Update Content - 2022-03-15

content/article/alkhatib03_activ_struc_vibrat_contr.md

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