{aligned}
 
 Joint (\\(l\\)) and Cartesian (\\(\mathcal{X}\\)) terms are still mixed.
@@ -162,12 +161,10 @@ In the next section, a connection between the two will be found to complete the
 
 ## Control Example {#control-example}
 
-# Bibliography
-<a class="bibtex-entry" id="mcinroy99_dynam">McInroy, J., *Dynamic modeling of flexure jointed hexapods for control purposes*, In , Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328) (pp. ) (1999). : .</a> [↩](#5da427f78c552aa92cd64c2a6df961f1)
 
-<a class="bibtex-entry" id="mcinroy02_model_desig_flexur_joint_stewar">McInroy, J., *Modeling and design of flexure jointed stewart platforms for control purposes*, IEEE/ASME Transactions on Mechatronics, *7(1)*, 95–99 (2002).  http://dx.doi.org/10.1109/3516.990892</a> [↩](#8bfe2d2dce902a584fa016e86a899044)
+## Bibliography {#bibliography}
 
-
-## Backlinks {#backlinks}
-
--   [Identification and decoupling control of flexure jointed hexapods]({{< relref "chen00_ident_decoup_contr_flexur_joint_hexap" >}})
+<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>
+  <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/nosova20_review_paral_struc_mechan_with_kinem_decoup.md

@@ -0,0 +1,40 @@
++++
+title = "A review of the parallel structure mechanisms with kinematic decoupling"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Parallel Manipulators](parallel_manipulators.md)
+
+Reference
+: ([Nosova 2020](#orgc1a99bc))
+
+Author(s)
+: Nosova, N. Y.
+
+Year
+: 2020
+
+
+## Introduction {#introduction}
+
+Parallel mechanisms can be characterized by high speeds, since the engines are mounted on the base and the links have a relatively small mass.
+The disadvantages are: limited working space, the presence of singularities in the immediate vicinity of the workspace.
+
+The kinematic decoupling for a parallel structure manipulator consists in that one movement of the output platform is provided by only one input link or group of links of the kinematic chain.
+
+
+## Types of Kinematic Decoupling {#types-of-kinematic-decoupling}
+
+There are three different types of decoupling:
+
+1.  **strong coupling**: where each configuration parameter is a function of all joint variable (e.g. Stewart platform)
+2.  **complete decoupling**: each configuration parameter is a function of only one joint variable (e.g. Ortoglide)
+3.  **partial decoupling**: some configuration parameters are in function of only some joint variables
+
+
+
+## Bibliography {#bibliography}
+
+<a id="orgc1a99bc"></a>Nosova, N. Yu. 2020. “A Review of the Parallel Structure Mechanisms with Kinematic Decoupling.” _Advanced Technologies in Robotics and Intelligent Systems_. Springer International Publishing, 247–55. <https://doi.org/10.1007/978-3-030-33491-8%5F30>.

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]({{< relref "motion_control" >}})
+: [Motion Control]({{< relref "motion_control.md" >}})
 
 Reference
-: <sup id="73fd325bd20a6ef8972145e535f38198"><a class="reference-link" href="#oomen18_advan_motion_contr_precis_mechat" title="Tom Oomen, Advanced Motion Control for Precision Mechatronics:  Control, Identification, and Learning of Complex Systems, {IEEJ Journal of Industry Applications}, v(2), 127-140 (2018).">(Tom Oomen, 2018)</a></sup>
+: (<a href="#citeproc_bib_item_1">Oomen 2018</a>)
 
 Author(s)
 : Oomen, T.
@@ -16,9 +16,170 @@ Author(s)
 Year
 : 2018
 
-<a id="org5cf2052"></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}
 
-# Bibliography
-<a class="bibtex-entry" id="oomen18_advan_motion_contr_precis_mechat">Oomen, T., *Advanced motion control for precision mechatronics: control, identification, and learning of complex systems*, IEEJ Journal of Industry Applications, *7(2)*, 127–140 (2018).  http://dx.doi.org/10.1541/ieejjia.7.127</a> [↩](#73fd325bd20a6ef8972145e535f38198)
+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}
+
+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:
+
+\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/poel10_explor_activ_hard_mount_vibrat.md

@@ -1,20 +0,0 @@
-+++
-title = "An exploration of active hard mount vibration isolation for precision equipment"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Vibration Isolation]({{< relref "vibration_isolation" >}})
-
-Reference
-: <sup id="bcab548922e0e1ad6a2c310f63879596"><a class="reference-link" href="#poel10_explor_activ_hard_mount_vibrat" title="van der Poel, An Exploration of Active Hard Mount Vibration Isolation for  Precision Equipment (2010).">(van der Poel, 2010)</a></sup>
-
-Author(s)
-: van der Poel, G. W.
-
-Year
-: 2010
-
-# Bibliography
-<a class="bibtex-entry" id="poel10_explor_activ_hard_mount_vibrat">van der Poel, G. W., *An exploration of active hard mount vibration isolation for precision equipment* (2010). University of Twente.</a> [↩](#bcab548922e0e1ad6a2c310f63879596)

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
-: <sup id="525e1e237b885f81fae3c25a3036ba6f"><a class="reference-link" href="#preumont02_force_feedb_versus_accel_feedb" title="Preumont, Fran\ccois, Bossens, \&amp; Abu-Hanieh, Force Feedback Versus Acceleration Feedback in Active  Vibration Isolation, {Journal of Sound and Vibration}, v(4), 605-613 (2002).">(Preumont {\it et al.}, 2002)</a></sup>
+: (<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](#org307b349)), the acceleration feedback gives larger damping on the higher mode.
--   For heavy payload (Figure [2](#orgc0c4ad3)), the acceleration feedback do not give alternating poles and zeros and thus for high control gains, the system becomes unstable
+-   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](#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="org307b349"></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="orgc0c4ad3"></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:
 
@@ -45,5 +45,9 @@ 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
-<a class="bibtex-entry" id="preumont02_force_feedb_versus_accel_feedb">Preumont, A., A. Fran\ccois, Bossens, F., & Abu-Hanieh, A., *Force feedback versus acceleration feedback in active vibration isolation*, Journal of Sound and Vibration, *257(4)*, 605–613 (2002).  http://dx.doi.org/10.1006/jsvi.2002.5047</a> [↩](#525e1e237b885f81fae3c25a3036ba6f)
+
+## 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>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
-: <sup id="8096d5b2df73551d836ef96b7ca7efa4"><a class="reference-link" href="#preumont07_six_axis_singl_stage_activ" title="Preumont, Horodinca, Romanescu, de, Marneffe, Avraam, Deraemaeker, Bossens, \&amp; Abu Hanieh, A Six-Axis Single-Stage Active Vibration Isolator Based on  Stewart Platform, {Journal of Sound and Vibration}, v(3-5), 644-661 (2007).">(Preumont {\it et al.}, 2007)</a></sup>
+: (<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., …
@@ -18,32 +18,36 @@ Year
 
 Summary:
 
--   **Cubic** Stewart platform (Figure [3](#org2d41889))
+-   **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](#orgf58a4b4))
+-   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](#org6835865))
+-   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="org6835865"></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="orgf58a4b4"></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="org2d41889"></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
-<a class="bibtex-entry" id="preumont07_six_axis_singl_stage_activ">Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., …, *A six-axis single-stage active vibration isolator based on stewart platform*, Journal of Sound and Vibration, *300(3-5)*, 644–661 (2007).  http://dx.doi.org/10.1016/j.jsv.2006.07.050</a> [↩](#8096d5b2df73551d836ef96b7ca7efa4)
+
+## 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>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
-: <sup id="14f767d8ba71d58fa8a3ec876628d750"><a class="reference-link" href="#saxena12_advan_inter_model_contr_techn" title="Sahaj Saxena \&amp; YogeshV Hote, Advances in Internal Model Control Technique: a Review and  Future Prospects, {IETE Technical Review}, v(6), 461 (2012).">(Sahaj Saxena \& YogeshV Hote, 2012)</a></sup>
+: (<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\*}
 
@@ -84,5 +84,9 @@ 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
-<a class="bibtex-entry" id="saxena12_advan_inter_model_contr_techn">Saxena, S., & Hote, Y., *Advances in internal model control technique: a review and future prospects*, IETE Technical Review, *29(6)*, 461 (2012).  http://dx.doi.org/10.4103/0256-4602.105001</a> [↩](#14f767d8ba71d58fa8a3ec876628d750)
+
+## 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>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/sayed01_survey_spect_factor_method.md

@@ -1,21 +0,0 @@
-+++
-title = "A survey of spectral factorization methods"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-:
-
-
-Reference
-: <sup id="e71cc5e3ec879813f2344a6dce1ac11f"><a href="#sayed01_survey_spect_factor_method" title="Sayed \&amp; Kailath, A Survey of Spectral Factorization Methods, {Numerical Linear Algebra with Applications}, v(6-7), 467-496 (2001).">(Sayed \& Kailath, 2001)</a></sup>
-
-Author(s)
-: Sayed, A. H., & Kailath, T.
-
-Year
-: 2001
-
-# Bibliography
-<a id="sayed01_survey_spect_factor_method"></a>Sayed, A. H., & Kailath, T., *A survey of spectral factorization methods*, Numerical Linear Algebra with Applications, *8(6-7)*, 467–496 (2001).  http://dx.doi.org/10.1002/nla.250 [↩](#e71cc5e3ec879813f2344a6dce1ac11f)

content/article/schellekens98_desig_precis.md

@@ -1,20 +1,24 @@
 +++
 title = "Design for precision: current status and trends"
-author = ["Thomas Dehaeze"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
-: [Precision Engineering]({{< relref "precision_engineering" >}})
+: [Precision Engineering]({{< relref "precision_engineering.md" >}})
 
 Reference
-: <sup id="89f7d8f4c31f79f83e3666017687f525"><a class="reference-link" href="#schellekens98_desig_precis" title="Schellekens, Rosielle, Vermeulen, , Vermeulen, Wetzels \&amp; Pril, Design for Precision: Current Status and Trends, {Cirp Annals}, v(2), 557-586 (1998).">(Schellekens {\it et al.}, 1998)</a></sup>
+: (<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
-<a class="bibtex-entry" id="schellekens98_desig_precis">Schellekens, P., Rosielle, N., Vermeulen, H., Vermeulen, M., Wetzels, S., & Pril, W., *Design for precision: current status and trends*, Cirp Annals, *(2)*, 557–586 (1998).  http://dx.doi.org/10.1016/s0007-8506(07)63243-0</a> [↩](#89f7d8f4c31f79f83e3666017687f525)
+
+## 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>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"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
@@ -9,13 +9,17 @@ Tags
 
 
 Reference
-: <sup id="ee9f1b2ad5707e86bf7c26e8c325b324"><a class="reference-link" href="#schroeck01_compen_desig_linear_time_invar" title="Schroeck, Messner \&amp; McNab, On Compensator Design for Linear Time-Invariant Dual-Input  Single-Output Systems, {IEEE/ASME Transactions on Mechatronics}, v(1), 50-57 (2001).">(Schroeck {\it et al.}, 2001)</a></sup>
+: (<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
-<a class="bibtex-entry" id="schroeck01_compen_desig_linear_time_invar">Schroeck, S., Messner, W., & McNab, R., *On compensator design for linear time-invariant dual-input single-output systems*, IEEE/ASME Transactions on Mechatronics, *6(1)*, 50–57 (2001).  http://dx.doi.org/10.1109/3516.914391</a> [↩](#ee9f1b2ad5707e86bf7c26e8c325b324)
+
+## 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>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

@@ -1,20 +1,24 @@
 +++
 title = "Nanopositioning with multiple sensors: a case study in data storage"
-author = ["Thomas Dehaeze"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
-: [Sensor Fusion]({{< relref "sensor_fusion" >}})
+: [Sensor Fusion]({{< relref "sensor_fusion.md" >}})
 
 Reference
-: <sup id="eb5a15a8c900d93de0b9bab520e1b6da"><a class="reference-link" href="#sebastian12_nanop_with_multip_sensor" title="Abu Sebastian \&amp; Angeliki Pantazi, Nanopositioning With Multiple Sensors: a Case Study in Data  Storage, {IEEE Transactions on Control Systems Technology}, v(2), 382-394 (2012).">(Abu Sebastian \& Angeliki Pantazi, 2012)</a></sup>
+: (<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
-<a class="bibtex-entry" id="sebastian12_nanop_with_multip_sensor">Sebastian, A., & Pantazi, A., *Nanopositioning with multiple sensors: a case study in data storage*, IEEE Transactions on Control Systems Technology, *20(2)*, 382–394 (2012).  http://dx.doi.org/10.1109/tcst.2011.2177982</a> [↩](#eb5a15a8c900d93de0b9bab520e1b6da)
+
+## 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>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]({{< relref "active_damping" >}})
+: [Active Damping]({{< relref "active_damping.md" >}})
 
 Reference
-: <sup id="d5c1263eebe6caa1e91b078b620d72f1"><a class="reference-link" href="#souleille18_concep_activ_mount_space_applic" title="Souleille, Lampert, Lafarga, , Hellegouarch, Rondineau, Rodrigues, Gon\ccalo \&amp; Collette, A Concept of Active Mount for Space Applications, {CEAS Space Journal}, v(2), 157--165 (2018).">(Souleille {\it et al.}, 2018)</a></sup>
+: (<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](#orgec40a2d) 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="orgec40a2d"></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                                                   |
-| \\(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\_a\\) | \\(65\,[N/\mu m]\\)   | Stiffness of the actuator                                      |
-| \\(c\_1\\) | \\(10\,[N/(m/s)]\\)   | Added viscous damping                                          |
+|            | Value                  | Meaning                                                        |
+|------------|------------------------|----------------------------------------------------------------|
+| \\(m\\)    | \\(1\\,[kg]\\)         | Payload mass                                                   |
+| \\(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\_a\\) | \\(65\\,[N/\mu m]\\)   | Stiffness of the actuator                                      |
+| \\(c\_1\\) | \\(10\\,[N/(m/s)]\\)   | Added viscous damping                                          |
 
 The dynamic equation of the system is:
 
@@ -61,36 +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](#org656442f):
+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="org656442f"></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="orgd1fa41a"></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](#org59a9fbf)).
+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="org59a9fbf"></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](#orgb30c1f0), 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="orgb30c1f0"></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
-<a class="bibtex-entry" id="souleille18_concep_activ_mount_space_applic">Souleille, A., Lampert, T., Lafarga, V., Hellegouarch, S., Rondineau, A., Rodrigues, Gon\ccalo, & Collette, C., *A concept of active mount for space applications*, CEAS Space Journal, *10(2)*, 157–165 (2018). </a> [↩](#d5c1263eebe6caa1e91b078b620d72f1)
+
+## 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>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
-: <sup id="a48f6708d087625a42ca2375407a2bc4"><a class="reference-link" href="#spanos95_soft_activ_vibrat_isolat" title="Spanos, Rahman \&amp; Blackwood, A Soft 6-axis Active Vibration Isolator, nil, in in: {Proceedings of 1995 American Control Conference - ACC'95}, edited by (1995)">(Spanos {\it et al.}, 1995)</a></sup>
+: (<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](#org2d8aec6)):
+**Stewart Platform** ([Figure 1](#figure--fig:spanos95-stewart-platform)):
 
 -   Voice Coil
 -   Flexible joints (cross-blades)
 -   Force Sensors
 -   Cubic Configuration
 
-<a id="org2d8aec6"></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="org4f9f9d6"></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:
 
@@ -52,11 +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](#orgc669f80).
+The results in terms of transmissibility are shown in [Figure 3](#figure--fig:spanos95-results).
 
-<a id="orgc669f80"></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
-<a class="bibtex-entry" id="spanos95_soft_activ_vibrat_isolat">Spanos, J., Rahman, Z., & Blackwood, G., *A soft 6-axis active vibration isolator*, In , Proceedings of 1995 American Control Conference - ACC'95 (pp. ) (1995). : .</a> [↩](#a48f6708d087625a42ca2375407a2bc4)
+
+## 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>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
-: <sup id="abb1be5f48179255f7d8c45b1784bcf8"><a class="reference-link" href="#stankevic17_inter_charac_rotat_stages_x_ray_nanot" title="Tomas Stankevic, Christer Engblom, Florent Langlois, , Filipe Alves, Alain Lestrade, Nicolas Jobert, , Gilles Cauchon, Ulrich Vogt \&amp; Stefan Kubsky, Interferometric Characterization of Rotation Stages for  X-Ray Nanotomography, {Review of Scientific Instruments}, v(5), 053703 (2017).">(Tomas Stankevic {\it et al.}, 2017)</a></sup>
+: (<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., …
@@ -19,15 +19,19 @@ Year
 -   Similar Station than the NASS
 -   Similar Metrology with fiber based interferometers and cylindrical reference mirror
 
-<a id="orgc36dc2f"></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)
--   Non-repeatable errors => feedback
+-   Repeatable errors =&gt; feedforward (Look Up Table)
+-   Non-repeatable errors =&gt; feedback
 -   Result: 40nm runout error
 
-# Bibliography
-<a class="bibtex-entry" id="stankevic17_inter_charac_rotat_stages_x_ray_nanot">Stankevic, T., Engblom, C., Langlois, F., Alves, F., Lestrade, A., Jobert, N., Cauchon, G., …, *Interferometric characterization of rotation stages for x-ray nanotomography*, Review of Scientific Instruments, *88(5)*, 053703 (2017).  http://dx.doi.org/10.1063/1.4983405</a> [↩](#abb1be5f48179255f7d8c45b1784bcf8)
+
+## 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>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/stein03_respec_unstab.md

@@ -0,0 +1,127 @@
++++
+title = "Respect the unstable"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+:
+
+
+Reference
+: ([Stein 2003](#orge299f80))
+
+Author(s)
+: Stein, G.
+
+Year
+: 2003
+
+
+## Introduction {#introduction}
+
+> The second trend has been evident at our conferences, and certainly in our journal, over the years.
+> This trend is the increasing worship of abstract mathematical results in control at the expense of more specific examinations of their practical, physical consequences.
+
+<div class="important">
+  <div></div>
+
+**Basic facts about unstable plants**:
+
+-   Unstable systems are fundamentally, and quantifiably more difficult to control than stable ones
+-   Controllers for unstable systems are operationally critical
+-   Closed-loop systems with unstable components are only locally stable
+
+</div>
+
+
+## The Bode Integrals {#the-bode-integrals}
+
+<div class="important">
+  <div></div>
+
+**Bode Integrals**:
+
+The first integral applies to stable plants and the second to unstable plants.
+They are valid for every stabilizing controller, assuming only that both plan and controller have finite bandwidths.
+In words, the integrals state that the log of magnitude of sensitivity function of a SISO feedback system, integrated over frequency, is constant.
+The constant is zero for stable plants, and it is positive for unstable ones.
+It becomes larger as the number of unstable poles increases and/or as the poles more farther into the right-half plane.
+
+\begin{align}
+  \int\_0^\infty \ln |S(j\omega)| d \omega & = 0 \label{eq:bode\_integral\_stable} \\\\\\
+  \int\_0^\infty \ln |S(j\omega)| d \omega & = \pi \sum\_{p \in P} \text{Re}(p) \label{eq:bode\_integral\_unstable}
+\end{align}
+
+</div>
+
+
+## A Bode Integral Interpretation {#a-bode-integral-interpretation}
+
+Bode integral can be thought as **conservation laws**.
+They state that a certain quantity, the integrated value of the log of the magnitude of the sensitivity function, is conserved under the action of feedback.
+The total amount of this quantity is always the same.
+It is equal to zero for stable plant/compensator pairs, and it is equal to some fixed positive amount for unstable ones.
+
+Since we are talking about the log of sensitivity magnitude, it follows that negative values are good, and positive values are bad.
+
+<div class="definition">
+  <div></div>
+
+It is curious, somehow, that our field has not adopted a name for this quantity being conserved (i.e. the integrated log of sensitivity magnitude).
+It is here proposed to call it **dirt**
+
+</div>
+
+The job of a serious control designer is then to more dirt from one place to another, using appropriate tools, without being able to get rid of any of it (illustrated in Figure [1](#orgf166bde)).
+
+<a id="orgf166bde"></a>
+
+{{< figure src="/ox-hugo/stein03_serious_design.png" caption="Figure 1: Sensitivity reduction at low frequency unavoidably leads to sensitivity increase at higher frequencies" >}}
+
+In the same spirit, the job of a more academic control designer with more abstract tools such as LQG, \\(\mathcal{H}\_\infty\\), is to set parameters (weights) of a synthesis machine to adjust the contours of the machine's digging blades to get just the right shape for the sensitivity function (Figure [2](#org29aa88f)).
+
+<a id="org29aa88f"></a>
+
+{{< figure src="/ox-hugo/stein03_formal_design.png" caption="Figure 2: Sensitivity shaping automated by modern control tools" >}}
+
+
+## Available bandwidth {#available-bandwidth}
+
+An argument is sometimes made that the Bode integrals are not really restrictive because we only seek to dig holes over finite frequency bands.
+We then have an infinite frequency range left over into which to dump the dirt, so we can make the layer arbitrarily thin (Figure [3](#orgf23d7a5)).
+
+<a id="orgf23d7a5"></a>
+
+{{< figure src="/ox-hugo/stein03_spreading_it_thin.png" caption="Figure 3: It is possible to spead the increase of the sensitivity function over a larger frequency band" >}}
+
+The weakness of this argument is evident from standard classical theory.
+A thin layer, say with \\(\ln|S| = \epsilon\\) requires a loop transfer function whose Nyquist diagram falls on a near-unit circle, centered at \\((-1 + j 0)\\) with a radius \\(\approx (1-\epsilon)\\), over a wide frequency range.
+This means that the loop cannot simply attenuate at high frequencies but must attenuate in a very precise way.
+The loop must maintain very good frequency response fidelity over wide frequency ranges.
+
+But a key fact about physical systems is that they do not exhibit good frequency response fidelity beyond a certain bandwidth.
+This is due to uncertain or unmodeled dynamics in the plant, to digital control implementations, to power limits, to nonlinearities, and to many other factors.
+Let us call that bandwidth the available bandwidth" \\(\Omega\_a\\), to distinguish it from other bandwidths such as crossover or \\(3-dB\\) magnitude loss.
+The available bandwidth is the frequency up to which we can keep \\(G(j\omega) K(j\omega)\\) close to a nominal design and beyond which we can only guarantee that the actual loop magnitude will attenuate rapidly enough (e.g. \\(|G(j\omega) K(j\omeg\\))| < &delta;/&omega;^2$).
+In today's popular robust control jargon, the available bandwidth is the frequency range over which the unstructured multiplicative perturbations are substantially less than unity.
+
+Note that the available bandwidth is not a function of the compensator or of the control design process.
+Rather, it is an a priori constraint imposed by the physical hardware we use in the control loop.
+Most importantly, the available bandwidth is always finite.
+
+Given all this, Bode's integrals really reduce to finite integrals over the range \\(0 \ge \omega \ge \Omega\_a\\):
+
+\begin{align}
+  \int\_0^{\Omega\_a} \ln{|S(j \omega)|} d \omega &= \delta \\\\\\
+  \int\_0^{\Omega\_a} \ln{|S(j \omega)|} d \omega &= \pi \sum\_{p \in P} \text{Re}(p) + \delta
+\end{align}
+
+All the action of the feedback design, the sensitivity improvements as well as the sensitivity deterioration, must occur within \\(0 \ge \omega \ge \Omega\_a\\).
+Only a small error \\(\delta\\) occurs outside that range, associated with the tail of the complete integrals.
+
+
+
+## Bibliography {#bibliography}
+
+<a id="orge299f80"></a>Stein, Gunter. 2003. “Respect the Unstable.” _IEEE Control Systems Magazine_ 23 (4). IEEE:12–25.

content/article/steinbuch98_advan_motion_contr.md

@@ -0,0 +1,23 @@
++++
+title = "Advanced motion control: an industrial perspective"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: ([Steinbuch and Norg 1998](#org162af57))
+
+Author(s)
+: Steinbuch, M., & Norg, M.
+
+Year
+: 1998
+
+
+## Bibliography {#bibliography}
+
+<a id="org162af57"></a>Steinbuch, M., and M.L. Norg. 1998. “Advanced Motion Control: An Industrial Perspective.” _European Journal of Control_ 4 (4):278–93. <https://doi.org/10.1016/s0947-3580(98)70121-9>.

content/article/stoev17_tensor_method_mimo_decoup_contr.md

@@ -0,0 +1,202 @@
++++
+title = "Tensor methods for mimo decoupling and control design using frequency response functions"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Decoupled Control](decoupled_control.md), [Multivariable Control](multivariable_control.md)
+
+Reference
+: ([Stoev et al. 2017](#org29c5c20))
+
+Author(s)
+: Stoev, J., Ertveldt, J., Oomen, T., & Schoukens, J.
+
+Year
+: 2017
+
+
+## Introduction {#introduction}
+
+By appropriate system design, most systems are either decoupled or can be decoupled using static input-output transformations.
+Hence, most motion system and their motion software architecture use SISO control design method and solutions.
+
+The first step typically involves a FRF identification using specific excitation signals.
+Once the FRF is available, the controller \\(K\\) can be designed directly based on the FRF data.
+Many classical MIMO control design methods aim at decoupling the open loop function at some location in the feedback loop.
+Because their are strong non-intuitive aspect of MIMO loop-shaping, the following step-by-step approach is proposed, in which the design complexity is only increased if justified by the problem at hand:
+
+-   **[Interaction Analysis](interaction_analysis.md)**.
+    The goal is to identify two sided interactions in the plant dynamics.
+    If there is no two sided interaction, then feedback design becomes a standard multi-loop SISO design problem.
+    Two measured of the plant interaction are [Relative Gain Array](relative_gain_array.md) and [Structured Singular Value](structured_singular_value.md).
+-   **Decoupling transformations**.
+    To reduce interaction, one may redefine the input and output of the plant using a decoupling transformation.
+    For motion systems, most transformations are found on the basis of **kinematic model**.
+    Herein, combinations of the actuators are defined so that actuator variables act in independent (orthogonal) directions at the center of gravity.
+    Similarly, combinations of the sensors are defined so that each translation and rotation of the center of gravity can be measured independently.
+    This, this basically amounts to the **inversion of a kinematic model** of the plant.
+-   Independent feedback control design
+-   Sequential feedback control design
+-   Norm based control design
+
+All steps, except for the last, can be performed with a non-parametric model of the plant (i.e. an identified FRF).
+
+
+## MIMO frequency response decomposition {#mimo-frequency-response-decomposition}
+
+The problem addressed in this paper is to decouple a given set of MIMO FRF.
+Such decoupled representation, if existing, would permit the MIMO FRF to be written as a linear combination of parallel SISO FRFs.
+The existing methods to convert the MIMO FRF into equivalent combination of SISO FRF fall into two groups:
+
+-   **matrix decomposition methods** use linear algebra based on eigen-value, or singular value decomposition which are able to diagonalize the FRF at a single frequency.
+-   **optimization methods** formulate the problem of simultaneous diagonalization of the FRF at multiple frequencies as an optimization problem.
+
+At each frequency \\(\omega\_i, i = 1 \dots N\_f\\), we have a square matrix \\(H(\omega\_i) \in \mathbb{C}^{N \times N}\\) with the complex response of the system relating the inputs and outputs.
+
+**MIMO decoupling of dyadic system**:
+
+\begin{align}
+H(\omega\_i) &= T\_y S(\omega\_i) T\_u + E(\omega\_i), \ i = 1 \dots N\_f \label{eq:decomposition} \\\\\\
+S(\omega\_i) &= \begin{bmatrix}
+S\_1(\omega\_i) & 0 & 0 \\\\\\
+0 & \ddots & 0 \\\\\\
+0 & 0 & S\_N(\omega\_i)
+\end{bmatrix}
+\end{align}
+
+where \\(S(\omega\_i)\\) is a diagonal matrix containing SISO FRFs \\(S\_k(\omega\_i) \in \mathbb{C}\\) on the main diagonal, \\(T\_y \in \mathbb{R}^{N \times N}\\), \\(T\_u \in \mathbb{R}^{N \times N}\\), \\(E(\omega\_i)\\) is the error.
+
+The approximate MIMO system decoupling is shown in Figure [1](#org3f61a67).
+
+In practical cases, the matrix \\(\hat{S}(\omega\_i) = T\_y^{-1} H(\omega\_i) T\_u^{-1}\\) will not be purely diagonal, but rather diagonally dominated.
+
+<a id="org3f61a67"></a>
+
+{{< figure src="/ox-hugo/stoev17_decoupled_system_schematic.png" caption="Figure 1: MIMO FRF decomposition in parallel branches" >}}
+
+The array \\(H(\omega\_i), i = 1 \dots N\_f\\) of complex matrices can be represented as a 3-dimensional sensor \\(\underline{H}\\).
+
+<div class="important">
+  <div></div>
+
+The core result of this paper is that the decomposition can be found by rephrasing \eqref{eq:decomposition} as a "Canonical Polyadic Decomposition" (CPD).
+This is shown in Figure [2](#org58ed38e), where \\(T\_y,T\_u,S\_d\\) can be directly computed using a single Matlab function.
+
+</div>
+
+Mathematically equivalent form of CPD is shown in the lower part of Figure [2](#org58ed38e), where the tensor \\(\underline{S}\\) contains the rows of the matrix \\(S\_d\\) on each of its diagonals in the third dimension, which is exactly the problem of simultaneous diagonalization.
+
+The transformation effectively diagonalises the original frequency response tensor \\(\underline{H}\\) using two transformation matrices \\(T\_y, T\_u\\).
+This operation is closely related to the SVD on a single matrix, however in this case the diagonalisation occurs for a set of matrices, each describing the MIMO FRF at different frequency.
+
+<a id="org58ed38e"></a>
+
+{{< figure src="/ox-hugo/stoev17_decompos_3d_tensor.png" caption="Figure 2: Decomposition of 3D tensor" >}}
+
+The direct application of a CPD procedure on the above complex data tensor would result in complex solutions, including complex matrices \\(T\_y \in \mathbb{C}^{N \times N}\\), \\(T\_u \in \mathbb{C}^{N \times N}\\).
+This is not useful for a practical decoupling of physical systems as we require real solutions for \\(T\_y,T\_u\\).
+The direct solution we use for this is to take the imaginary and real part of the complex tensor \\(\underline{H} \in \mathbb{C}^{N \times N \times N\_f}\\), each of them a real tensor by itself, and stack them one behind the other in the dimension of the frequencies, thus getting an augmented real-valued tensor \\(\underline{\breve{H}} \in \mathbb{R}^{N \times N \times 2N\_f}\\).
+
+
+## Numerical Example {#numerical-example}
+
+Let's now make a Matlab example using the [Tensorlab](https://www.tensorlab.net/) toolbox.
+
+Let's define a 2x2 diagonal system:
+
+```matlab
+S = [4e3/(s^2 + 25*s + 4e3) 0
+     0 4e5/(s^2 + 250*s + 4e5)];
+```
+
+And coupled this system with two random matrices:
+
+```matlab
+Ty = [0.13 0.003
+      0.43 0.51];
+
+Tu = [0.32 0.67
+      0.95 0.006];
+```
+
+The couple system is defined:
+
+```matlab
+H = Ty * S * Tu;
+```
+
+Then, suppose with have the frequency response function of the coupled plant:
+
+```matlab
+freqs = logspace(0,3,1000);
+H_frf = freqresp(H, freqs, 'Hz');
+```
+
+<a id="orgba720df"></a>
+
+{{< figure src="/ox-hugo/stoev17_coupled_diagonal_plants.png" caption="Figure 3: Diagonal and coupled plants" >}}
+
+We take the real and imaginary part of the FRF and concatenate the two along the frequency dimension.
+
+```matlab
+H_frf_real = cat(3, real(H_frf), imag(H_frf));
+```
+
+Then random matrices are initialize the the CPD.
+
+```matlab
+U = cpd_rnd(size(H_frf_real), size(H_frf_real,1));
+```
+
+And the CPD is performed.
+
+```matlab
+[T, ~] = cpd3_sd(H_frf_real, U);
+```
+
+The obtained decoupling matrices are:
+
+```matlab
+Ty_est = T{1};
+```
+
+```text
+Ty_est =
+        -0.289402459385387      -0.00647742171539879
+        -0.957207509228524         -1.10111369041218
+```
+
+```matlab
+Tu_est = T{2};
+```
+
+```text
+Tu_est =
+         0.430893809258741         0.999980044721872
+         0.902402640256826       0.00631744869723862
+```
+
+And the decoupled plant using the estimated optimal decoupling matrices is:
+
+```matlab
+H_dec = inv(Ty_est) * H * inv(Tu_est);
+```
+
+<a id="orgcb9fe2a"></a>
+
+{{< figure src="/ox-hugo/stoev17_results_decoupling_example.png" caption="Figure 4: Diagonal, coupled and decoupled plants" >}}
+
+
+## Conclusion {#conclusion}
+
+The paper presents an application for the tensor decomposition for the design of a static decoupling of a MIMO system.
+The results in this paper are obtained on a _non-parametric_ frequency domain model of the plant and indicate that the procedure is more robust that the eigen-value based decoupling.
+The advantages of this method with respect to some of th existing methods can be found when the FRF data available is disturbed by noise.
+
+
+
+## Bibliography {#bibliography}
+
+<a id="org29c5c20"></a>Stoev, Julian, Julien Ertveldt, Tom Oomen, and Johan Schoukens. 2017. “Tensor Methods for Mimo Decoupling and Control Design Using Frequency Response Functions.” _Mechatronics_ 45:71–81. <https://doi.org/https://doi.org/10.1016/j.mechatronics.2017.05.009>.

content/article/tang18_decen_vibrat_contr_voice_coil.md

@@ -1,21 +1,24 @@
 +++
 title = "Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments"
-author = ["Thomas Dehaeze"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
-: [Stewart Platforms]({{< relref "stewart_platforms" >}})
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}})
 
 Reference
-: <sup id="85f81ff678aabc195636437548e4234a"><a class="reference-link" href="#tang18_decen_vibrat_contr_voice_coil" title="Jie Tang, Dengqing Cao \&amp; Tianhu Yu, 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}, v(1), 132-145 (2018).">(Jie Tang {\it et al.}, 2018)</a></sup>
+: (<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
-<a class="bibtex-entry" id="tang18_decen_vibrat_contr_voice_coil">Tang, J., Cao, D., & Yu, T., *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)*, 132–145 (2018).  http://dx.doi.org/10.1177/0954406218756941</a> [↩](#85f81ff678aabc195636437548e4234a)
+
+## 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>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

@@ -0,0 +1,23 @@
++++
+title = "Six-axis vibration isolation system using soft actuators and multiple sensors"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: ([Thayer et al. 2002](#org3291862))
+
+Author(s)
+: Thayer, D., Campbell, M., Vagners, J., & Flotow, A. v.
+
+Year
+: 2002
+
+
+## Bibliography {#bibliography}
+
+<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

@@ -0,0 +1,23 @@
++++
+title = "Fiber-Based Distance Sensing Interferometry"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+: [Interferometers]({{<relref "interferometers.md#" >}})
+
+Reference
+: ([Thurner et al. 2015](#org7174c7b))
+
+Author(s)
+: Thurner, K., Quacquarelli, F. P., Braun, Pierre-Francois, Dal Savio, C., & Karrai, K.
+
+Year
+: 2015
+
+
+
+## Bibliography {#bibliography}
+
+<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
-: <sup id="ef30bc07c91e9d46a42198757dc610de"><a class="reference-link" href="#tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip" title="Tjepkema, van Dijk \&amp; Soemers, Sensor Fusion for Active Vibration Isolation in Precision  Equipment, {Journal of Sound and Vibration}, v(4), 735-749 (2012).">(Tjepkema {\it et al.}, 2012)</a></sup>
+: (<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
@@ -43,8 +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
-<a class="bibtex-entry" id="tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip">Tjepkema, D., Dijk, J. v., & Soemers, H., *Sensor fusion for active vibration isolation in precision equipment*, Journal of Sound and Vibration, *331(4)*, 735–749 (2012).  http://dx.doi.org/10.1016/j.jsv.2011.09.022</a> [↩](#ef30bc07c91e9d46a42198757dc610de)
+
+## 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>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/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
-: <sup id="1bccbe15e35ed02229afbc6528c5057e"><a class="reference-link" href="#wang12_autom_marker_full_field_hard" title="Jun Wang, Yu-chen Karen Chen, Qingxi Yuan, Andrei, Tkachuk, Can Erdonmez, Benjamin Hornberger, Michael \&amp; Feser, Automated Markerless Full Field Hard X-Ray Microscopic  Tomography At Sub-50 Nm 3-dimension Spatial Resolution, {Applied Physics Letters}, v(14), 143107 (2012).">(Jun Wang {\it et al.}, 2012)</a></sup>
+: (<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
@@ -20,10 +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
-<a class="bibtex-entry" id="wang12_autom_marker_full_field_hard">Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., & Feser, M., *Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution*, Applied Physics Letters, *100(14)*, 143107 (2012).  http://dx.doi.org/10.1063/1.3701579</a> [↩](#1bccbe15e35ed02229afbc6528c5057e)
+
+## 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>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
-: <sup id="db95fac7cd46c14e2b4f38e8ca4158fe"><a class="reference-link" href="#wang16_inves_activ_vibrat_isolat_stewar" title="Wang, Xie, Chen, Zhang \&amp; Zhiyi, Investigation on Active Vibration Isolation of a Stewart  Platform With Piezoelectric Actuators, {Journal of Sound and Vibration}, v(), 1-19 (2016).">(Wang {\it et al.}, 2016)</a></sup>
+: (<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="orgd3fa417"></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
--   direct feedback of integrated forces => dampen vibration of inherent modes and thus reduce random vibrations
+-   the FxLMS-based adaptive inverse control =&gt; suppress transmission of periodic vibrations
+-   direct feedback of integrated forces =&gt; dampen vibration of inherent modes and thus reduce random vibrations
 
-Force Feedback (Figure [2](#org55d173d)).
+Force Feedback ([Figure 2](#figure--fig:wang16-force-feedback)).
 
 -   the force sensor is mounted **between the base and the strut**
 
-<a id="org55d173d"></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:
 
@@ -53,5 +53,9 @@ Sorts of HAC-LAC control:
 -   All 6 transfer function from actuator force to force sensors are almost the same (gain offset)
 -   Effectiveness of control methods are shown
 
-# Bibliography
-<a class="bibtex-entry" id="wang16_inves_activ_vibrat_isolat_stewar">Wang, C., Xie, X., Chen, Y., & Zhang, Z., *Investigation on active vibration isolation of a stewart platform with piezoelectric actuators*, Journal of Sound and Vibration, *383()*, 1–19 (2016).  http://dx.doi.org/10.1016/j.jsv.2016.07.021</a> [↩](#db95fac7cd46c14e2b4f38e8ca4158fe)
+
+## 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>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
-: <sup id="d39b6222c8dd2baf188d677733c2826c"><a class="reference-link" href="#yang19_dynam_model_decoup_contr_flexib" title="Yang, Wu, Chen, Kang, ShengZheng \&amp; Cheng, Dynamic Modeling and Decoupled Control of a Flexible  Stewart Platform for Vibration Isolation, {Journal of Sound and Vibration}, v(), 398-412 (2019).">(Yang {\it et al.}, 2019)</a></sup>
+: (<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](#org96fb07f)):
+**Stewart platform** ([Figure 1](#figure--fig:yang19-stewart-platform)):
 
 -   piezoelectric actuators
--   flexible joints (Figure [2](#org62b30be))
+-   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="org96fb07f"></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="org62b30be"></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](#org62b30be)) 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](#org6a06ad2).
+The block diagram of the control strategy is represented in [Figure 3](#figure--fig:yang19-control-arch).
 
-<a id="org6a06ad2"></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 \\]
@@ -121,17 +121,21 @@ 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](#orgb8bd696).
+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="orgb8bd696"></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.
 > The force feedback makes the six-DOF MIMO system decoupled into six SISO subsystems in modal space, where the control gains can be designed and analyzed more effectively and conveniently.
 > 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
-<a class="bibtex-entry" id="yang19_dynam_model_decoup_contr_flexib">Yang, X., Wu, H., Chen, B., Kang, S., & Cheng, S., *Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation*, Journal of Sound and Vibration, *439()*, 398–412 (2019).  http://dx.doi.org/10.1016/j.jsv.2018.10.007</a> [↩](#d39b6222c8dd2baf188d677733c2826c)
+
+## 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>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"]
-draft = false
+author = ["Dehaeze Thomas"]
+draft = true
 +++
 
 Tags
@@ -9,13 +9,17 @@ Tags
 
 
 Reference
-: <sup id="44caf201a37b1b3af63de65257785085"><a class="reference-link" href="#yun20_inves_two_stage_vibrat_suppr" title="Hai Yun, Lei Liu, Qing Li \&amp; Hongjie Yang, Investigation on Two-Stage Vibration Suppression and  Precision Pointing for Space Optical Payloads, {Aerospace Science and Technology}, v(nil), 105543 (2020).">(Hai Yun {\it et al.}, 2020)</a></sup>
+: (<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
-<a class="bibtex-entry" id="yun20_inves_two_stage_vibrat_suppr">Yun, H., Liu, L., Li, Q., & Yang, H., *Investigation on two-stage vibration suppression and precision pointing for space optical payloads*, Aerospace Science and Technology, *96(nil)*, 105543 (2020).  http://dx.doi.org/10.1016/j.ast.2019.105543</a> [↩](#44caf201a37b1b3af63de65257785085)
+
+## 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>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

@@ -1,18 +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
-: <sup id="a457d4de462d2fe52a1bbb848182b554"><a class="reference-link" href="#zhang11_six_dof" title="Zhen Zhang, J Liu, Jq Mao, Yx Guo \&amp; Yh Ma, Six DOF active vibration control using stewart platform  with non-cubic configuration, nil, in in: {2011 6th IEEE Conference on Industrial Electronics and
-                      Applications}, edited by (2011)">(Zhen Zhang {\it et al.}, 2011)</a></sup>
+: (<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
@@ -21,14 +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="org856ccde"></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
-<a class="bibtex-entry" id="zhang11_six_dof">Zhang, Z., Liu, J., Mao, J., Guo, Y., & Ma, Y., *Six dof active vibration control using stewart platform with non-cubic configuration*, In , 2011 6th IEEE Conference on Industrial Electronics and Applications (pp. ) (2011). : .</a> [↩](#a457d4de462d2fe52a1bbb848182b554)
+
+## 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>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

@@ -1,46 +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
-: <sup id="e9037e3bf20089c45ab77215406558ca"><a class="reference-link" href="#zuo04_elemen_system_desig_activ_passiv_vibrat_isolat" title="Zuo, Element and System Design for Active and Passive Vibration  Isolation (2004).">(Zuo, 2004)</a></sup>
-
-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.
-
-<a id="org0286cf1"></a>
-
-{{< figure src="/ox-hugo/zuo04_piezo_spring_series.png" caption="Figure 1: PZT actuator and spring in series" >}}
-
-<a id="org679f77c"></a>
-
-{{< figure src="/ox-hugo/zuo04_voice_coil_spring_parallel.png" caption="Figure 2: Voice coil actuator and spring in parallel" >}}
-
-<a id="orged24ee6"></a>
-
-{{< figure src="/ox-hugo/zuo04_piezo_plant.png" caption="Figure 3: Transmission from PZT voltage to geophone output" >}}
-
-<a id="org9b75d10"></a>
-
-{{< figure src="/ox-hugo/zuo04_voice_coil_plant.png" caption="Figure 4: Transmission from voice coil voltage to geophone output" >}}
-
-# Bibliography
-<a class="bibtex-entry" id="zuo04_elemen_system_desig_activ_passiv_vibrat_isolat">Zuo, L., *Element and system design for active and passive vibration isolation* (2004). Massachusetts Institute of Technology.</a> [↩](#e9037e3bf20089c45ab77215406558ca)

content/book/albertos04_multiv_contr_system.md

@@ -1,20 +0,0 @@
-+++
-title = "Multivariable control systems: an engineering approach"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Multivariable Control]({{< relref "multivariable_control" >}})
-
-Reference
-: <sup id="51789ae56fcd2284b8426153d90595c8"><a href="#albertos04_multiv_contr_system" title="Albertos \&amp; Antonio, Multivariable Control Systems: an Engineering Approach, Springer-Verlag (2004).">(Albertos \& Antonio, 2004)</a></sup>
-
-Author(s)
-: Albertos, P., & Antonio, S.
-
-Year
-: 2004
-
-# Bibliography
-<a id="albertos04_multiv_contr_system"></a>Albertos, P., & Antonio, S., *Multivariable control systems: an engineering approach* (2004), : Springer-Verlag. [↩](#51789ae56fcd2284b8426153d90595c8)

content/book/du10_model_contr_vibrat_mechan_system.md

@@ -1,22 +1,540 @@
 +++
 title = "Modeling and control of vibration in mechanical systems"
-author = ["Thomas Dehaeze"]
-draft = false
+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
-: <sup id="1d38bd128d92142dd456ab4e9bb4eb84"><a href="#du10_model_contr_vibrat_mechan_system" title="Chunling Du \&amp; Lihua Xie, Modeling and Control of Vibration in Mechanical Systems, CRC Press (2010).">(Chunling Du \& Lihua Xie, 2010)</a></sup>
+: (<a href="#citeproc_bib_item_1">Du and Xie 2010</a>)
 
 Author(s)
-: Du, C., & Xie, L.
+: Du, C., &amp; Xie, L.
 
 Year
 : 2010
 
-Read Chapter 1 and 3.
 
-# Bibliography
-<a id="du10_model_contr_vibrat_mechan_system"></a>Du, C., & Xie, L., *Modeling and control of vibration in mechanical systems* (2010), : CRC Press. [↩](#1d38bd128d92142dd456ab4e9bb4eb84)
+## 1. Mechanical Systems and Vibration {#1-dot-mechanical-systems-and-vibration}
+
+
+### 1.1 Magnetic recording system {#1-dot-1-magnetic-recording-system}
+
+
+### 1.2 Stewart platform {#1-dot-2-stewart-platform}
+
+
+### 1.3 Vibration sources and descriptions {#1-dot-3-vibration-sources-and-descriptions}
+
+
+### 1.4 Types of vibration {#1-dot-4-types-of-vibration}
+
+
+#### 1.4.1 Free and forced vibration {#1-dot-4-dot-1-free-and-forced-vibration}
+
+
+#### 1.4.2 Damped and undamped vibration {#1-dot-4-dot-2-damped-and-undamped-vibration}
+
+
+#### 1.4.3 Linear and nonlinear vibration {#1-dot-4-dot-3-linear-and-nonlinear-vibration}
+
+
+#### 1.4.4 Deterministic and random vibration {#1-dot-4-dot-4-deterministic-and-random-vibration}
+
+
+#### 1.4.5 Periodic and nonperiodic vibration {#1-dot-4-dot-5-periodic-and-nonperiodic-vibration}
+
+
+#### 1.4.6 Broad-band and narrow-band vibration {#1-dot-4-dot-6-broad-band-and-narrow-band-vibration}
+
+
+### 1.5 Random vibration {#1-dot-5-random-vibration}
+
+
+#### 1.5.1 Random process {#1-dot-5-dot-1-random-process}
+
+
+#### 1.5.2 Stationary random process {#1-dot-5-dot-2-stationary-random-process}
+
+
+#### 1.5.3 Gaussian random process {#1-dot-5-dot-3-gaussian-random-process}
+
+
+### 1.6 Vibration analysis {#1-dot-6-vibration-analysis}
+
+
+#### 1.6.1 Fourier transform and spectrum analysis {#1-dot-6-dot-1-fourier-transform-and-spectrum-analysis}
+
+
+#### 1.6.2 Relationship between the Fourier and Laplace transforms {#1-dot-6-dot-2-relationship-between-the-fourier-and-laplace-transforms}
+
+
+#### 1.6.3 Spectral analysis {#1-dot-6-dot-3-spectral-analysis}
+
+
+## 2. Modeling of Disk Drive System and Its Vibration {#2-dot-modeling-of-disk-drive-system-and-its-vibration}
+
+
+### 2.1 Introduction {#2-dot-1-introduction}
+
+
+### 2.2 System description {#2-dot-2-system-description}
+
+
+### 2.3 System modeling {#2-dot-3-system-modeling}
+
+
+#### 2.3.1 Modeling of a VCM actuator {#2-dot-3-dot-1-modeling-of-a-vcm-actuator}
+
+
+#### 2.3.2 Modeling of friction {#2-dot-3-dot-2-modeling-of-friction}
+
+
+#### 2.3.3 Modeling of a PZT microactuator {#2-dot-3-dot-3-modeling-of-a-pzt-microactuator}
+
+
+#### 2.3.4 An example {#2-dot-3-dot-4-an-example}
+
+
+### 2.4 Vibration modeling {#2-dot-4-vibration-modeling}
+
+
+#### 2.4.1 Spectrum-based vibration modeling {#2-dot-4-dot-1-spectrum-based-vibration-modeling}
+
+
+#### 2.4.2 Adaptive modeling of disturbance {#2-dot-4-dot-2-adaptive-modeling-of-disturbance}
+
+
+### 2.5 Conclusion {#2-dot-5-conclusion}
+
+
+## 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}
+
+
+### 3.2 System description and governing equations {#3-dot-2-system-description-and-governing-equations}
+
+
+### 3.3 Modeling using adaptive filtering approach {#3-dot-3-modeling-using-adaptive-filtering-approach}
+
+
+#### 3.3.1 Adaptive filtering theory {#3-dot-3-dot-1-adaptive-filtering-theory}
+
+
+#### 3.3.2 Modeling of a Stewart platform {#3-dot-3-dot-2-modeling-of-a-stewart-platform}
+
+
+### 3.4 Conclusion {#3-dot-4-conclusion}
+
+
+## 4. Classical Vibration Control {#4-dot-classical-vibration-control}
+
+
+### 4.1 Introduction {#4-dot-1-introduction}
+
+
+### 4.2 Passive control {#4-dot-2-passive-control}
+
+
+#### 4.2.1 Isolators {#4-dot-2-dot-1-isolators}
+
+
+#### 4.2.2 Absorbers {#4-dot-2-dot-2-absorbers}
+
+
+#### 4.2.3 Resonators {#4-dot-2-dot-3-resonators}
+
+
+#### 4.2.4 Suspension {#4-dot-2-dot-4-suspension}
+
+
+#### 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}
+
+
+### 4.4 Active vibration control {#4-dot-4-active-vibration-control}
+
+
+#### 4.4.1 Actuators {#4-dot-4-dot-1-actuators}
+
+
+#### 4.4.2 Active systems {#4-dot-4-dot-2-active-systems}
+
+
+#### 4.4.3 Control strategy {#4-dot-4-dot-3-control-strategy}
+
+
+### 4.5 Conclusion {#4-dot-5-conclusion}
+
+
+## 5. Introduction to Optimal and Robust Control {#5-dot-introduction-to-optimal-and-robust-control}
+
+
+### 5.1 Introduction {#5-dot-1-introduction}
+
+
+### 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&amp;#8734; norm {#5-dot-2-dot-2-h-and-8734-norm}
+
+
+### 5.3 H2 optimal control {#5-dot-3-h2-optimal-control}
+
+
+#### 5.3.1 Continuous-time case {#5-dot-3-dot-1-continuous-time-case}
+
+
+#### 5.3.2 Discrete-time case {#5-dot-3-dot-2-discrete-time-case}
+
+
+### 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}
+
+
+#### 5.4.2 Discrete-time case {#5-dot-4-dot-2-discrete-time-case}
+
+
+### 5.5 Robust control {#5-dot-5-robust-control}
+
+
+### 5.6 Controller parametrization {#5-dot-6-controller-parametrization}
+
+
+### 5.7 Performance limitation {#5-dot-7-performance-limitation}
+
+
+#### 5.7.1 Bode integral constraint {#5-dot-7-dot-1-bode-integral-constraint}
+
+
+#### 5.7.2 Relationship between system gain and phase {#5-dot-7-dot-2-relationship-between-system-gain-and-phase}
+
+
+#### 5.7.3 Sampling {#5-dot-7-dot-3-sampling}
+
+
+### 5.8 Conclusion {#5-dot-8-conclusion}
+
+
+## 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&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}
+
+
+### 6.4 Method 2: an improved slack variable approach {#6-dot-4-method-2-an-improved-slack-variable-approach}
+
+
+### 6.5 Application in servo loop design for hard disk drives {#6-dot-5-application-in-servo-loop-design-for-hard-disk-drives}
+
+
+#### 6.5.1 Problem formulation {#6-dot-5-dot-1-problem-formulation}
+
+
+#### 6.5.2 Design results {#6-dot-5-dot-2-design-results}
+
+
+### 6.6 Conclusion {#6-dot-6-conclusion}
+
+
+## 7. Low-Hump Sensitivity Control Design for Hard Disk Drive Systems {#7-dot-low-hump-sensitivity-control-design-for-hard-disk-drive-systems}
+
+
+### 7.1 Introduction {#7-dot-1-introduction}
+
+
+### 7.2 Problem statement {#7-dot-2-problem-statement}
+
+
+### 7.3 Design in continuous-time domain {#7-dot-3-design-in-continuous-time-domain}
+
+
+#### 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}
+
+
+#### 7.3.3 Implementation on a hard disk drive {#7-dot-3-dot-3-implementation-on-a-hard-disk-drive}
+
+
+### 7.4 Design in discrete-time domain {#7-dot-4-design-in-discrete-time-domain}
+
+
+#### 7.4.1 Synthesis method for low-hump sensitivity function {#7-dot-4-dot-1-synthesis-method-for-low-hump-sensitivity-function}
+
+
+#### 7.4.2 An application example {#7-dot-4-dot-2-an-application-example}
+
+
+#### 7.4.3 Implementation on a hard disk drive {#7-dot-4-dot-3-implementation-on-a-hard-disk-drive}
+
+
+### 7.5 Conclusion {#7-dot-5-conclusion}
+
+
+## 8. Generalized KYP Lemma-Based Loop Shaping Control Design {#8-dot-generalized-kyp-lemma-based-loop-shaping-control-design}
+
+
+### 8.1 Introduction {#8-dot-1-introduction}
+
+
+### 8.2 Problem description {#8-dot-2-problem-description}
+
+
+### 8.3 Generalized KYP lemma-based control design method {#8-dot-3-generalized-kyp-lemma-based-control-design-method}
+
+
+### 8.4 Peak filter {#8-dot-4-peak-filter}
+
+
+#### 8.4.1 Conventional peak filter {#8-dot-4-dot-1-conventional-peak-filter}
+
+
+#### 8.4.2 Phase lead peak filter {#8-dot-4-dot-2-phase-lead-peak-filter}
+
+
+#### 8.4.3 Group peak filter {#8-dot-4-dot-3-group-peak-filter}
+
+
+### 8.5 Application in high frequency vibration rejection {#8-dot-5-application-in-high-frequency-vibration-rejection}
+
+
+### 8.6 Application in mid-frequency vibration rejection {#8-dot-6-application-in-mid-frequency-vibration-rejection}
+
+
+### 8.7 Conclusion {#8-dot-7-conclusion}
+
+
+## 9. Combined H2 and KYP Lemma-Based Control Design {#9-dot-combined-h2-and-kyp-lemma-based-control-design}
+
+
+### 9.1 Introduction {#9-dot-1-introduction}
+
+
+### 9.2 Problem formulation {#9-dot-2-problem-formulation}
+
+
+### 9.3 Controller design for specific disturbance rejection and overall error minimization {#9-dot-3-controller-design-for-specific-disturbance-rejection-and-overall-error-minimization}
+
+
+#### 9.3.1 Q parametrization to meet specific specifications {#9-dot-3-dot-1-q-parametrization-to-meet-specific-specifications}
+
+
+#### 9.3.2 Q parametrization to minimize H2 performance {#9-dot-3-dot-2-q-parametrization-to-minimize-h2-performance}
+
+
+#### 9.3.3 Design steps {#9-dot-3-dot-3-design-steps}
+
+
+### 9.4 Simulation and implementation results {#9-dot-4-simulation-and-implementation-results}
+
+
+#### 9.4.1 System models {#9-dot-4-dot-1-system-models}
+
+
+#### 9.4.2 Rejection of specific disturbance and H2 performance minimization {#9-dot-4-dot-2-rejection-of-specific-disturbance-and-h2-performance-minimization}
+
+
+#### 9.4.3 Rejection of two disturbances with H[sub(2)] performance minimization {#9-dot-4-dot-3-rejection-of-two-disturbances-with-h-sub--2--performance-minimization}
+
+
+### 9.5 Conclusion {#9-dot-5-conclusion}
+
+
+## 10. Blending Control for Multi-Frequency Disturbance Rejection {#10-dot-blending-control-for-multi-frequency-disturbance-rejection}
+
+
+### 10.1 Introduction {#10-dot-1-introduction}
+
+
+### 10.2 Control blending {#10-dot-2-control-blending}
+
+
+#### 10.2.1 State feedback control blending {#10-dot-2-dot-1-state-feedback-control-blending}
+
+
+#### 10.2.2 Output feedback control blending {#10-dot-2-dot-2-output-feedback-control-blending}
+
+
+### 10.3 Control blending application in multi-frequency disturbance rejection {#10-dot-3-control-blending-application-in-multi-frequency-disturbance-rejection}
+
+
+#### 10.3.1 Problem formulation {#10-dot-3-dot-1-problem-formulation}
+
+
+#### 10.3.2 Controller design via the control blending technique {#10-dot-3-dot-2-controller-design-via-the-control-blending-technique}
+
+
+### 10.4 Simulation and experimental results {#10-dot-4-simulation-and-experimental-results}
+
+
+#### 10.4.1 Rejecting high-frequency disturbances {#10-dot-4-dot-1-rejecting-high-frequency-disturbances}
+
+
+#### 10.4.2 Rejecting a combined mid and high frequency disturbance {#10-dot-4-dot-2-rejecting-a-combined-mid-and-high-frequency-disturbance}
+
+
+### 10.5 Conclusion {#10-dot-5-conclusion}
+
+
+## 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}
+
+
+### 11.2 Conventional disturbance observer {#11-dot-2-conventional-disturbance-observer}
+
+
+### 11.3 A general form of disturbance observer {#11-dot-3-a-general-form-of-disturbance-observer}
+
+
+### 11.4 Application results {#11-dot-4-application-results}
+
+
+### 11.5 Conclusion {#11-dot-5-conclusion}
+
+
+## 12. Two-Dimensional H2 Control for Error Minimization {#12-dot-two-dimensional-h2-control-for-error-minimization}
+
+
+### 12.1 Introduction {#12-dot-1-introduction}
+
+
+### 12.2 2-D stabilization control {#12-dot-2-2-d-stabilization-control}
+
+
+### 12.3 2-D H2 control {#12-dot-3-2-d-h2-control}
+
+
+### 12.4 SSTW process and modeling {#12-dot-4-sstw-process-and-modeling}
+
+
+#### 12.4.1 SSTW servo loop {#12-dot-4-dot-1-sstw-servo-loop}
+
+
+#### 12.4.2 Two-dimensional model {#12-dot-4-dot-2-two-dimensional-model}
+
+
+### 12.5 Feedforward compensation method {#12-dot-5-feedforward-compensation-method}
+
+
+### 12.6 2-D control formulation for SSTW {#12-dot-6-2-d-control-formulation-for-sstw}
+
+
+### 12.7 2-D stabilization control for error propagation containment {#12-dot-7-2-d-stabilization-control-for-error-propagation-containment}
+
+
+#### 12.7.1 Simulation results {#12-dot-7-dot-1-simulation-results}
+
+
+### 12.8 2-D H2 control for error minimization {#12-dot-8-2-d-h2-control-for-error-minimization}
+
+
+#### 12.8.1 Simulation results {#12-dot-8-dot-1-simulation-results}
+
+
+#### 12.8.2 Experimental results {#12-dot-8-dot-2-experimental-results}
+
+
+### 12.9 Conclusion {#12-dot-9-conclusion}
+
+
+## 13. Nonlinearity Compensation and Nonlinear Control {#13-dot-nonlinearity-compensation-and-nonlinear-control}
+
+
+### 13.1 Introduction {#13-dot-1-introduction}
+
+
+### 13.2 Nonlinearity compensation {#13-dot-2-nonlinearity-compensation}
+
+
+### 13.3 Nonlinear control {#13-dot-3-nonlinear-control}
+
+
+#### 13.3.1 Design of a composite control law {#13-dot-3-dot-1-design-of-a-composite-control-law}
+
+
+#### 13.3.2 Experimental results in hard disk drives {#13-dot-3-dot-2-experimental-results-in-hard-disk-drives}
+
+
+### 13.4 Conclusion {#13-dot-4-conclusion}
+
+
+## 14. Quantization Effect on Vibration Rejection and Its Compensation {#14-dot-quantization-effect-on-vibration-rejection-and-its-compensation}
+
+
+### 14.1 Introduction {#14-dot-1-introduction}
+
+
+### 14.2 Description of control system with quantizer {#14-dot-2-description-of-control-system-with-quantizer}
+
+
+### 14.3 Quantization effect on error rejection {#14-dot-3-quantization-effect-on-error-rejection}
+
+
+#### 14.3.1 Quantizer frequency response measurement {#14-dot-3-dot-1-quantizer-frequency-response-measurement}
+
+
+#### 14.3.2 Quantization effect on error rejection {#14-dot-3-dot-2-quantization-effect-on-error-rejection}
+
+
+### 14.4 Compensation of quantization effect on error rejection {#14-dot-4-compensation-of-quantization-effect-on-error-rejection}
+
+
+### 14.5 Conclusion {#14-dot-5-conclusion}
+
+
+## 15. Adaptive Filtering Algorithms for Active Vibration Control {#15-dot-adaptive-filtering-algorithms-for-active-vibration-control}
+
+
+### 15.1 Introduction {#15-dot-1-introduction}
+
+
+### 15.2 Adaptive feedforward algorithm {#15-dot-2-adaptive-feedforward-algorithm}
+
+
+### 15.3 Adaptive feedback algorithm {#15-dot-3-adaptive-feedback-algorithm}
+
+
+### 15.4 Comparison between feedforward and feedback controls {#15-dot-4-comparison-between-feedforward-and-feedback-controls}
+
+
+### 15.5 Application in Stewart platform {#15-dot-5-application-in-stewart-platform}
+
+
+#### 15.5.1 Multi-channel adaptive feedback AVC system {#15-dot-5-dot-1-multi-channel-adaptive-feedback-avc-system}
+
+
+#### 15.5.2 Multi-channel adaptive feedback algorithm for hexapod platform {#15-dot-5-dot-2-multi-channel-adaptive-feedback-algorithm-for-hexapod-platform}
+
+
+#### 15.5.3 Simulation and implementation {#15-dot-5-dot-3-simulation-and-implementation}
+
+
+### 15.6 Conclusion {#15-dot-6-conclusion}
+
+
+## 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>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 +1,8 @@
 +++
 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
 +++
 
@@ -9,14 +11,27 @@ Tags
 
 
 Reference
-: <sup id="28e6aa60b8446943c921ff0d6578ac85"><a href="#du19_multi_actuat_system_contr" title="Chunling Du \&amp; Chee Khiang Pang, Multi-stage Actuation Systems and Control, CRC Press (2019).">(Chunling Du \& Chee Khiang Pang, 2019)</a></sup>
+: (<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
 
+<div style="display: none;">
+\(
+\newcommand{\SI}[2]{#1\,#2}
+% Simulate SIunitx
+\newcommand{\ang}[1]{#1^{\circ}}
+\newcommand{\degree}{^{\circ}}
+\newcommand{\radian}{\text{rad}}
+\newcommand{\percent}{\%}
+\newcommand{\decibel}{\text{dB}}
+\newcommand{\per}{/}
+\)
+</div>
+
 
 ## Mechanical Actuation Systems {#mechanical-actuation-systems}
 
@@ -28,11 +43,11 @@ When high bandwidth, high position accuracy and long stroke are required simulta
 Popular choices for coarse actuator are:
 
 -   DC motor
--   Voice coil motor (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 actuator 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.
 
@@ -60,43 +75,43 @@ 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{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{\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](#orgb678385)) 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="orgb678385"></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>
 
-|             | Elect.                                        | PZT                                           | Thermal                    |
-|-------------|-----------------------------------------------|-----------------------------------------------|----------------------------|
-| TF          | \\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\\) | \\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\\) | \\(\frac{K}{\tau s + 1}\\) |
-| \\(\tau\\)  | \\(<\SI{0.1}{ms}\\)                           | \\(<\SI{0.05}{ms}\\)                          | \\(>\SI{0.1}{ms}\\)        |
-| \\(omega\\) | \\(1-\SI{2}{kHz}\\)                           | \\(20-\SI{25}{kHz}\\)                         | \\(>\SI{15}{kHz}\\)        |
+|              | Elect.                                        | PZT                                           | Thermal                    |
+|--------------|-----------------------------------------------|-----------------------------------------------|----------------------------|
+| TF           | \\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\\) | \\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\\) | \\(\frac{K}{\tau s + 1}\\) |
+| \\(\tau\\)   | \\(<\SI{0.1}{ms}\\)                           | \\(<\SI{0.05}{ms}\\)                          | \\(>\SI{0.1}{ms}\\)        |
+| \\(\omega\\) | \\(1-\SI{2}{kHz}\\)                           | \\(20-\SI{25}{kHz}\\)                         | \\(>\SI{15}{kHz}\\)        |
 
 
 ### Single-Stage Actuation Systems {#single-stage-actuation-systems}
 
-A typical closed-loop control system is shown on figure [2](#orgcf5d697), 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="orgcf5d697"></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}
@@ -104,9 +119,9 @@ A typical closed-loop control system is shown on figure [2](#orgcf5d697), 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="orga011b51"></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}
@@ -130,7 +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](#org7def875).
+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\\).
@@ -138,9 +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="org7def875"></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) \\]
@@ -160,16 +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](#orgbb3c494).
+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="orgbb3c494"></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.
 
@@ -177,7 +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](#orge3f8703) 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
 
@@ -187,11 +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="orge3f8703"></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](#orgc402b0c) 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}
@@ -204,18 +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](#org402df06), 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="org402df06"></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](#orge904ce1), 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="orge904ce1"></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.
@@ -246,15 +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](#org8c31dd5) 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="org8c31dd5"></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
 
@@ -265,8 +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\_p(z) &= P\_p(z) C\_p(z) \\\\\\
+  G\_v(z) &= P\_v(z) C\_v(z) \\\\
+  G\_p(z) &= P\_p(z) C\_p(z) \\\\
   G\_m(z) &= P\_m(z) C\_m(z)
 \end{align\*}
 
@@ -281,17 +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](#orgd95bc97).
+The open-loop frequency responses of the three stages are shown on [Figure 10](#figure--fig:open-loop-three-stage).
 
-<a id="orgd95bc97"></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](#org50990f8).
+The obtained sensitivity function is shown on [Figure 11](#figure--fig:sensitivity-three-stage).
 
-<a id="org50990f8"></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}
@@ -304,13 +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](#org8c31dd5), 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\_m &= C\_m e,\ y\_m = P\_m C\_m 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\_v &= C\_v ( 1 + \hat{P}\_pC\_p ) e,\ y\_v = P\_v ( u\_v + d\_1 )
 \end{align\*}
 
@@ -320,11 +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](#org7ec3564)).
+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](#org6bf8240) 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\\)
@@ -333,23 +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="org7ec3564"></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\_m &= C\_m e, \ y\_m = P\_m M\_m e \\\\\\
+  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\_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](#org56aeb13)).
+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="org56aeb13"></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}
@@ -655,5 +670,9 @@ Specific usage of PZT elements has been produced for system performance improvem
 Using PZT elements as a sensor to deal with high-frequency vibration beyond the bandwidth has been proposed and systematic controller design methods have been developed.
 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
-<a id="du19_multi_actuat_system_contr"></a>Du, C., & Pang, C. K., *Multi-stage actuation systems and control* (2019), Boca Raton, FL: CRC Press. [↩](#28e6aa60b8446943c921ff0d6578ac85)
+
+## 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>Du, Chunling, and Chee Khiang Pang. 2019. <i>Multi-Stage Actuation Systems and Control</i>. Boca Raton, FL: CRC Press.</div>
+</div>

content/book/fleming14_desig_model_contr_nanop_system.md

@@ -1,21 +1,858 @@
 +++
 title = "Design, modeling and control of nanopositioning systems"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
+description = "Talks about various topics related to nano-positioning systems."
+keywords = ["Control", "Metrology", "Flexible Joints"]
 draft = false
 +++
 
 Tags
-:
-
+: [Piezoelectric Actuators]({{< relref "piezoelectric_actuators.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}})
 
 Reference
-: <sup id="1851788e0c4aa5b06afe3362c73ea5eb"><a href="#fleming14_desig_model_contr_nanop_system" title="Andrew Fleming \&amp; Kam Leang, Design, Modeling and Control of Nanopositioning Systems, Springer International Publishing (2014).">(Andrew Fleming \& Kam Leang, 2014)</a></sup>
+: (<a href="#citeproc_bib_item_1">Fleming and Leang 2014</a>)
 
 Author(s)
-: Fleming, A. J., & Leang, K. K.
+: Fleming, A. J., &amp; Leang, K. K.
 
 Year
 : 2014
 
-# Bibliography
-<a id="fleming14_desig_model_contr_nanop_system"></a>Fleming, A. J., & Leang, K. K., *Design, modeling and control of nanopositioning systems* (2014), : Springer International Publishing. [↩](#1851788e0c4aa5b06afe3362c73ea5eb)
+
+## Introduction to Nanotechnology {#introduction-to-nanotechnology}
+
+
+## Introduction to Nanopositioning {#introduction-to-nanopositioning}
+
+
+## Scanning Probe Microscopy {#scanning-probe-microscopy}
+
+
+## Challenges with Nanopositioning Systems {#challenges-with-nanopositioning-systems}
+
+
+### Hysteresis {#hysteresis}
+
+
+### Creep {#creep}
+
+
+### Thermal Drift {#thermal-drift}
+
+
+### Mechanical Resonance {#mechanical-resonance}
+
+
+## Control of Nanopositioning Systems {#control-of-nanopositioning-systems}
+
+
+### Feedback Control {#feedback-control}
+
+
+### Feedforward Control {#feedforward-control}
+
+
+## Book Summary {#book-summary}
+
+
+### Assumed Knowledge {#assumed-knowledge}
+
+
+### Content Summary {#content-summary}
+
+
+## References {#references}
+
+
+## The Piezoelectric Effect {#the-piezoelectric-effect}
+
+
+## Piezoelectric Compositions {#piezoelectric-compositions}
+
+
+## Manufacturing Piezoelectric Ceramics {#manufacturing-piezoelectric-ceramics}
+
+
+## Piezoelectric Transducers {#piezoelectric-transducers}
+
+
+## Application Considerations {#application-considerations}
+
+
+## Response of Piezoelectric Actuators {#response-of-piezoelectric-actuators}
+
+
+## Modeling Creep and Vibration in Piezoelectric Actuators {#modeling-creep-and-vibration-in-piezoelectric-actuators}
+
+
+## Chapter Summary {#chapter-summary}
+
+
+## References {#references}
+
+
+## Piezoelectric Tube Nanopositioners {#piezoelectric-tube-nanopositioners}
+
+
+### 63mm Piezoelectric Tube {#63mm-piezoelectric-tube}
+
+
+### 40mm Piezoelectric Tube Nanopositioner {#40mm-piezoelectric-tube-nanopositioner}
+
+
+## Piezoelectric Stack Nanopositioners {#piezoelectric-stack-nanopositioners}
+
+
+### Phyisk Instrumente P-734 Nanopositioner {#phyisk-instrumente-p-734-nanopositioner}
+
+
+### Phyisk Instrumente P-733.3DD Nanopositioner {#phyisk-instrumente-p-733-dot-3dd-nanopositioner}
+
+
+### Vertical Nanopositioners {#vertical-nanopositioners}
+
+
+### Rotational Nanopositioners {#rotational-nanopositioners}
+
+
+### Low Temperature and UHV Nanopositioners {#low-temperature-and-uhv-nanopositioners}
+
+
+### Tilting Nanopositioners {#tilting-nanopositioners}
+
+
+### Optical Objective Nanopositioners {#optical-objective-nanopositioners}
+
+
+## References {#references}
+
+
+## Introduction {#introduction}
+
+
+## Operating Environment {#operating-environment}
+
+
+## Methods for Actuation {#methods-for-actuation}
+
+
+## Flexure Hinges {#flexure-hinges}
+
+
+### Introduction {#introduction}
+
+
+### Types of Flexures {#types-of-flexures}
+
+
+### Flexure Hinge Compliance Equations {#flexure-hinge-compliance-equations}
+
+
+### Stiff Out-of-Plane Flexure Designs {#stiff-out-of-plane-flexure-designs}
+
+
+### Failure Considerations {#failure-considerations}
+
+
+### Finite Element Approach for Flexure Design {#finite-element-approach-for-flexure-design}
+
+
+## Material Considerations {#material-considerations}
+
+
+### Materials for Flexure and Platform Design {#materials-for-flexure-and-platform-design}
+
+
+### Thermal Stability of Materials {#thermal-stability-of-materials}
+
+
+## Manufacturing Techniques {#manufacturing-techniques}
+
+
+## Design Example: A High-Speed Serial-Kinematic Nanopositioner {#design-example-a-high-speed-serial-kinematic-nanopositioner}
+
+
+### State-of-the-Art Designs {#state-of-the-art-designs}
+
+
+### Tradeoffs and Limitations in Speed {#tradeoffs-and-limitations-in-speed}
+
+
+### Serial- Versus Parallel-Kinematic Configurations {#serial-versus-parallel-kinematic-configurations}
+
+
+### Piezoactuator Considerations {#piezoactuator-considerations}
+
+
+### Preloading Piezo-Stack Actuators {#preloading-piezo-stack-actuators}
+
+
+### Flexure Design for Lateral Positioning {#flexure-design-for-lateral-positioning}
+
+
+### Design of Vertical Stage {#design-of-vertical-stage}
+
+
+### Fabrication and Assembly {#fabrication-and-assembly}
+
+
+### Drive Electronics {#drive-electronics}
+
+\*\*\*\*0 Experimental Results
+
+
+## Chapter Summary {#chapter-summary}
+
+
+## References {#references}
+
+
+## Introduction {#introduction}
+
+
+## Sensor Characteristics {#sensor-characteristics}
+
+
+### Calibration and Nonlinearity {#calibration-and-nonlinearity}
+
+
+### Drift and Stability {#drift-and-stability}
+
+
+### Bandwidth {#bandwidth}
+
+
+### Noise {#noise}
+
+
+### Resolution {#resolution}
+
+
+### Combining Errors {#combining-errors}
+
+
+### Metrological Traceability {#metrological-traceability}
+
+
+## Nanometer Position Sensors {#nanometer-position-sensors}
+
+
+### Resistive Strain Sensors {#resistive-strain-sensors}
+
+
+### Piezoresistive Strain Sensors {#piezoresistive-strain-sensors}
+
+
+### Piezoelectric Strain Sensors {#piezoelectric-strain-sensors}
+
+
+### Capacitive Sensors {#capacitive-sensors}
+
+
+### MEMs Capacitive and Thermal Sensors {#mems-capacitive-and-thermal-sensors}
+
+
+### Eddy-Current Sensors {#eddy-current-sensors}
+
+
+### Linear Variable Displacement Transformers {#linear-variable-displacement-transformers}
+
+
+### Laser Interferometers {#laser-interferometers}
+
+
+### Linear Encoders {#linear-encoders}
+
+
+## Comparison and Summary {#comparison-and-summary}
+
+
+## Outlook and Future Requirements {#outlook-and-future-requirements}
+
+
+## References {#references}
+
+
+## Introduction {#introduction}
+
+
+## Shunt Circuit Modeling {#shunt-circuit-modeling}
+
+
+### Open-Loop {#open-loop}
+
+
+### Shunt Damping {#shunt-damping}
+
+
+## Implementation {#implementation}
+
+
+## Experimental Results {#experimental-results}
+
+
+### Tube Dynamics {#tube-dynamics}
+
+
+### Amplifier Performance {#amplifier-performance}
+
+
+### Shunt Damping Performance {#shunt-damping-performance}
+
+
+## Chapter Summary {#chapter-summary}
+
+
+## References {#references}
+
+
+## Introduction {#introduction}
+
+
+## Experimental Setup {#experimental-setup}
+
+
+## PI Control {#pi-control}
+
+
+## PI Control with Notch Filters {#pi-control-with-notch-filters}
+
+
+## PI Control with IRC Damping {#pi-control-with-irc-damping}
+
+
+## Performance Comparison {#performance-comparison}
+
+
+## Noise and Resolution {#noise-and-resolution}
+
+
+## Analog Implementation {#analog-implementation}
+
+
+## Application to AFM Imaging {#application-to-afm-imaging}
+
+
+## References {#references}
+
+
+## Introduction {#introduction}
+
+
+## Modeling {#modeling}
+
+
+### Actuator Dynamics {#actuator-dynamics}
+
+
+### Sensor Dynamics {#sensor-dynamics}
+
+
+### Sensor Noise {#sensor-noise}
+
+
+### Mechanical Dynamics {#mechanical-dynamics}
+
+
+### System Properties {#system-properties}
+
+
+### Example System {#example-system}
+
+
+## Damping Control {#damping-control}
+
+
+## Tracking Control {#tracking-control}
+
+
+### Relationship Between Force and Displacement {#relationship-between-force-and-displacement}
+
+
+### Integral Displacement Feedback {#integral-displacement-feedback}
+
+
+### Direct Tracking Control {#direct-tracking-control}
+
+
+### Dual Sensor Feedback {#dual-sensor-feedback}
+
+
+### Low Frequency Bypass {#low-frequency-bypass}
+
+
+### Feedforward Inputs {#feedforward-inputs}
+
+
+### Higher-Order Modes {#higher-order-modes}
+
+
+## Experimental Results {#experimental-results}
+
+
+### Experimental Nanopositioner {#experimental-nanopositioner}
+
+
+### Actuators and Force Sensors {#actuators-and-force-sensors}
+
+
+### Control Design {#control-design}
+
+
+### Noise Performance {#noise-performance}
+
+
+## Chapter Summary {#chapter-summary}
+
+
+## References {#references}
+
+
+## Why Feedforward? {#why-feedforward}
+
+
+## Modeling for Feedforward Control {#modeling-for-feedforward-control}
+
+
+## Feedforward Control of Dynamics and Hysteresis {#feedforward-control-of-dynamics-and-hysteresis}
+
+
+### Simple DC-Gain Feedforward Control {#simple-dc-gain-feedforward-control}
+
+
+### An Inversion-Based Feedforward Approach  for Linear Dynamics {#an-inversion-based-feedforward-approach-for-linear-dynamics}
+
+
+### Frequency-Weighted Inversion: The Optimal Inverse {#frequency-weighted-inversion-the-optimal-inverse}
+
+
+### Application to AFM Imaging {#application-to-afm-imaging}
+
+
+## Feedforward and Feedback Control {#feedforward-and-feedback-control}
+
+
+### Application to AFM Imaging {#application-to-afm-imaging}
+
+
+## Iterative Feedforward Control {#iterative-feedforward-control}
+
+
+### The ILC Problem {#the-ilc-problem}
+
+
+### Model-Based ILC {#model-based-ilc}
+
+
+### Nonlinear ILC {#nonlinear-ilc}
+
+
+### Conclusions {#conclusions}
+
+
+## References {#references}
+
+
+## 10.1 Introduction {#10-dot-1-introduction}
+
+
+### 10.1.1 Background {#10-dot-1-dot-1-background}
+
+
+### 10.1.2 The Optimal Periodic Input {#10-dot-1-dot-2-the-optimal-periodic-input}
+
+
+## 10.2 Signal Optimization {#10-dot-2-signal-optimization}
+
+
+## 10.3 Frequency Domain Cost Functions {#10-dot-3-frequency-domain-cost-functions}
+
+
+### 10.3.1 Background: Discrete Fourier Series {#10-dot-3-dot-1-background-discrete-fourier-series}
+
+
+### 10.3.2 Minimizing Signal Power {#10-dot-3-dot-2-minimizing-signal-power}
+
+
+### 10.3.3 Minimizing Frequency Weighted Power {#10-dot-3-dot-3-minimizing-frequency-weighted-power}
+
+
+### 10.3.4 Minimizing Velocity and Acceleration {#10-dot-3-dot-4-minimizing-velocity-and-acceleration}
+
+
+### 10.3.5 Single-Sided Frequency Domain Calculations {#10-dot-3-dot-5-single-sided-frequency-domain-calculations}
+
+
+## 10.4 Time Domain Cost Function {#10-dot-4-time-domain-cost-function}
+
+
+### 10.4.1 Minimum Velocity {#10-dot-4-dot-1-minimum-velocity}
+
+
+### 10.4.2 Minimum Acceleration {#10-dot-4-dot-2-minimum-acceleration}
+
+
+### 10.4.3 Frequency Weighted Objectives {#10-dot-4-dot-3-frequency-weighted-objectives}
+
+
+## 10.5 Application to Scan Generation {#10-dot-5-application-to-scan-generation}
+
+
+### 10.5.1 Choosing β and K {#10-dot-5-dot-1-choosing-β-and-k}
+
+
+### 10.5.2 Improving Feedback and Feedforward Controllers {#10-dot-5-dot-2-improving-feedback-and-feedforward-controllers}
+
+
+## 10.6 Comparison to Other Techniques {#10-dot-6-comparison-to-other-techniques}
+
+
+## 10.7 Experimental Application {#10-dot-7-experimental-application}
+
+
+## 10.8 Chapter Summary {#10-dot-8-chapter-summary}
+
+
+## References {#references}
+
+
+## 11.1 Introduction {#11-dot-1-introduction}
+
+
+## 11.2 Modeling Hysteresis {#11-dot-2-modeling-hysteresis}
+
+
+### 11.2.1 Simple Polynomial Model {#11-dot-2-dot-1-simple-polynomial-model}
+
+
+### 11.2.2 Maxwell Slip Model {#11-dot-2-dot-2-maxwell-slip-model}
+
+
+### 11.2.3 Duhem Model {#11-dot-2-dot-3-duhem-model}
+
+
+### 11.2.4 Preisach Model {#11-dot-2-dot-4-preisach-model}
+
+
+### 11.2.5 Classical Prandlt-Ishlinksii Model {#11-dot-2-dot-5-classical-prandlt-ishlinksii-model}
+
+
+## 11.3 Feedforward Hysteresis Compensation {#11-dot-3-feedforward-hysteresis-compensation}
+
+
+### 11.3.1 Feedforward Control Using the Presiach Model {#11-dot-3-dot-1-feedforward-control-using-the-presiach-model}
+
+
+### 11.3.2 Feedforward Control Using the Prandlt-Ishlinksii Model {#11-dot-3-dot-2-feedforward-control-using-the-prandlt-ishlinksii-model}
+
+
+## 11.4 Chapter Summary {#11-dot-4-chapter-summary}
+
+
+## References {#references}
+
+
+## 12.1 Introduction {#12-dot-1-introduction}
+
+
+## 12.2 Charge Drives {#12-dot-2-charge-drives}
+
+
+## 12.3 Application to Piezoelectric Stack Nanopositioners {#12-dot-3-application-to-piezoelectric-stack-nanopositioners}
+
+
+## 12.4 Application to Piezoelectric Tube Nanopositioners {#12-dot-4-application-to-piezoelectric-tube-nanopositioners}
+
+
+## 12.5 Alternative Electrode Configurations {#12-dot-5-alternative-electrode-configurations}
+
+
+### 12.5.1 Grounded Internal Electrode {#12-dot-5-dot-1-grounded-internal-electrode}
+
+
+### 12.5.2 Quartered Internal Electrode {#12-dot-5-dot-2-quartered-internal-electrode}
+
+
+## 12.6 Charge Versus Voltage {#12-dot-6-charge-versus-voltage}
+
+
+### 12.6.1 Advantages {#12-dot-6-dot-1-advantages}
+
+
+### 12.6.2 Disadvantages {#12-dot-6-dot-2-disadvantages}
+
+
+## 12.7 Impact on Closed-Loop Control {#12-dot-7-impact-on-closed-loop-control}
+
+
+## 12.8 Chapter Summary {#12-dot-8-chapter-summary}
+
+
+## References {#references}
+
+
+## 13.1 Introduction {#13-dot-1-introduction}
+
+
+## 13.2 Review of Random Processes {#13-dot-2-review-of-random-processes}
+
+
+### 13.2.1 Probability Distributions {#13-dot-2-dot-1-probability-distributions}
+
+
+### 13.2.2 Expected Value, Moments, Variance, and RMS {#13-dot-2-dot-2-expected-value-moments-variance-and-rms}
+
+
+### 13.2.3 Gaussian Random Variables {#13-dot-2-dot-3-gaussian-random-variables}
+
+
+### 13.2.4 Continuous Random Processes {#13-dot-2-dot-4-continuous-random-processes}
+
+
+### 13.2.5 Joint Density Functions and Stationarity {#13-dot-2-dot-5-joint-density-functions-and-stationarity}
+
+
+### 13.2.6 Correlation Functions {#13-dot-2-dot-6-correlation-functions}
+
+
+### 13.2.7 Gaussian Random Processes {#13-dot-2-dot-7-gaussian-random-processes}
+
+
+### 13.2.8 Power Spectral Density {#13-dot-2-dot-8-power-spectral-density}
+
+
+### 13.2.9 Filtered Random Processes {#13-dot-2-dot-9-filtered-random-processes}
+
+
+### 13.2.10 White Noise {#13-dot-2-dot-10-white-noise}
+
+
+### 13.2.11 Spectral Density in V/sqrtHz {#13-dot-2-dot-11-spectral-density-in-v-sqrthz}
+
+
+### 13.2.12 Single- and Double-Sided Spectra {#13-dot-2-dot-12-single-and-double-sided-spectra}
+
+
+## 13.3 Resolution and Noise {#13-dot-3-resolution-and-noise}
+
+
+## 13.4 Sources of Nanopositioning Noise {#13-dot-4-sources-of-nanopositioning-noise}
+
+
+### 13.4.1 Sensor Noise {#13-dot-4-dot-1-sensor-noise}
+
+
+### 13.4.2 External Noise {#13-dot-4-dot-2-external-noise}
+
+
+### 13.4.3 Amplifier Noise {#13-dot-4-dot-3-amplifier-noise}
+
+
+## 13.5 Closed-Loop Position Noise {#13-dot-5-closed-loop-position-noise}
+
+
+### 13.5.1 Noise Sensitivity Functions {#13-dot-5-dot-1-noise-sensitivity-functions}
+
+
+### 13.5.2 Closed-Loop Position Noise Spectral Density {#13-dot-5-dot-2-closed-loop-position-noise-spectral-density}
+
+
+### 13.5.3 Closed-Loop Noise Approximations with Integral Control {#13-dot-5-dot-3-closed-loop-noise-approximations-with-integral-control}
+
+
+### 13.5.4 Closed-Loop Position Noise Variance {#13-dot-5-dot-4-closed-loop-position-noise-variance}
+
+
+### 13.5.5 A Note on Units {#13-dot-5-dot-5-a-note-on-units}
+
+
+## 13.6 Simulation Examples {#13-dot-6-simulation-examples}
+
+
+### 13.6.1 Integral Controller Noise Simulation {#13-dot-6-dot-1-integral-controller-noise-simulation}
+
+
+### 13.6.2 Noise Simulation with Inverse Model Controller {#13-dot-6-dot-2-noise-simulation-with-inverse-model-controller}
+
+
+### 13.6.3 Feedback Versus Feedforward Control {#13-dot-6-dot-3-feedback-versus-feedforward-control}
+
+
+## 13.7 Practical Frequency Domain Noise Measurements {#13-dot-7-practical-frequency-domain-noise-measurements}
+
+
+### 13.7.1 Preamplification {#13-dot-7-dot-1-preamplification}
+
+
+### 13.7.2 Spectrum Estimation {#13-dot-7-dot-2-spectrum-estimation}
+
+
+### 13.7.3 Direct Measurement of Position Noise {#13-dot-7-dot-3-direct-measurement-of-position-noise}
+
+
+### 13.7.4 Measurement of the External Disturbance {#13-dot-7-dot-4-measurement-of-the-external-disturbance}
+
+
+## 13.8 Experimental Demonstration {#13-dot-8-experimental-demonstration}
+
+
+## 13.9 Time-Domain Noise Measurements {#13-dot-9-time-domain-noise-measurements}
+
+
+### 13.9.1 Total Integrated Noise {#13-dot-9-dot-1-total-integrated-noise}
+
+
+### 13.9.2 Estimating the Position Noise {#13-dot-9-dot-2-estimating-the-position-noise}
+
+
+### 13.9.3 Practical Considerations {#13-dot-9-dot-3-practical-considerations}
+
+
+### 13.9.4 Experimental Demonstration {#13-dot-9-dot-4-experimental-demonstration}
+
+
+## 13.10 A Simple Method for Measuring the Resolution  of Nanopositioning Systems {#13-dot-10-a-simple-method-for-measuring-the-resolution-of-nanopositioning-systems}
+
+
+## 13.11 Techniques for Improving Resolution {#13-dot-11-techniques-for-improving-resolution}
+
+
+## 13.12 Chapter Summary {#13-dot-12-chapter-summary}
+
+
+## References {#references}
+
+
+## Electrical Considerations {#electrical-considerations}
+
+
+### Amplifier and Piezo electrical models {#amplifier-and-piezo-electrical-models}
+
+<a id="figure--fig:fleming14-amplifier-model"></a>
+
+{{< figure src="/ox-hugo/fleming14_amplifier_model.png" caption="<span class=\"figure-number\">Figure 1: </span>A voltage source \\(V\_s\\) driving a piezoelectric load. The actuator is modeled by a capacitance \\(C\_p\\) and strain-dependent voltage source \\(V\_p\\). The resistance \\(R\_s\\) is the output impedance and \\(L\\) the cable inductance." >}}
+
+Consider the electrical circuit shown in [Figure 1](#figure--fig:fleming14-amplifier-model) where a voltage source is connected to a piezoelectric actuator.
+The actuator is modeled as a capacitance \\(C\_p\\) in series with a strain-dependent voltage source \\(V\_p\\).
+The resistance \\(R\_s\\) and inductance \\(L\\) are the source impedance and the cable inductance respectively.
+
+<div class="exampl">
+
+Typical inductance of standard RG-58 coaxial cable is \\(250 nH/m\\).
+Typical value of \\(R\_s\\) is between \\(10\\) and \\(100 \Omega\\).
+
+</div>
+
+When considering the effects of both output impedance and cable inductance, the transfer function from source voltage \\(V\_s\\) to load voltage \\(V\_L\\) is second-order low pass filter:
+
+\begin{equation}
+  \frac{V\_L(s)}{V\_s(s)} = \frac{1}{\frac{s^2}{\omega\_r^2} + 2 \xi \frac{s}{\omega\_r} + 1}
+\end{equation}
+
+with:
+
+-   \\(\omega\_r = \frac{1}{\sqrt{L C\_p}}\\)
+-   \\(\xi = \frac{R\_s \sqrt{L C\_p}}{2 L}\\)
+
+
+### Amplifier small-signal Bandwidth {#amplifier-small-signal-bandwidth}
+
+The most obvious bandwidth limitation is the small-signal bandwidth of the amplifier.
+
+If the inductance \\(L\\) is neglected, the transfer function from source voltage \\(V\_s\\) to load voltage \\(V\_L\\) forms a first order filter with a cut-off frequency
+
+\begin{equation}
+  \omega\_c = \frac{1}{R\_s C\_p}
+\end{equation}
+
+This is thus highly dependent of the load.
+
+The high capacitive impedance nature of piezoelectric loads introduces phase-lag into the feedback path.
+A rule of thumb is that closed-loop bandwidth cannot exceed one-tenth the cut-off frequency of the pole formed by the amplifier output impedance \\(R\_s\\) and load capacitance \\(C\_p\\) (see [Table 1](#table--tab:piezo-limitation-Rs) for values).
+
+<a id="table--tab:piezo-limitation-Rs"></a>
+<div class="table-caption">
+  <span class="table-number"><a href="#table--tab:piezo-limitation-Rs">Table 1</a>:</span>
+  Bandwidth limitation due to \(R_s\)
+</div>
+
+|              | Cp = 100 nF | Cp = 1 uF | Cp = 10 uF |
+|--------------|-------------|-----------|------------|
+| Rs = 1 Ohm   | 1.6 MHz     | 160 kHz   | 16 kHz     |
+| Rs = 10 Ohm  | 160 kHz     | 16 kHz    | 1.6 kHz    |
+| Rs = 100 Ohm | 16 kHz      | 1.6 kHz   | 160 Hz     |
+
+The inductance \\(L\\) does also play a role in the amplifier bandwidth as it changes the resonance frequency.
+Ideally, low inductance cables should be used.
+It is however usually quite high compare to \\(\omega\_c\\) as shown in [Table 2](#table--tab:piezo-limitation-L).
+
+<a id="table--tab:piezo-limitation-L"></a>
+<div class="table-caption">
+  <span class="table-number"><a href="#table--tab:piezo-limitation-L">Table 2</a>:</span>
+  Bandwidth limitation due to \(R_s\)
+</div>
+
+|             | Cp = 100 nF | Cp = 1 uF | Cp = 10 uF |
+|-------------|-------------|-----------|------------|
+| L = 25 nH   | 3.2 MHz     | 1 MHz     | 320 kHz    |
+| L = 250 nH  | 1 MHz       | 320 kHz   | 100 kHz    |
+| L = 2500 nH | 320 kHz     | 100 kHz   | 32 kHz     |
+
+
+### Amplifier maximum slew rate {#amplifier-maximum-slew-rate}
+
+Further bandwidth restrictions are imposed by the maximum **slew rate** of the amplifier.
+This is the maximum rate at which the output voltage can change and is usually expressed in \\(V/\mu s\\).
+
+For sinusoidal signals, the amplifiers slew rate must exceed:
+\\[ SR\_{\text{sin}} > V\_{p-p} \pi f \\]
+where \\(V\_{p-p}\\) is the peak to peak voltage and \\(f\\) is the frequency.
+
+<div class="exampl">
+
+If a 300kHz sine wave is to be reproduced with an amplitude of 10V, the required slew rate is \\(\approx 20 V/\mu s\\).
+
+</div>
+
+When dealing with capacitive loads, **the current limit is usually exceed well before the slew rate limit**.
+
+
+### Current and Power Limitations {#current-and-power-limitations}
+
+When driving the actuator off-resonance, the current delivered to a piezoelectric actuator is approximately:
+\\[ I\_L(s) = V\_L(s) C\_p s \\]
+
+For sinusoidal signals, the maximum positive and negative current is equal to:
+\\[ I\_L^\text{max} = V\_{p-p} \pi f C\_p \\]
+
+<a id="table--tab:piezo-required-current"></a>
+<div class="table-caption">
+  <span class="table-number"><a href="#table--tab:piezo-required-current">Table 3</a>:</span>
+  Minimum current requirements for a 10V sinusoid
+</div>
+
+|             | Cp = 100 nF | Cp = 1 uF | Cp = 10 uF |
+|-------------|-------------|-----------|------------|
+| f = 30 Hz   | 0.19 mA     | 1.9 mA    | 19 mA      |
+| f = 3 kHz   | 19 mA       | 190 mA    | 1.9 A      |
+| f = 300 kHz | 1.9 A       | 19 A      | 190 A      |
+
+
+### Chapter Summary {#chapter-summary}
+
+The bandwidth limitations  of standard piezoelectric drives were identified as:
+
+-   High output impedance
+-   The presence of a ple in the voltage-feedback loop due to output impedance and load capacitance
+-   Insufficient current capacity due to power dissipation
+-   High cable and connector inductance
+
+
+### References {#references}
+
+
+## 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>Fleming, Andrew J., and Kam K. Leang. 2014. <i>Design, Modeling and Control of Nanopositioning Systems</i>. Advances in Industrial Control. Springer International Publishing. doi:<a href="https://doi.org/10.1007/978-3-319-06617-2">10.1007/978-3-319-06617-2</a>.</div>
+</div>

content/book/horowitz15_art_of_elect_third_edition.md

@@ -1,14 +1,16 @@
 +++
-title = "The art of electronics - third edition"
-author = ["Thomas Dehaeze"]
+title = "The Art of Electronics - Third Edition"
+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
-: <sup id="b6e665e07855d8348f2f3aa70ec9b563"><a href="#horowitz15_art_of_elect_third_edition" title="Horowitz, The Art Of Electronics - Third Edition, Cambridge University Press (2015).">(Horowitz, 2015)</a></sup>
+: (<a href="#citeproc_bib_item_1">Horowitz 2015</a>)
 
 Author(s)
 : Horowitz, P.
@@ -16,5 +18,9 @@ Author(s)
 Year
 : 2015
 
-# Bibliography
-<a id="horowitz15_art_of_elect_third_edition"></a>Horowitz, P., *The art of electronics - third edition* (2015), New York, NY, USA: Cambridge University Press. [↩](#b6e665e07855d8348f2f3aa70ec9b563)
+
+## 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>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

@@ -1,14 +1,15 @@
 +++
 title = "Fundamental principles of engineering nanometrology"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
+keywords = ["Metrology"]
 draft = false
 +++
 
 Tags
-: [Metrology]({{< relref "metrology" >}})
+: [Metrology]({{< relref "metrology.md" >}})
 
 Reference
-: <sup id="58bd6e601168ed1397ab2ec3cc3bab2d"><a href="#leach14_fundam_princ_engin_nanom" title="Richard Leach, Fundamental Principles of Engineering Nanometrology, Elsevier (2014).">(Richard Leach, 2014)</a></sup>
+: (<a href="#citeproc_bib_item_1">Leach 2014</a>)
 
 Author(s)
 : Leach, R.
@@ -63,8 +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
-=> all the optical components are mounted to one central optic to reduce the susceptibility to thermal variations
+=&gt; fused silica optics housed in Invar mounts
+=&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.
 
@@ -86,5 +87,9 @@ The measurement of angles is then relative.
 
 This type of angular interferometer is used to measure small angles (less than \\(10deg\\)).
 
-# Bibliography
-<a id="leach14_fundam_princ_engin_nanom"></a>Leach, R., *Fundamental principles of engineering nanometrology* (2014), : Elsevier. [↩](#58bd6e601168ed1397ab2ec3cc3bab2d)
+
+## 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>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

@@ -1,20 +1,25 @@
 +++
 title = "Basics of precision engineering - 1st edition"
-author = ["Thomas Dehaeze"]
-draft = false
+author = ["Dehaeze Thomas"]
+keywords = ["Metrology", "Mechatronics"]
+draft = true
 +++
 
 Tags
-: [Precision Engineering]({{< relref "precision_engineering" >}})
+: [Precision Engineering]({{< relref "precision_engineering.md" >}})
 
 Reference
-: <sup id="cc6e42420309d21c1aa596152d84cf8b"><a href="#leach18_basic_precis_engin_edition" title="Richard Leach \&amp; Stuart Smith, Basics of Precision Engineering - 1st Edition, CRC Press (2018).">(Richard Leach \& Stuart Smith, 2018)</a></sup>
+: (<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
-<a id="leach18_basic_precis_engin_edition"></a>Leach, R., & Smith, S. T., *Basics of precision engineering - 1st edition* (2018), : CRC Press. [↩](#cc6e42420309d21c1aa596152d84cf8b)
+
+## 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>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/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

@@ -1,14 +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
-: <sup id="454500a3af67ef66a7a754d1f2e1bd4a"><a href="#preumont18_vibrat_contr_activ_struc_fourt_edition" title="Andre Preumont, Vibration Control of Active Structures - Fourth Edition, Springer International Publishing (2018).">(Andre Preumont, 2018)</a></sup>
+: (<a href="#citeproc_bib_item_1">Preumont 2018</a>)
 
 Author(s)
 : Preumont, A.
@@ -61,11 +63,11 @@ There are two radically different approached to disturbance rejection: feedback
 
 #### Feedback {#feedback}
 
-<a id="orgff2b033"></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](#orgff2b033). 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**.
@@ -87,23 +89,23 @@ The objective is to control a variable \\(y\\) to a desired value \\(r\\) in spi
 
 #### Feedforward {#feedforward}
 
-<a id="orgc74bab2"></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](#orgc74bab2).
+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>
 
@@ -123,11 +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="org4c2b243"></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](#org4c2b243).
+The various steps of the design of a controlled structure are shown in [Figure 3](#figure--fig:design-steps).
 
 The **starting point** is:
 
@@ -154,21 +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](#org1c8100c)):
+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="org1c8100c"></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}\\]
 
@@ -177,7 +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 \\]
 
@@ -186,14 +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](#orgbde617f).
+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="orgbde617f"></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}
@@ -252,7 +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
@@ -269,7 +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
@@ -297,14 +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 {#modal-decomposition}
+### [Modal Decomposition]({{< relref "modal_decomposition.md" >}}) {#modal-decomposition--modal-decomposition-dot-md}
 
 
 #### Structure Without Rigid Body Modes {#structure-without-rigid-body-modes}
@@ -312,7 +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
@@ -334,12 +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
@@ -353,11 +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>
 
@@ -370,15 +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**:
@@ -398,11 +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="orgac9e4c8"></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](#orgac9e4c8)).
+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 \\]
@@ -416,7 +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:
 
@@ -427,7 +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>
 
@@ -441,30 +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](#org6374ca8)).
+\\(G\_{kk}\\) is a monotonously increasing function of \\(\omega\\) ([Figure 7](#figure--fig:collocated-control-frf)).
 
-<a id="org6374ca8"></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](#org55d54ab).
+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="org55d54ab"></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**.
 
@@ -474,11 +467,11 @@ The open-loop poles are independant of the actuator and sensor configuration whi
 
 </div>
 
-By looking at figure [7](#org6374ca8), 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="org8cc5426"></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:
 
@@ -486,7 +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](#org8cc5426). 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.
 
 
@@ -508,14 +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](#orga882e0c)):
+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="orga882e0c"></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:
 
@@ -525,7 +518,6 @@ We note:
 -   \\(i\\) the current into the coil
 
 <div class="cbox">
-  <div></div>
 
 **Faraday's law**:
 
@@ -551,11 +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](#orgd7b8271)).
+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="orgd7b8271"></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 \\]
@@ -569,7 +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}
@@ -583,11 +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](#orgc8992eb)).
+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="orgc8992eb"></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}
@@ -598,7 +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\*}
 
@@ -610,25 +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="org2a6e175"></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](#org12ba88f).
+The consitutive behavior of a wide class of electromechanical transducers can be modelled as in [Figure 14](#figure--fig:electro-mechanical-transducer).
 
-<a id="org12ba88f"></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}
 
@@ -643,10 +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](#orgdf63f4a) 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
 
@@ -656,19 +647,19 @@ We can show that
 
 which is indeed a linear function of the velocity \\(v\\) at the mechanical terminals.
 
-<a id="orgdf63f4a"></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](#orgc0d19b7) 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="orgc0d19b7"></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}
@@ -676,14 +667,12 @@ Figure [16](#orgc0d19b7) 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.
 
@@ -694,11 +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}
@@ -718,16 +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.
@@ -735,13 +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:
@@ -750,7 +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}
@@ -761,16 +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](#orgc13be77)) 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
@@ -782,27 +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="orgc13be77"></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](#org24eee83).
+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
 
@@ -810,11 +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="org24eee83"></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}
@@ -828,7 +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:
@@ -844,12 +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](#org76e4915), 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="org76e4915"></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
 
@@ -866,11 +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](#orgba7797e)).
+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="orgba7797e"></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}
@@ -1002,13 +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.
@@ -1378,7 +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
@@ -1566,7 +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](#org278a785).
+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:
 
@@ -1574,9 +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="org278a785"></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}
@@ -1815,5 +1801,9 @@ This approach has the following advantages:
 
 ### Problems {#problems}
 
-# Bibliography
-<a id="preumont18_vibrat_contr_activ_struc_fourt_edition"></a>Preumont, A., *Vibration control of active structures - fourth edition* (2018), : Springer International Publishing. [↩](#454500a3af67ef66a7a754d1f2e1bd4a)
+
+## 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>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/schmidt14_desig_high_perfor_mechat_revis_edition.md

@@ -1,45 +0,0 @@
-+++
-title = "The design of high performance mechatronics - 2nd revised edition"
-author = ["Thomas Dehaeze"]
-draft = false
-+++
-
-Tags
-: [Reference Books]({{< relref "reference_books" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})
-
-Reference
-: <sup id="37468bbe5988cc7f4878fcd664d9cb7f"><a href="#schmidt14_desig_high_perfor_mechat_revis_edition" title="Schmidt, Schitter \&amp; Rankers, The Design of High Performance Mechatronics - 2nd Revised  Edition, Ios Press (2014).">(Schmidt {\it et al.}, 2014)</a></sup>
-
-Author(s)
-: Schmidt, R. M., Schitter, G., & Rankers, A.
-
-Year
-: 2014
-
-Section 2.2 Mechanics
-
-> The core of a mechatronic system is its mechanical construction and in spite of many decade of excellent designs, optimizing the mechanical structure in strength, mass and endurance, the mechanical behavior will always remain the limiting factor of the performance of any mechatronic system.
-
-Section 2.2.2 Force and Motion
-
-> _Statics_ deals with the stress levels that are present in the mechanical system when (quasi-)static forces are exerted on it.
-> It analyses the linear and non-linear strain effects that are caused by elastic and plastic deformation under these stress levels.
->
-> _Dynamics_ deals with the behaviour of the mechanical system under changing forces, while often the effects are linearised and limited to strain levels well below any irreversible plastic deformation.
-> One should however be aware that another non-destructive source of non-linearity is found in a tried important field of mechanics, called _kinematics_.
-> The relation between angles and positions is often non-linear in such a mechanism, because of the changing angles, and controlling these often requires special precautions to overcome the inherent non-linearities by linearisation around actual position and adapting the optimal settings of the controller to each position.
-
-<a id="org8d0a076"></a>
-
-{{< figure src="/ox-hugo/schmidt14_high_low_freq_regions.png" caption="Figure 1: Stabiliby condition and robustness of a feedback controlled system. The desired shape of these curves guide the control design by optimising the lvels and sloppes of the amplitude Bode-plot at low and high frequencies for suppression of the disturbances and of the base Bode-plot in the cross-over frequency region. This is called **loop shaping design**" >}}
-
-Section 4.3.3
-
-> On might say that a high value of the unity-gain crossover frequency and corresponding high-frequency bandwidth limit is rather an unwanted side-effect of the required high loop-gain at lower frequencies, than a target for the design of a control system as such.
-
-Section 9.3: Mass Dilemma
-
-> A reduced mass requires improved system dynamics that enable a higher control bandwidth to compensate for the increase sensitivity for external vibrations.
-
-# Bibliography
-<a id="schmidt14_desig_high_perfor_mechat_revis_edition"></a>Schmidt, R. M., Schitter, G., & Rankers, A., *The design of high performance mechatronics - 2nd revised edition* (2014), : Ios Press. [↩](#37468bbe5988cc7f4878fcd664d9cb7f)

content/book/schoukens12_master.md

@@ -0,0 +1,23 @@
++++
+title = "Mastering system identification in 100 exercises"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: ([Schoukens, Pintelon, and Rolain 2012](#org1193e9b))
+
+Author(s)
+: Schoukens, J., Pintelon, R., & Rolain, Y.
+
+Year
+: 2012
+
+
+## Bibliography {#bibliography}
+
+<a id="org1193e9b"></a>Schoukens, Johan, Rik Pintelon, and Yves Rolain. 2012. _Mastering System Identification in 100 Exercises_. John Wiley & Sons.

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

@@ -0,0 +1,25 @@
++++
+title = "The scientist and engineer's guide to digital signal processing - second edition"
+author = ["Dehaeze Thomas"]
+keywords = ["Signal Processing"]
+draft = true
++++
+
+Tags
+: [Digital Signal Processing]({{< relref "digital_signal_processing.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Smith 1999</a>)
+
+Author(s)
+: Smith, S. W.
+
+Year
+: 1999
+
+
+## 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>Smith, Steven W. 1999. <i>The Scientist and Engineer’s Guide to Digital Signal Processing - Second Edition</i>. California Technical Publishing.</div>
+</div>

content/inbook/albertos04_decen_decoup_contr.md

@@ -0,0 +1,190 @@
++++
+title = "Decentralized and decoupled control"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+: [Multivariable Control](multivariable_control.md), [Decoupled Control](decoupled_control.md)
+
+Reference
+: ([Albertos and Antonio 2004](#org8b56aa1))
+
+Author(s)
+: Albertos, P., & Antonio, S.
+
+Year
+: 2004
+
+
+## Introduction {#introduction}
+
+Decentralized control is decomposed into two steps:
+
+1.  decoupled the plant into several subsystems
+2.  control the subsystems
+
+The initial effort of decoupling the system results in subsequent easier design, implementation and tuning.
+
+Decentralized control tries to control multivariable plants by a suitable decomposition into SISO control loops.
+If the process has strong coupling or conditioning problems, centralized control may be required.
+It however requires the availability of a precise model.
+
+Two approaches can be used to control a coupled system with SISO techniques:
+
+-   **decentralized control** tries to divide the plant and design _independent_ controllers for each subsystems.
+    Two alternative arise:
+    -   neglect the coupling
+    -   carry out a _decoupling_ operation by "canceling" coupling by transforming the system into a diagonal or triangular structure bia a transformation matrix
+-   **cascade control**
+
+
+## Mutli-Loop Control, Pairing Selection {#mutli-loop-control-pairing-selection}
+
+The strategy called _multi-loop control_ consists of first proper input/output pairing, and then design of several SISO controllers.
+In this way, a complex control problem is divided into several simpler ones.
+
+The multi-loop control may not work in strongly coupled systems.
+Therefore, a methodology the access the degree of interaction between the loops is needed.
+
+
+### [Relative Gain Array](relative_gain_array.md) {#relative-gain-array--relative-gain-array-dot-md}
+
+The Relative Gain Array (RGA) \\(\Lambda(s)\\) is defined as:
+
+\begin{equation}
+\Lambda(s) = G(s) \times (G(s)^T)^{-1}
+\end{equation}
+
+The RGA is scaling-independent and controller-independent.
+These coefficients can be interpreted as the ratio between the open-loop SISO static gain and the gain with "perfect" control on the rest of the loops.
+
+For demanding control specifications, the values of \\(\Lambda\\) car be drawn as a function of frequency.
+In this case, at frequencies important for control stability robustness (around the peak of the sensitivity transfer function), if \\(\Lambda(j\omega)\\) approaches the identity matrix, stability problems are avoided in multi-loop control.
+
+
+## Decoupling {#decoupling}
+
+In cases when multi-loop control is not effective in reaching the desired specifications, a possible strategy for tackling the MIMO control could be to transform the transfer function matrix into a diagonal dominant one.
+This strategy is called **decoupling**.
+
+[Decoupled Control](decoupled_control.md) can be achieved in two ways:
+
+-   feedforward cancellation of the cross-coupling terms
+-   based on state measurements, via a feedback law
+
+
+### Feedforward Decoupling {#feedforward-decoupling}
+
+A pre-compensator (Figure [1](#orgb11b773)) can be added to transform the open-loop characteristics into a new one as chosen by the designer.
+This decoupler can be taken as the inverse of the plant provided it does not include RHP-zeros.
+
+<a id="orgb11b773"></a>
+
+{{< figure src="/ox-hugo/albertos04_pre_compensator_decoupling.png" caption="Figure 1: Decoupler pre-compensator" >}}
+
+**Approximate decoupling**:
+To design low-bandwidth loops, insertion of the inverse DC-gain before the loop ensures decoupling at least at steady-state.
+If further bandwidth extension is desired, an approximation of \\(G^{-1}\\) valid in low frequencies can be used.
+
+Although at first glance, decoupling seems an appealing idea, there are some drawbacks:
+
+-   as decoupling is achieved via the coordination of sensors and actuators to achieve an "apparent" diagonal behavior, the failure of one the actuators may heavily affects all loops.
+-   a decoupling design (inverse-based controller) may not be desirable for all disturbance-rejection tasks.
+-   many MIMO non-minimum phase systems, when feedforward decoupled, increase the RHP-zero multiplicity so performance limitations due to its presence are exacerbated.
+-   decoupling may be very sensitive to modeling errors, specially for ill-conditionned plants
+-   feedback decoupling needs full state measurements
+
+
+### SVD Decoupling {#svd-decoupling}
+
+A matrix \\(M\\) can be expressed, using the [Singular Value Decomposition](singular_value_decomposition.md) as:
+
+\begin{equation}
+M = U \Sigma V^T
+\end{equation}
+
+where \\(U\\) and \\(V\\) are orthogonal matrices and \\(\Sigma\\) is diagonal.
+
+The SVD can be used to obtain decoupled equations between linear combinations of sensors and linear combinations of actuators.
+In this way, although losing part of its intuitive sense, a decoupled design can be carried out even for non-square plants.
+
+If sensors are multiplied by \\(U^T\\) and control actions multiplied by \\(V\\), as in Figure [2](#org7029ff7), then the loop, in the transformed variables, is decoupled, so a diagonal controller \\(K\_D\\) can be used.
+Usually, the sensor and actuator transformations are obtained using the DC gain, or a real approximation of \\(G(j\omega)\\), where \\(\omega\\) is around the desired closed-loop bandwidth.
+
+<a id="org7029ff7"></a>
+
+{{< figure src="/ox-hugo/albertos04_svd_decoupling.png" caption="Figure 2: SVD decoupling: \\(K\_D\\) is a diagonal controller designed for \\(\Sigma\\)" >}}
+
+The transformed sensor-actuator pair corresponding to the maximum singular value is the direction with biggest "gain" on the plant, that is, the combination of variables being "easiest to control".
+
+In ill-conditioned plants, the ratio between the biggest and lower singular value is large (for reference, greater than 20).
+They are very sensitive to input uncertainty as some "input directions" have much bigger gain than other ones.
+
+SVD decoupling produces the most suitable combinations for independent "multi-loop" control in the transformed variables, so its performance may be better than RGA-based design (at the expense of losing physical interpretability).
+If some of the vectors in \\(V\\) (input directions) have a significant component on a particular input, and the corresponding output direction is also significantly pointing to a particular output, that combination is a good candidate for an independent multi-loop control.
+
+
+## Conclusions {#conclusions}
+
+In this chapter, the control of systems with multiple inputs and outputs is discussed using SISO-based tools, either directly or after some multivariable decoupling transformations.
+
+Multi-loop strategies, if suitable, may present th advantages of fault tolerance, as well as simplicity.
+However, in some cases, tuning may be difficult and coupling may severely limit their performance.
+
+Decoupling is based on mathematical transformations of the system models into diagonal form.
+Feedforward decoupling can be used in many cases.
+Feedback decoupling achieves its objective if state is measurable and system is minimum-phase.
+However, decoupling may be very sensitive to modelling errors and it is not the optimal strategy for disturbance rejection.
+
+Cascade control is widely used in industry to improve the behaviour of basic SISO loops via the addition of extra sensors and actuators.
+However, ease of tuning requires that different time constants are involved in different subsystems.
+In general, addition of extra sensors and actuators in a SISO or MIMO loop, will improve achievable performance and/or tolerance to modelling errors.
+The level of improvement must be traded off against the cost of additional instrumentation.
+
+
+## Implementation and Other Issues {#implementation-and-other-issues}
+
+There are two main categories for the implementation of MIMO control:
+
+-   Decentralized, Decoupled, Cascade
+-   Centralized, optimization based
+
+A fundamental reason to use cascade and decentralized control in most practical applications is because they require less modelling effort.
+Other advantages of cascade and decentralized control are:
+
+-   its behaviour can be easily understood
+-   standard equipment can be used (PID controllers, etc.)
+-   their decoupled behavior enables easier tuning with model-free strategies
+-   decentralized implementation tends to be more fault-tolerant, as individual loops will try to keep their set-points even in the case some other components have failed.
+
+
+### [Anti-Windup Control](anti_windup_control.md) {#anti-windup-control--anti-windup-control-dot-md}
+
+In practice, it is possible that an actuator saturate.
+In such case, the feedback path is broken, and this has several implications:
+
+-   unstable processes: the process output might go out of control
+-   multi-loop and centralized control: even with stable plants, opening a feedback path may cause the overall loop to become unstable
+
+The wind-up problem can appear with integral action regulators: during significative step changes in the set point, the integral of the error keeps accumulation and when reaching the desired set-point the accumulated integral action produces a significant overshoot increment.
+In SISO PID regulators, anti-windup schemes are implemented by either stopping integration if the actuator is saturated or by implementing the following control law:
+
+\begin{equation}
+u = K(r - y) - K T\_D \frac{dy}{dt} + \int K T\_i^{-1} (r - y) + T\_t^{-1} (u\_m - u) dt \label{eq:antiwindup\_pid}
+\end{equation}
+
+where \\(u\\) is the calculated control action and \\(u\_m\\) is the actual control action applied to the plant.
+In non-saturated behaviour, \\(u=u\_m\\) and the equation is the ordinary PID.
+In saturation, \\(u\_m\\) is a constant and the resulting equations drive \\(u\\) down towards \\(u\_m\\) dynamically, with time constant \\(T\_T\\).
+
+
+### [Bumpless Transfer](bumpless_transfer.md) {#bumpless-transfer--bumpless-transfer-dot-md}
+
+When switching on the regulator, significant transient behavior can be seen and the controller may saturate the actuators.
+The solution is similar to that of the wind-up phenomenon: the regulator should be always on, carrying out calculations by using \eqref{eq:antiwindup_pid}.
+
+
+## Bibliography {#bibliography}
+
+<a id="org8b56aa1"></a>Albertos, P., and S. Antonio. 2004. “Decentralized and Decoupled Control.” In _Multivariable Control Systems: An Engineering Approach_, 125–62. Advanced Textbooks in Control and Signal Processing. Springer-Verlag. <https://doi.org/10.1007/b97506>.

content/inbook/steinbuch11_advan_motion_contr_desig.md

@@ -0,0 +1,236 @@
++++
+title = "Advanced Motion Control Design"
+author = ["Thomas Dehaeze"]
+draft = false
++++
+
+Tags
+:
+
+
+Reference
+: ([Steinbuch et al. 2011](#orgf3b81ed))
+
+Author(s)
+: Steinbuch, M., Merry, R., Boerlage, M., Ronde, M., & Molengraft, M.
+
+Year
+: 2011
+
+
+## Introduction {#introduction}
+
+The industrial state of the art control of motion systems can be summarized as follows.
+Most systems, by design, are either decoupled, or can be decoupled using static input-output transformations.
+Hence, most motion systems and their motion software architecture use SISO control design methods and solutions.
+
+Feedback design is mostly done in the frequency domain, using [Loop-Shaping](loop_shaping.md) techniques.
+A typical motion controller has a PID structure, with a low pass at high frequencies and one or two notch filters to compensate flexible dynamics.
+In addition to the feedback controller, a feedforward controller is applied with acceleration, velocity from the reference signal.
+
+The setpoint itself is a result of a setpoint generator with jerk limitation profiles (see [Trajectory Generation](trajectory_generation.md)).
+If the requirements increase, the dynamic coupling between the various DOFs can no longer be neglected and more advanced MIMO control is required.
+
+<div class="definition">
+  <div></div>
+
+[Centralized control](decoupled_control.md)
+: the transfer function matrix of the controller is allowed to have any structure
+
+Decentralized control
+: diagonal controller transfer function, but constant decoupling manipulations of inputs and outputs are allowed
+
+Independent decentralized control
+: a single loop is designed without taking into account the effect of earlier or later designed loops
+
+Sequential decentralized control
+: a single loop is designed with taking into account the effect of all earlier closed loops
+
+</div>
+
+
+## Motion Systems {#motion-systems}
+
+Here, we focus on the control of linear time invariant electromechanical motion systems that have the same number of actuators and sensors as Rigid Body modes.
+The dynamics of such systems are often dominated by the mechanics, such that:
+
+\begin{equation}
+G\_p(s) = \sum\_{i=1}^{N\_{rb}} \frac{c\_i b\_i^T}{s^2} + \sum\_{i=N\_{rb} + 1}^{N} \frac{c\_ib\_i^T}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2}
+\end{equation}
+
+with \\(N\_{rb}\\) is the number of rigid body modes.
+The vectors \\(c\_i,b\_i\\) span the directions of the ith mode shapes.
+
+If the resonance frequencies \\(\omega\_i\\) are high enough, the plant can be approximately decoupled using static input/output transformations \\(T\_u,T\_y\\) so that:
+
+\begin{equation}
+G\_{yu} = T\_y G\_p(s) T\_u = \frac{1}{s^2} \begin{bmatrix}
+m      & 0       & & \dots  &     & 0 \\\\\\
+0      & m       & &        &     & \\\\\\
+       & &       m & \ddots &     & \vdots \\\\\\
+\vdots & & \ddots & I\_x      &     & \\\\\\
+       & &       &          & I\_y & 0 \\\\\\
+0      & & \dots &          & 0   & I\_z
+\end{bmatrix} + G\_{\text{flex}}(s)
+\end{equation}
+
+
+## Feedback Control Design {#feedback-control-design}
+
+
+### [Loop-Shaping](loop_shaping.md) - The SISO case {#loop-shaping--loop-shaping-dot-md--the-siso-case}
+
+The key idea of loopshaping is the modification of the controller such that the open-loop is made according to specifications.
+The reason this works well is that the controller enters linearly into the open-loop transfer function \\(L(s) = G(s)K(s)\\).
+However, in practice all specifications are of course given in terms of the final system performance, that is, as _closed-loop_ specifications.
+So we should convert the closed-loop specifications into specifications on the open-loop.
+
+Take as an example the simple case of a disturbance being a sinusoid of known amplitude and frequency.
+If we know the specifications on the error amplitude, we can derive the requirement on the process sensitivity at that frequency.
+Since at low frequency the sensitivity can be approximated as the inverse of the open-loop, we can translate this into a specification of the open-loop at that frequency.
+Because we know that the slope of the open-loop of a well tuned motion system will be between -2 and -1, we can estimate the required crossover frequency.
+
+
+### Loop-Shaping - The MIMO case {#loop-shaping-the-mimo-case}
+
+In MIMO systems, it is much less trivial to apply loopshaping.
+The stability is determined by the closed-loop polynomial, \\(\det(I + L(s))\\), and the characteristic loci (eigenvalues of the FRF \\(L(j\omega)\\) in the complex plane) can be used for this graphically.
+A system with N inputs and N outputs has N characteristic loci.
+
+If each eigen value locus does not encircle the point (-1,0), the MIMO system is closed-loop stable.
+The shaping of these eigenvalue loci is not straightforward if the plant has large off-diagonal elements.
+In that case, a single element of the controller will affect more eigenvalue loci.
+
+The strong non-intuitive aspect of MIMO loopshaping and the fact that SISO loopshaping is used often, are major obstacles in application of modern design tools in industrial motion systems.
+
+<div class="important">
+  <div></div>
+
+For that reason, the step-by-step approach is proposed:
+
+1.  [Interaction Analysis](interaction_analysis.md)
+2.  Decoupling Transformations
+3.  Independent SISO design
+4.  Sequential SISO design
+5.  Norm-based MIMO design
+
+</div>
+
+
+#### Interaction Analysis {#interaction-analysis}
+
+The goal of the interaction analysis is to identify two-sided interactions in the plant dynamics.
+Two measured for plant interactions can be used:
+
+-   [Relative Gain Array](relative_gain_array.md) (RGA) per frequency
+
+    <div class="definition">
+      <div></div>
+
+    The frequency dependent relative gain array is calculated as:
+
+    \begin{equation}
+    \text{RGA}(G(j\omega)) = G(j\omega) \times (G(j\omega)^{-1})^{T}
+    \end{equation}
+
+    where \\(\times\\) denotes element wise multiplication.
+
+    </div>
+-   [Structure Singular Value](structured_singular_value.md) (SSV) of interaction as multiplicative output uncertainty
+
+    <div class="definition">
+      <div></div>
+
+    The structured singular value interaction measure is the following condition:
+
+    \begin{equation}
+    \mu\_D(E\_T(j\omega)) < \frac{1}{2}, \forall \omega
+    \end{equation}
+
+    with \\(E\_T(j\omega) = G\_{nd}(j\omega) G\_d^{-1}(j\omega)\\), \\(\mu\_D\\) is the structured singular value, with respect to the diagonal structure of the feedback controller.
+    \\(G\_d(s)\\) are the diagonal terms of the transfer function matrix, and \\(G\_{nd}(s) = G(s) - G\_d(s)\\).
+
+    If a diagonal transfer function matrix is used, controllers gains must be small at frequencies where this condition is not met.
+
+    </div>
+
+
+#### Decoupling Transformations {#decoupling-transformations}
+
+A common method to reduce plant interaction is to redefine the input and output of the plant.
+One can combine several inputs or outputs to control the system in more decoupled coordinates.
+For motion systems most of these transformations are found on the basis of _kinematic models_.
+Herein, combinations of the actuators are defined so that actuator variables act in independent (orthogonal) directions at the center of gravity.
+Likewise, combinations of the sensors are defined so that each translation and rotation of the center of gravity can be measured independently.
+This is basically the inversion of a kinematic model of the plant.
+
+As motion systems are often designed to be light and stiff, kinematic decoupling is often sufficient to achieve acceptable decoupling at the crossover frequency.
+
+
+#### Independent SISO design {#independent-siso-design}
+
+For systems where interaction is low, or the decoupling is almost successful, one can design a _diagonal_ controller by closing each control loop independently.
+The residual interaction can be accounted for in the analysis.
+
+For this, we make use of the following decomposition:
+
+\begin{equation}
+\det(I + GK) = \det(I + E\_T T\_d) \det(I + G\_d K)
+\end{equation}
+
+with \\(T\_d = G\_d K (I + G\_d K)^{-1}\\).
+\\(G\_d(s)\\) is defined to be only the diagonal terms of the plant transfer function matrix.
+The effect of the non-diagonal terms of the plant \\(G\_{nd}(s) = G(s) - G\_d(s)\\) is accounted for in \\(E\_T(s)\\).
+
+<div class="important">
+  <div></div>
+
+Then the MIMO closed-loop stability assessment can be slit up in two assessments:
+
+-   the first for stability of N non-interacting loops, namely \\(\det(I + G\_d(s)K(s))\\)
+-   the second for stability of \\(\det(I + E\_T(s)T\_d(s))\\)
+
+</div>
+
+If \\(G(s)\\) and \\(T\_d(s)\\) are stable, one can use the _small gain theorem_ to find a sufficient condition of stability of \\(\det(I + E\_TT\_d)\\) as
+
+\begin{equation}
+\rho(E\_T(j\omega) T\_d(j\omega)) < 1, \forall \omega
+\end{equation}
+
+where \\(\rho\\) is the spectral radius.
+
+Due to the fact that a sufficient condition is used, independent loop closing usually leads to conservative designs.
+
+
+#### Sequential SISO design {#sequential-siso-design}
+
+If the interaction is larger, the sequential loop closing method is appropriate.
+The controller is still a diagonal transfer function matrix, but each control designs are now dependent.
+In principle, one starts with the open-loop FRF of the MIMO Plant.
+Then one loop is closed using SISO loopshaping.
+The controller is taken into the plant description, and a new FRF is obtained with one input and output less.
+Then, the next loop is designed and so on.
+
+The multivariable system is nominally closed-loop stable if in each design step the system is closed-loop stable.
+However, the robustness margins in each design step do not guarantee robust stability of the final multivariable system.
+
+Drawbacks of sequential design are:
+
+-   the ordering of the design steps may have great impact on the achievable performance.
+    There is no general approach to determine the best sequence.
+-   there are no guarantees that robustness margins in earlier loops are preserved.
+-   as each design step usually considers only a single output, the responses in earlier designed loops may degrade.
+
+
+#### Norm-based MIMO design {#norm-based-mimo-design}
+
+If sequential SISO design is not successful, the next step is to start norm-based control design.
+This method requires a parametric model and weighting filters to express the control problem in terms of an operator norm like \\(H\_2\\) or \\(H\_\infty\\).
+
+Parametric models are usually build up step-by-step, first considering the unmodeled dynamics as (unstructured) uncertainty.
+
+
+## Bibliography {#bibliography}
+
+<a id="orgf3b81ed"></a>Steinbuch, Maarten, Roel Merry, Matthijs Boerlage, Michael Ronde, and Marinus Molengraft. 2011. “Advanced Motion Control Design.” In _Control System Applications_, 651–76. CRC Press.

content/inproceedings/abramovitch23_tutor_real_time_comput_issues_contr_system.md

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+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/avraam05.md

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+title = "A six degrees of freedom active isolator based on …"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (NO\_ITEM\_DATA:avraam05)
+
+Author(s)
+: Avraam, M., Marneffe, B. d., Romanescu, I., Horodinca, M., Deraemaeker, A., & Preumont, A.
+
+Year
+: 2005
+
+
+## Bibliography {#bibliography}
+
+NO\_ITEM\_DATA:avraam05

content/inproceedings/heertjes20_contr.md

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+title = "Control of wafer scanners: methods and developments"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: ([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., …
+
+Year
+: 2020
+
+
+## Bibliography {#bibliography}
+
+<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

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+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/loughridge13.md

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+title = "A tutorial on laser interferometry for precision measurements"
+author = ["Thomas Dehaeze"]
+draft = true
++++
+
+Tags
+:
+
+
+Reference
+: (NO\_ITEM\_DATA:loughridge13)
+
+Author(s)
+: Loughridge, R., & Abramovitch, D. Y.
+
+Year
+: 2013
+
+
+## Bibliography {#bibliography}
+
+NO\_ITEM\_DATA:loughridge13