Update files for new definition of hexapods

2020-05-05 11:38:52 +02:00
parent 2deb41939d
commit f7714a1449
33 changed files with 4627 additions and 2915 deletions
--- a/docs/optimal_stiffness_control.html
+++ b/docs/optimal_stiffness_control.html
@@ -4,7 +4,7 @@
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2020-04-17 ven. 14:10 -->
+<!-- 2020-05-05 mar. 10:34 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Control of the NASS with optimal stiffness</title>
 <meta name="generator" content="Org mode" />
@@ -42,7 +42,7 @@
 <li><a href="#orgfef1a3f">1.3. Controller Design</a></li>
 <li><a href="#org3c73014">1.4. Effect of the Low Authority Control on the Primary Plant</a></li>
 <li><a href="#orgee5dbee">1.5. Effect of the Low Authority Control on the Sensibility to Disturbances</a></li>
-<li><a href="#org882e1ac">1.6. Conclusion</a></li>
+<li><a href="#org8c0882d">1.6. Conclusion</a></li>
 </ul>
 </li>
 <li><a href="#org81dc0a8">2. Primary Control in the leg space</a>
@@ -50,21 +50,38 @@
 <li><a href="#org1e7a412">2.1. Plant in the leg space</a></li>
 <li><a href="#orgf39520c">2.2. Control in the leg space</a></li>
 <li><a href="#org16d192f">2.3. Sensibility to Disturbances and Noise Budget</a></li>
-<li><a href="#org84f68cc">2.4. Simulations</a></li>
+<li><a href="#org8f34c09">2.4. Simulations of Tomography Experiment</a></li>
 <li><a href="#orgbeadec8">2.5. Results</a></li>
-<li><a href="#orgd61852c">2.6. Conclusion</a></li>
+<li><a href="#orgf709759">2.6. Actuator Stroke and Forces</a></li>
+<li><a href="#orgb0f5db9">2.7. Conclusion</a></li>
 </ul>
 </li>
-<li><a href="#org9bd2bf8">3. Primary Control in the task space</a>
+<li><a href="#org56b28cd">3. Further More complex simulations</a>
 <ul>
-<li><a href="#org07b4a9d">3.1. Plant in the task space</a></li>
-<li><a href="#org7d888f9">3.2. Control in the task space</a>
+<li><a href="#org6c1ddb5">3.1. Simulation with Micro-Hexapod Offset</a>
 <ul>
-<li><a href="#orgb28634b">3.2.1. Stability</a></li>
+<li><a href="#org57e2cfd">3.1.1. Simulation</a></li>
+<li><a href="#org2c93370">3.1.2. Results</a></li>
 </ul>
 </li>
-<li><a href="#org57e2cfd">3.3. Simulation</a></li>
-<li><a href="#org8c0882d">3.4. Conclusion</a></li>
+<li><a href="#org5cb899b">3.2. Simultaneous Translation scans and Spindle&rsquo;s rotation</a>
+<ul>
+<li><a href="#org6710f28">3.2.1. Simulation</a></li>
+<li><a href="#org035df39">3.2.2. Results</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li><a href="#org9bd2bf8">4. Primary Control in the task space</a>
+<ul>
+<li><a href="#org07b4a9d">4.1. Plant in the task space</a></li>
+<li><a href="#org7d888f9">4.2. Control in the task space</a>
+<ul>
+<li><a href="#orgb28634b">4.2.1. Stability</a></li>
+</ul>
+</li>
+<li><a href="#org9ea6a0a">4.3. Simulation</a></li>
+<li><a href="#org21304f7">4.4. Conclusion</a></li>
 </ul>
 </li>
 </ul>
@@ -98,10 +115,10 @@ initializeAxisc();
 initializeMirror();

 initializeSimscapeConfiguration();
-initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
-initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'none'</span>);
+initializeDisturbances('enable', false);
+initializeLoggingConfiguration('log', 'none');

-initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-dvf'</span>);
+initializeController('type', 'hac-dvf');
 </pre>
 </div>

@@ -109,7 +126,7 @@ initializeController(<span class="org-string">'type'</span>, <span class="org-st
 We set the stiffness of the payload fixation:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">Kp = 1e8; <span class="org-comment">% [N/m]</span>
+<pre class="src src-matlab">Kp = 1e8; % [N/m]
 </pre>
 </div>
 </div>
@@ -136,7 +153,7 @@ We identify the system for the following payload masses:
 The nano-hexapod has the following leg&rsquo;s stiffness and damping.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'k'</span>, 1e5, <span class="org-string">'c'</span>, 2e2);
+<pre class="src src-matlab">initializeNanoHexapod('k', 1e5, 'c', 2e2);
 </pre>
 </div>
 </div>
@@ -185,7 +202,7 @@ Damping as function of the gain
 Finally, we use the following controller for the Decentralized Direct Velocity Feedback:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">Kdvf = 5e3<span class="org-type">*</span>s<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1e3)<span class="org-type">*</span>eye(6);
+<pre class="src src-matlab">Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
 </pre>
 </div>
 </div>
@@ -308,8 +325,8 @@ Decentralized Direct Velocity Feedback is shown to increase the effect of stages
 </div>
 </div>

-<div id="outline-container-org882e1ac" class="outline-3">
-<h3 id="org882e1ac"><span class="section-number-3">1.6</span> Conclusion</h3>
+<div id="outline-container-org8c0882d" class="outline-3">
+<h3 id="org8c0882d"><span class="section-number-3">1.6</span> Conclusion</h3>
 <div class="outline-text-3" id="text-1-6">
 <div class="important">
 <p>
@@ -403,11 +420,11 @@ The loop gain is shown in Figure <a href="#orgbcc0acb">12</a>.

 <div class="org-src-container">
 <pre class="src src-matlab">h = 2.0;
-Kl = 2e7 <span class="org-type">*</span> eye(6) <span class="org-type">*</span> ...
-     1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
-     1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>200<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>200<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
-     (s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10) <span class="org-type">*</span> ...
-     1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>300);
+Kl = 2e7 * eye(6) * ...
+     1/h*(s/(2*pi*100/h) + 1)/(s/(2*pi*100*h) + 1) * ...
+     1/h*(s/(2*pi*200/h) + 1)/(s/(2*pi*200*h) + 1) * ...
+     (s/2/pi/10 + 1)/(s/2/pi/10) * ...
+     1/(1 + s/2/pi/300);
 </pre>
 </div>

@@ -422,8 +439,8 @@ Kl = 2e7 <span class="org-type">*</span> eye(6) <span class="org-type">*</span>
 Finally, we include the Jacobian in the control and we ignore the measurement of the vertical rotation as for the real system.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
-K = Kl<span class="org-type">*</span>nano_hexapod.J<span class="org-type">*</span>diag([1, 1, 1, 1, 1, 0]);
+<pre class="src src-matlab">load('mat/stages.mat', 'nano_hexapod');
+K = Kl*nano_hexapod.kinematics.J*diag([1, 1, 1, 1, 1, 0]);
 </pre>
 </div>
 </div>
@@ -477,8 +494,8 @@ Then, we load the Power Spectral Density of the perturbations and we look at the
 </div>
 </div>

-<div id="outline-container-org84f68cc" class="outline-3">
-<h3 id="org84f68cc"><span class="section-number-3">2.4</span> Simulations</h3>
+<div id="outline-container-org8f34c09" class="outline-3">
+<h3 id="org8f34c09"><span class="section-number-3">2.4</span> Simulations of Tomography Experiment</h3>
 <div class="outline-text-3" id="text-2-4">
 <p>
 Let&rsquo;s now simulate a tomography experiment.
@@ -486,8 +503,8 @@ To do so, we include all disturbances except vibrations of the translation stage
 </p>
 <div class="org-src-container">
 <pre class="src src-matlab">initializeDisturbances();
-initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
-initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
+initializeSimscapeConfiguration('gravity', false);
+initializeLoggingConfiguration('log', 'all');
 </pre>
 </div>

@@ -537,9 +554,28 @@ Finally, the time domain position error signals are shown in Figure <a href="#or
 </div>
 </div>

-<div id="outline-container-orgd61852c" class="outline-3">
-<h3 id="orgd61852c"><span class="section-number-3">2.6</span> Conclusion</h3>
+<div id="outline-container-orgf709759" class="outline-3">
+<h3 id="orgf709759"><span class="section-number-3">2.6</span> Actuator Stroke and Forces</h3>
 <div class="outline-text-3" id="text-2-6">
+
+<div id="orgf9d6367" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_L_act_force.png" alt="opt_stiff_hac_dvf_L_act_force.png" />
+</p>
+<p><span class="figure-number">Figure 20: </span>Force applied by the actuator during the simulation</p>
+</div>
+
+
+<div id="org11b8730" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_L_act_stroke.png" alt="opt_stiff_hac_dvf_L_act_stroke.png" />
+</p>
+<p><span class="figure-number">Figure 21: </span>Leg&rsquo;s stroke during the simulation</p>
+</div>
+</div>
+</div>
+
+<div id="outline-container-orgb0f5db9" class="outline-3">
+<h3 id="orgb0f5db9"><span class="section-number-3">2.7</span> Conclusion</h3>
+<div class="outline-text-3" id="text-2-7">
 <div class="important">
 <p>

@@ -550,14 +586,128 @@ Finally, the time domain position error signals are shown in Figure <a href="#or
 </div>
 </div>

-<div id="outline-container-org9bd2bf8" class="outline-2">
-<h2 id="org9bd2bf8"><span class="section-number-2">3</span> Primary Control in the task space</h2>
+<div id="outline-container-org56b28cd" class="outline-2">
+<h2 id="org56b28cd"><span class="section-number-2">3</span> Further More complex simulations</h2>
 <div class="outline-text-2" id="text-3">
+</div>
+<div id="outline-container-org6c1ddb5" class="outline-3">
+<h3 id="org6c1ddb5"><span class="section-number-3">3.1</span> Simulation with Micro-Hexapod Offset</h3>
+<div class="outline-text-3" id="text-3-1">
+</div>
+<div id="outline-container-org57e2cfd" class="outline-4">
+<h4 id="org57e2cfd"><span class="section-number-4">3.1.1</span> Simulation</h4>
+<div class="outline-text-4" id="text-3-1-1">
+<p>
+The micro-hexapod is inducing a 10mm offset of the sample center of mass with the rotation axis.
+A tomography experiment is then simulated.
+</p>
+
+<div class="org-src-container">
+<pre class="src src-matlab">initializeDisturbances();
+initializeSimscapeConfiguration('gravity', false);
+initializeLoggingConfiguration('log', 'all');
+
+initializeSample('mass', 1, 'freq', 200);
+initializeMicroHexapod('AP', [10e-3 0 0]);
+initializeReferences('Rz_type', 'rotating', 'Rz_period', 1, ...
+                     'Dh_pos', [10e-3; 0; 0; 0; 0; 0]);
+</pre>
+</div>
+
+<div class="org-src-container">
+<pre class="src src-matlab">load('mat/conf_simulink.mat');
+set_param(conf_simulink, 'StopTime', '3');
+sim('nass_model');
+</pre>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org2c93370" class="outline-4">
+<h4 id="org2c93370"><span class="section-number-4">3.1.2</span> Results</h4>
+<div class="outline-text-4" id="text-3-1-2">
+
+<div id="org6be7e46" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_Dh_offset_disp_error.png" alt="opt_stiff_hac_dvf_Dh_offset_disp_error.png" />
+</p>
+</div>
+
+
+<div id="org07fa12d" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_Dh_offset_F.png" alt="opt_stiff_hac_dvf_Dh_offset_F.png" />
+</p>
+</div>
+
+
+<div id="orga4d03c5" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_Dh_offset_dL.png" alt="opt_stiff_hac_dvf_Dh_offset_dL.png" />
+</p>
+</div>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org5cb899b" class="outline-3">
+<h3 id="org5cb899b"><span class="section-number-3">3.2</span> Simultaneous Translation scans and Spindle&rsquo;s rotation</h3>
+<div class="outline-text-3" id="text-3-2">
+</div>
+<div id="outline-container-org6710f28" class="outline-4">
+<h4 id="org6710f28"><span class="section-number-4">3.2.1</span> Simulation</h4>
+<div class="outline-text-4" id="text-3-2-1">
+<p>
+A simulation is now performed with translation scans and spindle rotation at the same time.
+</p>
+
+<p>
+The sample has a mass one 1kg, the spindle rotation speed is 60rpm and the translation scans have a period of 4s and a triangular shape.
+</p>
+
+<div class="org-src-container">
+<pre class="src src-matlab">initializeDisturbances();
+initializeSimscapeConfiguration('gravity', false);
+initializeLoggingConfiguration('log', 'all');
+
+initializeSample('mass', 1, 'freq', 200);
+initializeReferences('Rz_type', 'rotating', 'Rz_period', 1, ...
+                     'Dy_type', 'triangular', 'Dy_amplitude', 5e-3, 'Dy_period', 4);
+</pre>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org035df39" class="outline-4">
+<h4 id="org035df39"><span class="section-number-4">3.2.2</span> Results</h4>
+<div class="outline-text-4" id="text-3-2-2">
+
+<div id="orgbfa1d02" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_Dy_scans_disp_error.png" alt="opt_stiff_hac_dvf_Dy_scans_disp_error.png" />
+</p>
+</div>
+
+
+<div id="org760b96c" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_Dy_scans_F.png" alt="opt_stiff_hac_dvf_Dy_scans_F.png" />
+</p>
+</div>
+
+
+<div id="orgae36e3d" class="figure">
+<p><img src="figs/opt_stiff_hac_dvf_Dy_scans_dL.png" alt="opt_stiff_hac_dvf_Dy_scans_dL.png" />
+</p>
+</div>
+</div>
+</div>
+</div>
+</div>
+
+<div id="outline-container-org9bd2bf8" class="outline-2">
+<h2 id="org9bd2bf8"><span class="section-number-2">4</span> Primary Control in the task space</h2>
+<div class="outline-text-2" id="text-4">
 <p>
 <a id="orge9c2f9a"></a>
 </p>
 <p>
-In this section, the control architecture shown in Figure <a href="#org7e70ccc">20</a> is applied and consists of:
+In this section, the control architecture shown in Figure <a href="#org7e70ccc">28</a> is applied and consists of:
 </p>
 <ul class="org-ul">
 <li>an inner Low Authority Control loop consisting of a decentralized direct velocity control controller</li>
@@ -568,12 +718,12 @@ In this section, the control architecture shown in Figure <a href="#org7e70ccc">
 <div id="org7e70ccc" class="figure">
 <p><img src="figs/control_architecture_hac_dvf_pos_X.png" alt="control_architecture_hac_dvf_pos_X.png" />
 </p>
-<p><span class="figure-number">Figure 20: </span>HAC-LAC architecture</p>
+<p><span class="figure-number">Figure 28: </span>HAC-LAC architecture</p>
 </div>
 </div>
 <div id="outline-container-org07b4a9d" class="outline-3">
-<h3 id="org07b4a9d"><span class="section-number-3">3.1</span> Plant in the task space</h3>
-<div class="outline-text-3" id="text-3-1">
+<h3 id="org07b4a9d"><span class="section-number-3">4.1</span> Plant in the task space</h3>
+<div class="outline-text-3" id="text-4-1">
 <p>
 Let&rsquo;s look \(\bm{G}_\mathcal{X}(s)\).
 </p>
@@ -581,60 +731,60 @@ Let&rsquo;s look \(\bm{G}_\mathcal{X}(s)\).
 </div>

 <div id="outline-container-org7d888f9" class="outline-3">
-<h3 id="org7d888f9"><span class="section-number-3">3.2</span> Control in the task space</h3>
-<div class="outline-text-3" id="text-3-2">
+<h3 id="org7d888f9"><span class="section-number-3">4.2</span> Control in the task space</h3>
+<div class="outline-text-3" id="text-4-2">
 <div class="org-src-container">
 <pre class="src src-matlab">Kx = tf(zeros(6));

 h = 2.5;
-Kx<span class="org-type">(1,1) </span>= 3e7 <span class="org-type">*</span> ...
-          1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
-          (s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
+Kx(1,1) = 3e7 * ...
+          1/h*(s/(2*pi*100/h) + 1)/(s/(2*pi*100*h) + 1) * ...
+          (s/2/pi/1 + 1)/(s/2/pi/1);

-Kx<span class="org-type">(2,2) </span>= Kx(1,1);
+Kx(2,2) = Kx(1,1);

 h = 2.5;
-Kx<span class="org-type">(3,3) </span>= 3e7 <span class="org-type">*</span> ...
-          1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
-          (s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
+Kx(3,3) = 3e7 * ...
+          1/h*(s/(2*pi*100/h) + 1)/(s/(2*pi*100*h) + 1) * ...
+          (s/2/pi/1 + 1)/(s/2/pi/1);
 </pre>
 </div>

 <div class="org-src-container">
 <pre class="src src-matlab">h = 1.5;
-Kx<span class="org-type">(4,4) </span>= 5e5 <span class="org-type">*</span> ...
-          1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
-          (s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
+Kx(4,4) = 5e5 * ...
+          1/h*(s/(2*pi*100/h) + 1)/(s/(2*pi*100*h) + 1) * ...
+          (s/2/pi/1 + 1)/(s/2/pi/1);

-Kx<span class="org-type">(5,5) </span>= Kx(4,4);
+Kx(5,5) = Kx(4,4);

 h = 1.5;
-Kx<span class="org-type">(6,6) </span>= 5e4 <span class="org-type">*</span> ...
-          1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>30<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>30<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
-          (s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
+Kx(6,6) = 5e4 * ...
+          1/h*(s/(2*pi*30/h) + 1)/(s/(2*pi*30*h) + 1) * ...
+          (s/2/pi/1 + 1)/(s/2/pi/1);
 </pre>
 </div>
 </div>

 <div id="outline-container-orgb28634b" class="outline-4">
-<h4 id="orgb28634b"><span class="section-number-4">3.2.1</span> Stability</h4>
-<div class="outline-text-4" id="text-3-2-1">
+<h4 id="orgb28634b"><span class="section-number-4">4.2.1</span> Stability</h4>
+<div class="outline-text-4" id="text-4-2-1">
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Ms)</span>
-    isstable(feedback(Gm_x{<span class="org-constant">i</span>}<span class="org-type">*</span>Kx, eye(6), <span class="org-type">-</span>1))
-<span class="org-keyword">end</span>
+<pre class="src src-matlab">for i = 1:length(Ms)
+    isstable(feedback(Gm_x{i}*Kx, eye(6), -1))
+end
 </pre>
 </div>
 </div>
 </div>
 </div>

-<div id="outline-container-org57e2cfd" class="outline-3">
-<h3 id="org57e2cfd"><span class="section-number-3">3.3</span> Simulation</h3>
+<div id="outline-container-org9ea6a0a" class="outline-3">
+<h3 id="org9ea6a0a"><span class="section-number-3">4.3</span> Simulation</h3>
 </div>
-<div id="outline-container-org8c0882d" class="outline-3">
-<h3 id="org8c0882d"><span class="section-number-3">3.4</span> Conclusion</h3>
-<div class="outline-text-3" id="text-3-4">
+<div id="outline-container-org21304f7" class="outline-3">
+<h3 id="org21304f7"><span class="section-number-3">4.4</span> Conclusion</h3>
+<div class="outline-text-3" id="text-4-4">
 <div class="important">
 <p>

@@ -647,7 +797,7 @@ Kx<span class="org-type">(6,6) </span>= 5e4 <span class="org-type">*</span> ...
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-04-17 ven. 14:10</p>
+<p class="date">Created: 2020-05-05 mar. 10:34</p>
 </div>
 </body>
 </html>