Update nano-hexapod parameters

- STEPS files from SolidWorks
- configurable APA, flexible joints, etc.

.SimulinkProject/Root.type.Files/STEPS.type.File.xml

@@ -0,0 +1,2 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<Info />

.SimulinkProject/Root.type.Files/STEPS.type.File/1.type.DIR_SIGNIFIER.xml

@@ -0,0 +1,2 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<Info />

.SimulinkProject/Root.type.Files/STEPS.type.File/nano_hexapod.type.File.xml

@@ -0,0 +1,2 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<Info />

.SimulinkProject/Root.type.Files/STEPS.type.File/nano_hexapod.type.File/1.type.DIR_SIGNIFIER.xml

@@ -0,0 +1,2 @@
+<?xml version='1.0' encoding='UTF-8'?>
+<Info />

.SimulinkProject/Root.type.ProjectPath/2e7b7a5d-07f5-4e60-bf5b-0686d86dbb21.type.Reference.xml

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+<?xml version='1.0' encoding='UTF-8'?>
+<Info Ref="STEPS/png" Type="Relative" />

.SimulinkProject/Root.type.ProjectPath/6cf1cee4-862b-45ea-9e86-a1762825df9e.type.Reference.xml

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+<?xml version='1.0' encoding='UTF-8'?>
+<Info Ref="STEPS/nano_hexapod" Type="Relative" />

.gitignore

@@ -1,4 +1,9 @@
+*.bbl
+*.synctex.gz
+.auctex-auto/
+_minted*
 auto/
+org/*.pdf
 *.tex
 
 nohup.out

STEPS/nano_hexapod/nut_concave.STEP

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+ISO-10303-21;
+HEADER;
+FILE_DESCRIPTION (( 'STEP AP214' ),
+    '1' );
+FILE_NAME ('12600011.STEP',
+    '2021-03-15T09:41:30',
+    ( '' ),
+    ( '' ),
+    'SwSTEP 2.0',
+    'SolidWorks 2020',
+    '' );
+FILE_SCHEMA (( 'AUTOMOTIVE_DESIGN' ));
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docs/alternative-micro-station-architecture.html

@@ -1,45 +1,39 @@
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-<?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
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-<!-- 2020-05-07 jeu. 14:04 -->
+<!-- 2021-02-20 sam. 23:08 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Alternative Micro-Station Architecture</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
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- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Alternative Micro-Station Architecture</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#orgfc342c6">1. Current Micro-Station Architecture</a></li>
-<li><a href="#orgc09ec50">2. Alternative Micro-Station Architecture</a></li>
-<li><a href="#org247d72d">3. Alternative Metrology Architecture</a></li>
-<li><a href="#orge88a434">4. First rough specification of the stages - Maneuverability</a></li>
-<li><a href="#org44e1330">5. Advantages</a></li>
-<li><a href="#org62007a3">6. Disadvantages</a></li>
+<li><a href="#org0cd332b">1. Current Micro-Station Architecture</a></li>
+<li><a href="#orgd7cf2e3">2. Alternative Micro-Station Architecture</a></li>
+<li><a href="#org824aa14">3. Alternative Metrology Architecture</a></li>
+<li><a href="#org107818e">4. First rough specification of the stages - Maneuverability</a></li>
+<li><a href="#org5a1297a">5. Advantages</a></li>
+<li><a href="#org880bc68">6. Disadvantages</a></li>
 </ul>
 </div>
 </div>
 
-<div id="outline-container-orgfc342c6" class="outline-2">
-<h2 id="orgfc342c6"><span class="section-number-2">1</span> Current Micro-Station Architecture</h2>
+<div id="outline-container-org0cd332b" class="outline-2">
+<h2 id="org0cd332b"><span class="section-number-2">1</span> Current Micro-Station Architecture</h2>
 <div class="outline-text-2" id="text-1">
 <p>
 <b>Motion Requirements</b>:
@@ -62,11 +56,11 @@ For each of these motion requirements, a position stage is associated:
 </ol>
 
 <p>
-The architecture is shown in Figure <a href="#org41ed0af">1</a>.
+The architecture is shown in Figure <a href="#org8583068">1</a>.
 </p>
 
 
-<div id="org41ed0af" class="figure">
+<div id="org8583068" class="figure">
 <p><img src="figs/nass_schematic.png" alt="nass_schematic.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Architecture of the Micro-Station</p>
@@ -92,8 +86,8 @@ Requirements on Tx an Rx motions are not specified.
 </div>
 </div>
 
-<div id="outline-container-orgc09ec50" class="outline-2">
-<h2 id="orgc09ec50"><span class="section-number-2">2</span> Alternative Micro-Station Architecture</h2>
+<div id="outline-container-orgd7cf2e3" class="outline-2">
+<h2 id="orgd7cf2e3"><span class="section-number-2">2</span> Alternative Micro-Station Architecture</h2>
 <div class="outline-text-2" id="text-2">
 <p>
 If we remove the requirement of having to control each motion with an independent position stage, we can think of other mechanical architectures.
@@ -118,7 +112,7 @@ A short stroke hexapod with flexible hinges can be used to compensate the positi
 </p>
 
 <p>
-The mechanical architecture can then be composed of (see Figures <a href="#orgac922d2">2</a> and <a href="#org4c0d31a">3</a>):
+The mechanical architecture can then be composed of (see Figures <a href="#org8000986">2</a> and <a href="#org9b0e1ac">3</a>):
 </p>
 <ul class="org-ul">
 <li>One long stroke hexapod for position</li>
@@ -127,14 +121,14 @@ The mechanical architecture can then be composed of (see Figures <a href="#orgac
 </ul>
 
 
-<div id="orgac922d2" class="figure">
+<div id="org8000986" class="figure">
 <p><img src="figs/nass_concept.png" alt="nass_concept.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Alternative Micro-Station Architecture</p>
 </div>
 
 
-<div id="org4c0d31a" class="figure">
+<div id="org9b0e1ac" class="figure">
 <p><img src="figs/alternative_nass_concept.jpg" alt="alternative_nass_concept.jpg" />
 </p>
 <p><span class="figure-number">Figure 3: </span>Alternative Micro-Station Architecture</p>
@@ -142,8 +136,8 @@ The mechanical architecture can then be composed of (see Figures <a href="#orgac
 </div>
 </div>
 
-<div id="outline-container-org247d72d" class="outline-2">
-<h2 id="org247d72d"><span class="section-number-2">3</span> Alternative Metrology Architecture</h2>
+<div id="outline-container-org824aa14" class="outline-2">
+<h2 id="org824aa14"><span class="section-number-2">3</span> Alternative Metrology Architecture</h2>
 <div class="outline-text-2" id="text-3">
 <p>
 As the motion of the sample does not change, the metrology could be the same as the one planned for the current micro-station architecture.
@@ -172,8 +166,8 @@ Kinematic mount of the metrology frame supporting both the spherical mirrors and
 </div>
 </div>
 
-<div id="outline-container-orge88a434" class="outline-2">
-<h2 id="orge88a434"><span class="section-number-2">4</span> First rough specification of the stages - Maneuverability</h2>
+<div id="outline-container-org107818e" class="outline-2">
+<h2 id="org107818e"><span class="section-number-2">4</span> First rough specification of the stages - Maneuverability</h2>
 <div class="outline-text-2" id="text-4">
 <p>
 The required maneuverability of the <b>long stroke hexapod</b> corresponds to the wanted 6d pose of the sample (except the Rz rotation done by the Spindle):
@@ -201,8 +195,8 @@ Moreover the dynamical errors of each stage are very difficult to estimate, thus
 </div>
 </div>
 
-<div id="outline-container-org44e1330" class="outline-2">
-<h2 id="org44e1330"><span class="section-number-2">5</span> Advantages</h2>
+<div id="outline-container-org5a1297a" class="outline-2">
+<h2 id="org5a1297a"><span class="section-number-2">5</span> Advantages</h2>
 <div class="outline-text-2" id="text-5">
 <p>
 <b>Mechanics</b>:
@@ -252,8 +246,8 @@ Also Tx scans and Rx scans can be performed.</li>
 </div>
 </div>
 
-<div id="outline-container-org62007a3" class="outline-2">
-<h2 id="org62007a3"><span class="section-number-2">6</span> Disadvantages</h2>
+<div id="outline-container-org880bc68" class="outline-2">
+<h2 id="org880bc68"><span class="section-number-2">6</span> Disadvantages</h2>
 <div class="outline-text-2" id="text-6">
 <ul class="org-ul">
 <li>Possible singularities in the required maneuverability for the Long stroke Hexapod?
@@ -273,7 +267,7 @@ The require displacement of each leg of the hexapod can be computed with the inv
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-05-07 jeu. 14:04</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>

docs/centrifugal_forces.html

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 <head>
-<!-- 2020-05-07 jeu. 14:05 -->
+<!-- 2021-02-20 sam. 23:09 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Centrifugal Forces</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
-<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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-<script src="./js/jquery.stickytableheaders.min.js"></script>
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+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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+<script>
+           MathJax = {
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              tex: {
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-            macros: {bm: ["\\boldsymbol{#1}",1],}
+               tags: "ams",
+               multlineWidth: "%MULTLINEWIDTH",
+               tagSide: "right",
+                       macros: {bm: ["\\boldsymbol{#1}",1],},
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-          <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+           <script id="MathJax-script" async
+             src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Centrifugal Forces</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org49834ed">1. Parameters</a></li>
-<li><a href="#org4b7747e">2. Centrifugal forces for light and heavy sample</a></li>
-<li><a href="#org92c9f54">3. Centrifugal forces as a function of the rotation speed</a></li>
-<li><a href="#orgb7f1acf">4. Maximum rotation speed as a function of the mass</a></li>
+<li><a href="#org5199302">1. Parameters</a></li>
+<li><a href="#orga2ea10d">2. Centrifugal forces for light and heavy sample</a></li>
+<li><a href="#orgf375b50">3. Centrifugal forces as a function of the rotation speed</a></li>
+<li><a href="#orge7fb13d">4. Maximum rotation speed as a function of the mass</a></li>
 </ul>
 </div>
 </div>
@@ -52,7 +56,7 @@ This is the case then the sample is moved by the micro-hexapod.
 </p>
 
 <p>
-The centrifugal forces are defined as represented Figure <a href="#orgd84fe6e">1</a> where:
+The centrifugal forces are defined as represented Figure <a href="#org91ed599">1</a> where:
 </p>
 <ul class="org-ul">
 <li>\(M\) is the total mass of the rotating elements in \([kg]\)</li>
@@ -61,14 +65,14 @@ The centrifugal forces are defined as represented Figure <a href="#orgd84fe6e">1
 </ul>
 
 
-<div id="orgd84fe6e" class="figure">
+<div id="org91ed599" class="figure">
 <p><img src="./figs/centrifugal.png" alt="centrifugal.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Centrifugal forces</p>
 </div>
 
-<div id="outline-container-org49834ed" class="outline-2">
-<h2 id="org49834ed"><span class="section-number-2">1</span> Parameters</h2>
+<div id="outline-container-org5199302" class="outline-2">
+<h2 id="org5199302"><span class="section-number-2">1</span> Parameters</h2>
 <div class="outline-text-2" id="text-1">
 <p>
 We define some parameters for the computation.
@@ -79,8 +83,8 @@ The mass of the sample can vary from \(1\,kg\) to \(50\,kg\) to which is added t
 </p>
 
 <div class="org-src-container">
-<pre class="src src-matlab">M_light = 16; % mass of excentred parts mooving [kg]
-M_heavy = 65; % [kg]
+<pre class="src src-matlab">  M_light = 16; <span class="org-comment">% mass of excentred parts mooving [kg]</span>
+  M_heavy = 65; <span class="org-comment">% [kg]</span>
 </pre>
 </div>
 
@@ -88,8 +92,8 @@ M_heavy = 65; % [kg]
 For the light mass, the rotation speed is 60rpm whereas for the heavy mass, it is equal to 1rpm.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">w_light = 2*pi; % rotational speed [rad/s]
-w_heavy = 2*pi/60; % rotational speed [rad/s]
+<pre class="src src-matlab">  w_light = 2<span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% rotational speed [rad/s]</span>
+  w_heavy = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">/</span>60; <span class="org-comment">% rotational speed [rad/s]</span>
 </pre>
 </div>
 
@@ -97,14 +101,14 @@ w_heavy = 2*pi/60; % rotational speed [rad/s]
 Finally, we consider a mass eccentricity of \(10\,mm\).
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">R = 0.01; % Excentricity [m]
+<pre class="src src-matlab">  R = 0.01; <span class="org-comment">% Excentricity [m]</span>
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org4b7747e" class="outline-2">
-<h2 id="org4b7747e"><span class="section-number-2">2</span> Centrifugal forces for light and heavy sample</h2>
+<div id="outline-container-orga2ea10d" class="outline-2">
+<h2 id="orga2ea10d"><span class="section-number-2">2</span> Centrifugal forces for light and heavy sample</h2>
 <div class="outline-text-2" id="text-2">
 <p>
 From the formula \(F_c = m \omega^2 r\), we obtain the values shown below.
@@ -139,15 +143,15 @@ From the formula \(F_c = m \omega^2 r\), we obtain the values shown below.
 </div>
 </div>
 
-<div id="outline-container-org92c9f54" class="outline-2">
-<h2 id="org92c9f54"><span class="section-number-2">3</span> Centrifugal forces as a function of the rotation speed</h2>
+<div id="outline-container-orgf375b50" class="outline-2">
+<h2 id="orgf375b50"><span class="section-number-2">3</span> Centrifugal forces as a function of the rotation speed</h2>
 <div class="outline-text-2" id="text-3">
 <p>
-The centrifugal forces as a function of the rotation speed for light and heavy sample is shown on Figure <a href="#orgfaf795f">2</a>.
+The centrifugal forces as a function of the rotation speed for light and heavy sample is shown on Figure <a href="#org87b7644">2</a>.
 </p>
 
 
-<div id="orgfaf795f" class="figure">
+<div id="org87b7644" class="figure">
 <p><img src="figs/centrifugal_forces_rpm.png" alt="centrifugal_forces_rpm.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Centrifugal forces function of the rotation speed</p>
@@ -155,29 +159,29 @@ The centrifugal forces as a function of the rotation speed for light and heavy s
 </div>
 </div>
 
-<div id="outline-container-orgb7f1acf" class="outline-2">
-<h2 id="orgb7f1acf"><span class="section-number-2">4</span> Maximum rotation speed as a function of the mass</h2>
+<div id="outline-container-orge7fb13d" class="outline-2">
+<h2 id="orge7fb13d"><span class="section-number-2">4</span> Maximum rotation speed as a function of the mass</h2>
 <div class="outline-text-2" id="text-4">
 <p>
-We plot the maximum rotation speed as a function of the mass for different maximum force that we can use to counteract the centrifugal forces (Figure <a href="#org6ee8f38">3</a>).
+We plot the maximum rotation speed as a function of the mass for different maximum force that we can use to counteract the centrifugal forces (Figure <a href="#org8fe6a07">3</a>).
 </p>
 
 <p>
-From a specified maximum allowed centrifugal force (here set to \(10\,[N]\)), the maximum rotation speed as a function of the sample&rsquo;s mass is shown in Figure <a href="#org6ee8f38">3</a>.
+From a specified maximum allowed centrifugal force (here set to \(10\,[N]\)), the maximum rotation speed as a function of the sample&rsquo;s mass is shown in Figure <a href="#org8fe6a07">3</a>.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-matlab">F_max = 10; % Maximum accepted centrifugal forces [N]
+<pre class="src src-matlab">  F_max = 10; <span class="org-comment">% Maximum accepted centrifugal forces [N]</span>
 
-R = 0.01;
+  R = 0.01;
 
-M_sample = 0:1:100;
-M_reflector = 15;
+  M_sample = 0<span class="org-type">:</span>1<span class="org-type">:</span>100;
+  M_reflector = 15;
 </pre>
 </div>
 
 
-<div id="org6ee8f38" class="figure">
+<div id="org8fe6a07" class="figure">
 <p><img src="figs/max_force_rpm.png" alt="max_force_rpm.png" />
 </p>
 <p><span class="figure-number">Figure 3: </span>Maximum rotation speed as a function of the sample mass for an allowed centrifugal force of \(100\,[N]\)</p>
@@ -187,7 +191,7 @@ M_reflector = 15;
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-05-07 jeu. 14:05</p>
+<p class="date">Created: 2021-02-20 sam. 23:09</p>
 </div>
 </body>
 </html>

docs/compensation_gravity_forces.html

@@ -1,37 +1,32 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "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. 09:34 -->
+<!-- 2021-02-20 sam. 23:07 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Compensating the gravity forces to start at steady state</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
-<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
-<script src="./js/jquery.min.js"></script>
-<script src="./js/bootstrap.min.js"></script>
-<script src="./js/jquery.stickytableheaders.min.js"></script>
-<script src="./js/readtheorg.js"></script>
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Compensating the gravity forces to start at steady state</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org356e04b">1. Initialization of the Experimental Conditions</a></li>
-<li><a href="#org263e5db">2. Without compensation</a></li>
-<li><a href="#orgfd6d9e9">3. Simulation to compute the required force in each joint</a></li>
-<li><a href="#org44bde7a">4. New simulation with compensation of gravity forces</a></li>
-<li><a href="#orgb714922">5. Conclusion</a></li>
+<li><a href="#orgb5e305a">1. Initialization of the Experimental Conditions</a></li>
+<li><a href="#org96a269f">2. Without compensation</a></li>
+<li><a href="#orged240b5">3. Simulation to compute the required force in each joint</a></li>
+<li><a href="#org25738bf">4. New simulation with compensation of gravity forces</a></li>
+<li><a href="#orgb003af1">5. Conclusion</a></li>
 </ul>
 </div>
 </div>
@@ -41,19 +36,19 @@ In this file is shown a technique used to compensate the gravity forces at t=0.
 </p>
 
 <p>
-The problem is that in presence of gravity, the system does not start at steady state and experience a transient phase (section <a href="#org4bc70b2">2</a>).
+The problem is that in presence of gravity, the system does not start at steady state and experience a transient phase (section <a href="#orgf3b9673">2</a>).
 </p>
 
 <p>
 In order to start the simulation at steady state in presence of gravity:
 </p>
 <ul class="org-ul">
-<li>section <a href="#org2de8ac1">3</a>: first the stages are initialize in such a way that they are rigid, and the forces/torques applied at the location of their joints is measured</li>
-<li>section <a href="#org5364ea3">4</a>: Then, the equilibrium position of each joint is modified in such a way that at t=0, the forces in each joints exactly compensate the forces due to gravity forces</li>
+<li>section <a href="#orgaf044de">3</a>: first the stages are initialize in such a way that they are rigid, and the forces/torques applied at the location of their joints is measured</li>
+<li>section <a href="#orga475c79">4</a>: Then, the equilibrium position of each joint is modified in such a way that at t=0, the forces in each joints exactly compensate the forces due to gravity forces</li>
 </ul>
 
-<div id="outline-container-org356e04b" class="outline-2">
-<h2 id="org356e04b"><span class="section-number-2">1</span> Initialization of the Experimental Conditions</h2>
+<div id="outline-container-orgb5e305a" class="outline-2">
+<h2 id="orgb5e305a"><span class="section-number-2">1</span> Initialization of the Experimental Conditions</h2>
 <div class="outline-text-2" id="text-1">
 <p>
 We don&rsquo;t inject any perturbations and no reference tracking.
@@ -76,11 +71,11 @@ initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span clas
 </div>
 </div>
 
-<div id="outline-container-org263e5db" class="outline-2">
-<h2 id="org263e5db"><span class="section-number-2">2</span> Without compensation</h2>
+<div id="outline-container-org96a269f" class="outline-2">
+<h2 id="org96a269f"><span class="section-number-2">2</span> Without compensation</h2>
 <div class="outline-text-2" id="text-2">
 <p>
-<a id="org4bc70b2"></a>
+<a id="orgf3b9673"></a>
 Let&rsquo;s simulate the system without any compensation of gravity forces.
 </p>
 
@@ -111,10 +106,10 @@ sim_no_compensation = simout;
 </div>
 
 <p>
-And we can observe on Figure <a href="#org0568928">1</a> that there are some motion in the system.
+And we can observe on Figure <a href="#org3568468">1</a> that there are some motion in the system.
 </p>
 
-<div id="org0568928" class="figure">
+<div id="org3568468" class="figure">
 <p><img src="figs/transient_phase_gravity_no_compensation.png" alt="transient_phase_gravity_no_compensation.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Motion of the sample at the start of the simulation in presence of gravity (<a href="./figs/transient_phase_gravity_no_compensation.png">png</a>, <a href="./figs/transient_phase_gravity_no_compensation.pdf">pdf</a>)</p>
@@ -122,11 +117,11 @@ And we can observe on Figure <a href="#org0568928">1</a> that there are some mot
 </div>
 </div>
 
-<div id="outline-container-orgfd6d9e9" class="outline-2">
-<h2 id="orgfd6d9e9"><span class="section-number-2">3</span> Simulation to compute the required force in each joint</h2>
+<div id="outline-container-orged240b5" class="outline-2">
+<h2 id="orged240b5"><span class="section-number-2">3</span> Simulation to compute the required force in each joint</h2>
 <div class="outline-text-2" id="text-3">
 <p>
-<a id="org2de8ac1"></a>
+<a id="orgaf044de"></a>
 We here wish to simulate the system in order to compute the required force in each joint to compensate the gravity forces.
 </p>
 
@@ -318,11 +313,11 @@ We save these forces in <code>Foffset.mat</code>.
 </div>
 </div>
 
-<div id="outline-container-org44bde7a" class="outline-2">
-<h2 id="org44bde7a"><span class="section-number-2">4</span> New simulation with compensation of gravity forces</h2>
+<div id="outline-container-org25738bf" class="outline-2">
+<h2 id="org25738bf"><span class="section-number-2">4</span> New simulation with compensation of gravity forces</h2>
 <div class="outline-text-2" id="text-4">
 <p>
-<a id="org5364ea3"></a>
+<a id="orga475c79"></a>
 We now initialize the stages with the option <code>Foffset</code>.
 </p>
 <div class="org-src-container">
@@ -358,17 +353,17 @@ sim_compensation = simout;
 Verification that nothing is moving
 </p>
 
-<div id="orgc677acf" class="figure">
+<div id="org2b3d436" class="figure">
 <p><img src="figs/transient_phase_gravity_compensation.png" alt="transient_phase_gravity_compensation.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Motion of the sample at the start of the simulation in presence of gravity when compensating the gravity forces  (<a href="./figs/transient_phase_gravity_compensation.png">png</a>, <a href="./figs/transient_phase_gravity_compensation.pdf">pdf</a>)</p>
 </div>
 </div>
 </div>
-<div id="outline-container-orgb714922" class="outline-2">
-<h2 id="orgb714922"><span class="section-number-2">5</span> Conclusion</h2>
+<div id="outline-container-orgb003af1" class="outline-2">
+<h2 id="orgb003af1"><span class="section-number-2">5</span> Conclusion</h2>
 <div class="outline-text-2" id="text-5">
-<div class="important">
+<div class="important" id="org3329ee9">
 <p>
 This initialization technique permits to compute the required forces/torques to be applied in each joint in order to compensate for gravity forces.
 This initialization should be redone for each configuration (change of sample mass, change of tilt angle), but not when changing the stiffness of joints, for instant when changing from lorentz based nano-hexapod or piezo based.
@@ -380,7 +375,7 @@ This initialization should be redone for each configuration (change of sample ma
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-04-17 ven. 09:34</p>
+<p class="date">Created: 2021-02-20 sam. 23:07</p>
 </div>
 </body>
 </html>

docs/control.html

@@ -1,73 +1,77 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "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. 09:35 -->
+<!-- 2021-02-20 sam. 23:08 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Control of the Nano-Active-Stabilization-System</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
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-<script src="./js/jquery.min.js"></script>
-<script src="./js/bootstrap.min.js"></script>
-<script src="./js/jquery.stickytableheaders.min.js"></script>
-<script src="./js/readtheorg.js"></script>
-<script>MathJax = {
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
+<script>
+           MathJax = {
+             svg: {
+               scale: 1,
+               fontCache: "global"
+             },
              tex: {
-            tags: 'ams',
-            macros: {bm: ["\\boldsymbol{#1}",1],}
+               tags: "ams",
+               multlineWidth: "%MULTLINEWIDTH",
+               tagSide: "right",
+                       macros: {bm: ["\\boldsymbol{#1}",1],},
+               tagIndent: ".8em"
              }
            };
            </script>
-          <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+           <script id="MathJax-script" async
+             src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Control of the Nano-Active-Stabilization-System</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org15699e9">1. Control Configuration - Introduction</a></li>
-<li><a href="#org2be3166">2. Tracking Control in the Frame of the Nano-Hexapod - Basic Architectures</a>
+<li><a href="#org25c471e">1. Control Configuration - Introduction</a></li>
+<li><a href="#orgcd0731f">2. Tracking Control in the Frame of the Nano-Hexapod - Basic Architectures</a>
 <ul>
-<li><a href="#org970ab39">2.1. Control in the frame of the Legs</a></li>
-<li><a href="#org82193fb">2.2. Control in the Cartesian frame</a></li>
+<li><a href="#orgbc69eea">2.1. Control in the frame of the Legs</a></li>
+<li><a href="#org65bc213">2.2. Control in the Cartesian frame</a></li>
 </ul>
 </li>
-<li><a href="#org7d7b7f4">3. Active Damping Architecture - Collocated Control (link)</a>
+<li><a href="#org9ef6b25">3. Active Damping Architecture - Collocated Control (link)</a>
 <ul>
-<li><a href="#org3546873">3.1. Integral Force Feedback</a></li>
-<li><a href="#org722b371">3.2. Direct Relative Velocity Feedback</a></li>
+<li><a href="#orge25231e">3.1. Integral Force Feedback</a></li>
+<li><a href="#org66ad123">3.2. Direct Relative Velocity Feedback</a></li>
 </ul>
 </li>
-<li><a href="#orgca70c79">4. HAC-LAC Architectures (link)</a>
+<li><a href="#orgf83465a">4. HAC-LAC Architectures (link)</a>
 <ul>
-<li><a href="#orgd9c84f0">4.1. HAC-LAC using IFF and Tracking control in the frame of the Legs</a></li>
-<li><a href="#orgeb80da1">4.2. HAC-LAC using IFF and Tracking control in the Cartesian frame</a></li>
-<li><a href="#org8b2b21e">4.3. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the task space</a></li>
-<li><a href="#org1c04b26">4.4. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</a></li>
-<li><a href="#org83b9480">4.5. HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the task space</a></li>
-<li><a href="#orgdbdd7d4">4.6. HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</a></li>
+<li><a href="#org3a2dfa2">4.1. HAC-LAC using IFF and Tracking control in the frame of the Legs</a></li>
+<li><a href="#org27fd54b">4.2. HAC-LAC using IFF and Tracking control in the Cartesian frame</a></li>
+<li><a href="#org8454531">4.3. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the task space</a></li>
+<li><a href="#org89a2695">4.4. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</a></li>
+<li><a href="#orgac21cc9">4.5. HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the task space</a></li>
+<li><a href="#org6676bde">4.6. HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</a></li>
 </ul>
 </li>
-<li><a href="#orgab73896">5. Cascade Architectures (link)</a>
+<li><a href="#orge5dd5fd">5. Cascade Architectures (link)</a>
 <ul>
-<li><a href="#org3e5154f">5.1. Cascade Control with HAC-LAC Inner Loop and Primary Controller in the task space</a></li>
-<li><a href="#org4353aca">5.2. Cascade Control with HAC-LAC Inner Loop and Primary Controller in the joint space</a></li>
+<li><a href="#org9b331a4">5.1. Cascade Control with HAC-LAC Inner Loop and Primary Controller in the task space</a></li>
+<li><a href="#org2f8d9f9">5.2. Cascade Control with HAC-LAC Inner Loop and Primary Controller in the joint space</a></li>
 </ul>
 </li>
-<li><a href="#org4ac6d11">6. Force Control (link)</a></li>
-<li><a href="#org5840a0b">7. Other Control Architectures</a>
+<li><a href="#org3a980c5">6. Force Control (link)</a></li>
+<li><a href="#org73661f1">7. Other Control Architectures</a>
 <ul>
-<li><a href="#org5be51f2">7.1. Control to force the nano-hexapod to not do any vertical rotation</a></li>
+<li><a href="#org26f61ba">7.1. Control to force the nano-hexapod to not do any vertical rotation</a></li>
 </ul>
 </li>
 </ul>
@@ -75,7 +79,7 @@
 </div>
 
 <p>
-The system consist of the following inputs and outputs (Figure <a href="#org2d9f6d0">1</a>):
+The system consist of the following inputs and outputs (Figure <a href="#org37cd4b0">1</a>):
 </p>
 <ul class="org-ul">
 <li>\(\bm{\tau}\): Forces applied in each leg</li>
@@ -85,7 +89,7 @@ The system consist of the following inputs and outputs (Figure <a href="#org2d9f
 </ul>
 
 
-<div id="org2d9f6d0" class="figure">
+<div id="org37cd4b0" class="figure">
 <p><img src="figs/control_architecture_plant.png" alt="control_architecture_plant.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Block diagram with the inputs and outputs of the system</p>
@@ -94,7 +98,7 @@ The system consist of the following inputs and outputs (Figure <a href="#org2d9f
 <p>
 In order to position the Sample with respect to the granite, we must use the measurement \(\bm{\mathcal{X}}\) in the control loop.
 The wanted position of the sample with respect to the granite is represented by \(\bm{r}_\mathcal{X}\).
-From \(\bm{r}_\mathcal{X}\) and \(\bm{\mathcal{X}}\), we can compute the required small change of pose of the nano-hexapod&rsquo;s top platform expressed in the frame of the nano-hexapod&rsquo;s base as shown in Figure <a href="#orgc4acef7">2</a>.
+From \(\bm{r}_\mathcal{X}\) and \(\bm{\mathcal{X}}\), we can compute the required small change of pose of the nano-hexapod&rsquo;s top platform expressed in the frame of the nano-hexapod&rsquo;s base as shown in Figure <a href="#orgb843e60">2</a>.
 </p>
 
 <p>
@@ -106,7 +110,7 @@ This can we considered as:
 </ul>
 
 
-<div id="orgc4acef7" class="figure">
+<div id="orgb843e60" class="figure">
 <p><img src="figs/control_architecture_pos_error.png" alt="control_architecture_pos_error.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Block diagram corresponding to the computation of the position error in the frame of the nano-hexapod</p>
@@ -116,15 +120,15 @@ This can we considered as:
 In this document, we see how the different outputs of the system can be used to control of position \(\bm{\mathcal{X}}\).
 </p>
 
-<div id="outline-container-org15699e9" class="outline-2">
-<h2 id="org15699e9"><span class="section-number-2">1</span> Control Configuration - Introduction</h2>
+<div id="outline-container-org25c471e" class="outline-2">
+<h2 id="org25c471e"><span class="section-number-2">1</span> Control Configuration - Introduction</h2>
 <div class="outline-text-2" id="text-1">
 <p>
 In this section, we discuss the control configuration for the NASS.
 </p>
 
 <p>
-From <a class='org-ref-reference' href="#skogestad07_multiv_feedb_contr">skogestad07_multiv_feedb_contr</a>:
+From (<a href="#citeproc_bib_item_2">Skogestad and Postlethwaite 2007</a>):
 </p>
 <blockquote>
 <p>
@@ -149,24 +153,24 @@ Decoupling elements will be used to convert quantities from the joint space to t
 </p>
 
 <p>
-Decentralized controllers will be largely used both for Tracking control (Section <a href="#org251e3c9">2</a>) and for Active Damping techniques (Section <a href="#org1b3cc21">3</a>)
+Decentralized controllers will be largely used both for Tracking control (Section <a href="#orga1c5122">2</a>) and for Active Damping techniques (Section <a href="#orgaf5a850">3</a>)
 </p>
 
 <p>
-Combining both can be done in an HAC-LAC topology presented in Section <a href="#org31fa800">4</a>.
+Combining both can be done in an HAC-LAC topology presented in Section <a href="#org4b1b4af">4</a>.
 </p>
 
 <p>
-The use of decentralized controllers is proposed in Section <a href="#orga038762">5</a>.
+The use of decentralized controllers is proposed in Section <a href="#org697801a">5</a>.
 </p>
 </div>
 </div>
 
-<div id="outline-container-org2be3166" class="outline-2">
-<h2 id="org2be3166"><span class="section-number-2">2</span> Tracking Control in the Frame of the Nano-Hexapod - Basic Architectures</h2>
+<div id="outline-container-orgcd0731f" class="outline-2">
+<h2 id="orgcd0731f"><span class="section-number-2">2</span> Tracking Control in the Frame of the Nano-Hexapod - Basic Architectures</h2>
 <div class="outline-text-2" id="text-2">
 <p>
-<a id="org251e3c9"></a>
+<a id="orga1c5122"></a>
 </p>
 <p>
 In this section, we suppose that we want to track some reference position \(\bm{r}_{\mathcal{X}_n}\) corresponding to the pose of the nano-hexapod&rsquo;s mobile platform with respect to its fixed base.
@@ -184,11 +188,11 @@ However, thanks to the forward and inverse kinematics, the controller can either
 These to configuration are described in the next two sections.
 </p>
 </div>
-<div id="outline-container-org970ab39" class="outline-3">
-<h3 id="org970ab39"><span class="section-number-3">2.1</span> Control in the frame of the Legs</h3>
+<div id="outline-container-orgbc69eea" class="outline-3">
+<h3 id="orgbc69eea"><span class="section-number-3">2.1</span> Control in the frame of the Legs</h3>
 <div class="outline-text-3" id="text-2-1">
 <p>
-<a id="org8583193"></a>
+<a id="org92ab294"></a>
 </p>
 
 <p>
@@ -198,7 +202,7 @@ Finally, a diagonal (Decentralized) controller \(\bm{K}_\mathcal{L}\) can be use
 </p>
 
 
-<div id="org3211e10" class="figure">
+<div id="org6c88afe" class="figure">
 <p><img src="figs/control_architecture_leg_frame.png" alt="control_architecture_leg_frame.png" />
 </p>
 <p><span class="figure-number">Figure 3: </span>Control in the frame of the legs</p>
@@ -206,11 +210,11 @@ Finally, a diagonal (Decentralized) controller \(\bm{K}_\mathcal{L}\) can be use
 </div>
 </div>
 
-<div id="outline-container-org82193fb" class="outline-3">
-<h3 id="org82193fb"><span class="section-number-3">2.2</span> Control in the Cartesian frame</h3>
+<div id="outline-container-org65bc213" class="outline-3">
+<h3 id="org65bc213"><span class="section-number-3">2.2</span> Control in the Cartesian frame</h3>
 <div class="outline-text-3" id="text-2-2">
 <p>
-<a id="orgbd7e263"></a>
+<a id="orgd4d12e5"></a>
 </p>
 
 <p>
@@ -221,7 +225,7 @@ These forces are then converted to forces applied in each of the nano-hexapod&rs
 </p>
 
 
-<div id="org81b6823" class="figure">
+<div id="orga34a56c" class="figure">
 <p><img src="figs/control_architecture_cartesian_frame.png" alt="control_architecture_cartesian_frame.png" />
 </p>
 <p><span class="figure-number">Figure 4: </span>Control in the cartesian Frame (rotating frame attached to the nano-hexapod&rsquo;s base)</p>
@@ -230,14 +234,14 @@ These forces are then converted to forces applied in each of the nano-hexapod&rs
 </div>
 </div>
 
-<div id="outline-container-org7d7b7f4" class="outline-2">
-<h2 id="org7d7b7f4"><span class="section-number-2">3</span> Active Damping Architecture - Collocated Control (<a href="control_active_damping.html">link</a>)</h2>
+<div id="outline-container-org9ef6b25" class="outline-2">
+<h2 id="org9ef6b25"><span class="section-number-2">3</span> Active Damping Architecture - Collocated Control (<a href="control_active_damping.html">link</a>)</h2>
 <div class="outline-text-2" id="text-3">
 <p>
-<a id="org1b3cc21"></a>
+<a id="orgaf5a850"></a>
 </p>
 <p>
-From <a class='org-ref-reference' href="#preumont18_vibrat_contr_activ_struc_fourt_edition">preumont18_vibrat_contr_activ_struc_fourt_edition</a>:
+From (<a href="#citeproc_bib_item_1">Preumont 2018</a>):
 </p>
 <blockquote>
 <p>
@@ -258,11 +262,11 @@ These two active damping techniques are collocated control techniques.
 The active damping techniques are studied in <a href="control_active_damping.html">this</a> document.
 </p>
 </div>
-<div id="outline-container-org3546873" class="outline-3">
-<h3 id="org3546873"><span class="section-number-3">3.1</span> Integral Force Feedback</h3>
+<div id="outline-container-orge25231e" class="outline-3">
+<h3 id="orge25231e"><span class="section-number-3">3.1</span> Integral Force Feedback</h3>
 <div class="outline-text-3" id="text-3-1">
 <p>
-<a id="orgb398117"></a>
+<a id="org71c8197"></a>
 </p>
 
 <p>
@@ -286,7 +290,7 @@ A lead-lag can also be used instead of a pure integrator.
 </p>
 
 
-<div id="org19b5f2d" class="figure">
+<div id="orga842725" class="figure">
 <p><img src="figs/control_architecture_iff.png" alt="control_architecture_iff.png" />
 </p>
 <p><span class="figure-number">Figure 5: </span>Integral Force Feedback</p>
@@ -294,11 +298,11 @@ A lead-lag can also be used instead of a pure integrator.
 </div>
 </div>
 
-<div id="outline-container-org722b371" class="outline-3">
-<h3 id="org722b371"><span class="section-number-3">3.2</span> Direct Relative Velocity Feedback</h3>
+<div id="outline-container-org66ad123" class="outline-3">
+<h3 id="org66ad123"><span class="section-number-3">3.2</span> Direct Relative Velocity Feedback</h3>
 <div class="outline-text-3" id="text-3-2">
 <p>
-<a id="orgfaf575b"></a>
+<a id="org4acc137"></a>
 </p>
 
 <p>
@@ -315,7 +319,7 @@ Each diagonal element consists of:
 \end{equation}
 
 
-<div id="org402f972" class="figure">
+<div id="org76615cc" class="figure">
 <p><img src="figs/control_architecture_dvf.png" alt="control_architecture_dvf.png" />
 </p>
 <p><span class="figure-number">Figure 6: </span>Direct Velocity Feedback</p>
@@ -324,11 +328,11 @@ Each diagonal element consists of:
 </div>
 </div>
 
-<div id="outline-container-orgca70c79" class="outline-2">
-<h2 id="orgca70c79"><span class="section-number-2">4</span> HAC-LAC Architectures (<a href="control_hac_lac.html">link</a>)</h2>
+<div id="outline-container-orgf83465a" class="outline-2">
+<h2 id="orgf83465a"><span class="section-number-2">4</span> HAC-LAC Architectures (<a href="control_hac_lac.html">link</a>)</h2>
 <div class="outline-text-2" id="text-4">
 <p>
-<a id="org31fa800"></a>
+<a id="org4b1b4af"></a>
 </p>
 <p>
 Here we can combine Active Damping Techniques (Low authority control) with a tracking controller (high authority control).
@@ -336,11 +340,11 @@ Usually, the low authority controller is designed first, and the high authority
 </p>
 
 <p>
-From <a class='org-ref-reference' href="#preumont18_vibrat_contr_activ_struc_fourt_edition">preumont18_vibrat_contr_activ_struc_fourt_edition</a>:
+From (<a href="#citeproc_bib_item_1">Preumont 2018</a>):
 </p>
 <blockquote>
 <p>
-The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure <a href="#org1b2c5c7">7</a>.
+The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure <a href="#orgfe203dc">7</a>.
 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:
 </p>
@@ -352,29 +356,29 @@ This approach has the following advantages:
 </blockquote>
 
 
-<div id="org1b2c5c7" class="figure">
+<div id="orgfe203dc" class="figure">
 <p><img src="figs/control_architecture_hac_lac.png" alt="control_architecture_hac_lac.png" />
 </p>
 <p><span class="figure-number">Figure 7: </span>HAC-LAC Control Architecture</p>
 </div>
 
 <p>
-If there is only one input to the system, the HAC-LAC topology can be represented as depicted in Figure <a href="#org91828a2">8</a>.
+If there is only one input to the system, the HAC-LAC topology can be represented as depicted in Figure <a href="#org8e5c9da">8</a>.
 Usually, the Low Authority Controller is first design, and then the High Authority Controller is designed based on the damped plant.
 </p>
 
 
-<div id="org91828a2" class="figure">
+<div id="org8e5c9da" class="figure">
 <p><img src="figs/control_architecture_hac_lac_one_input.png" alt="control_architecture_hac_lac_one_input.png" />
 </p>
 <p><span class="figure-number">Figure 8: </span>HAC-LAC Architecture with a system having only one input</p>
 </div>
 </div>
-<div id="outline-container-orgd9c84f0" class="outline-3">
-<h3 id="orgd9c84f0"><span class="section-number-3">4.1</span> HAC-LAC using IFF and Tracking control in the frame of the Legs</h3>
+<div id="outline-container-org3a2dfa2" class="outline-3">
+<h3 id="org3a2dfa2"><span class="section-number-3">4.1</span> HAC-LAC using IFF and Tracking control in the frame of the Legs</h3>
 <div class="outline-text-3" id="text-4-1">
 
-<div id="orgd235561" class="figure">
+<div id="org259b2b4" class="figure">
 <p><img src="figs/control_architecture_hac_iff_L.png" alt="control_architecture_hac_iff_L.png" />
 </p>
 <p><span class="figure-number">Figure 9: </span>IFF + Control in the frame of the legs</p>
@@ -382,11 +386,11 @@ Usually, the Low Authority Controller is first design, and then the High Authori
 </div>
 </div>
 
-<div id="outline-container-orgeb80da1" class="outline-3">
-<h3 id="orgeb80da1"><span class="section-number-3">4.2</span> HAC-LAC using IFF and Tracking control in the Cartesian frame</h3>
+<div id="outline-container-org27fd54b" class="outline-3">
+<h3 id="org27fd54b"><span class="section-number-3">4.2</span> HAC-LAC using IFF and Tracking control in the Cartesian frame</h3>
 <div class="outline-text-3" id="text-4-2">
 
-<div id="orgb89bca0" class="figure">
+<div id="org0bde593" class="figure">
 <p><img src="figs/control_architecture_hac_iff_X.png" alt="control_architecture_hac_iff_X.png" />
 </p>
 <p><span class="figure-number">Figure 10: </span>IFF + Control in the cartesian frame</p>
@@ -394,44 +398,44 @@ Usually, the Low Authority Controller is first design, and then the High Authori
 </div>
 </div>
 
-<div id="outline-container-org8b2b21e" class="outline-3">
-<h3 id="org8b2b21e"><span class="section-number-3">4.3</span> HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the task space</h3>
+<div id="outline-container-org8454531" class="outline-3">
+<h3 id="org8454531"><span class="section-number-3">4.3</span> HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the task space</h3>
 <div class="outline-text-3" id="text-4-3">
 
-<div class="figure">
+<div id="orgd88bdcb" class="figure">
 <p><img src="figs/control_architecture_hac_iff_pos_X.png" alt="control_architecture_hac_iff_pos_X.png" />
 </p>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org1c04b26" class="outline-3">
-<h3 id="org1c04b26"><span class="section-number-3">4.4</span> HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</h3>
+<div id="outline-container-org89a2695" class="outline-3">
+<h3 id="org89a2695"><span class="section-number-3">4.4</span> HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</h3>
 <div class="outline-text-3" id="text-4-4">
 
-<div class="figure">
+<div id="orgc4e63e2" class="figure">
 <p><img src="figs/control_architecture_hac_iff_pos_L.png" alt="control_architecture_hac_iff_pos_L.png" />
 </p>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org83b9480" class="outline-3">
-<h3 id="org83b9480"><span class="section-number-3">4.5</span> HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the task space</h3>
+<div id="outline-container-orgac21cc9" class="outline-3">
+<h3 id="orgac21cc9"><span class="section-number-3">4.5</span> HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the task space</h3>
 <div class="outline-text-3" id="text-4-5">
 
-<div class="figure">
+<div id="org4e63dc4" class="figure">
 <p><img src="figs/control_architecture_hac_dvf_pos_X.png" alt="control_architecture_hac_dvf_pos_X.png" />
 </p>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgdbdd7d4" class="outline-3">
-<h3 id="orgdbdd7d4"><span class="section-number-3">4.6</span> HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</h3>
+<div id="outline-container-org6676bde" class="outline-3">
+<h3 id="org6676bde"><span class="section-number-3">4.6</span> HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</h3>
 <div class="outline-text-3" id="text-4-6">
 
-<div class="figure">
+<div id="org2cc76e1" class="figure">
 <p><img src="figs/control_architecture_hac_dvf_pos_L.png" alt="control_architecture_hac_dvf_pos_L.png" />
 </p>
 </div>
@@ -439,26 +443,26 @@ Usually, the Low Authority Controller is first design, and then the High Authori
 </div>
 </div>
 
-<div id="outline-container-orgab73896" class="outline-2">
-<h2 id="orgab73896"><span class="section-number-2">5</span> Cascade Architectures (<a href="control_cascade.html">link</a>)</h2>
+<div id="outline-container-orge5dd5fd" class="outline-2">
+<h2 id="orge5dd5fd"><span class="section-number-2">5</span> Cascade Architectures (<a href="control_cascade.html">link</a>)</h2>
 <div class="outline-text-2" id="text-5">
 <p>
-<a id="orga038762"></a>
+<a id="org697801a"></a>
 </p>
 <p>
-The principle of Cascade control is shown in Figure <a href="#org03ef231">15</a> and explained as follow:
+The principle of Cascade control is shown in Figure <a href="#org8e45511">15</a> and explained as follow:
 </p>
 <blockquote>
 <p>
 To follow <b>two objectives</b> with different properties in one control system, usually a <b>hierarchy</b> of two feedback loops is used in practice.
 This kind of control topology is called <b>cascade control</b>, which is used when there are <b>several measurements and one prime control variable</b>.
-Cascade control is implemented by <b>nesting</b> the control loops, as shown in Figure <a href="#org03ef231">15</a>.
-The output control loop is called the <b>primary loop</b>, while the inner loop is called the secondary loop and is used to fulfill a secondary objective in the closed-loop system. &#x2013; <a class='org-ref-reference' href="#taghirad13_paral">taghirad13_paral</a>
+Cascade control is implemented by <b>nesting</b> the control loops, as shown in Figure <a href="#org8e45511">15</a>.
+The output control loop is called the <b>primary loop</b>, while the inner loop is called the secondary loop and is used to fulfill a secondary objective in the closed-loop system. &#x2013; (<a href="#citeproc_bib_item_3">Taghirad 2013</a>)
 </p>
 </blockquote>
 
 
-<div id="org03ef231" class="figure">
+<div id="org8e45511" class="figure">
 <p><img src="figs/control_architecture_cascade_control.png" alt="control_architecture_cascade_control.png" />
 </p>
 <p><span class="figure-number">Figure 15: </span>Cascade Control Architecture</p>
@@ -479,11 +483,11 @@ In the NASS&rsquo;s case:
 The inner loop can be composed of the system controlled with the HAC-LAC topology.
 </p>
 </div>
-<div id="outline-container-org3e5154f" class="outline-3">
-<h3 id="org3e5154f"><span class="section-number-3">5.1</span> Cascade Control with HAC-LAC Inner Loop and Primary Controller in the task space</h3>
+<div id="outline-container-org9b331a4" class="outline-3">
+<h3 id="org9b331a4"><span class="section-number-3">5.1</span> Cascade Control with HAC-LAC Inner Loop and Primary Controller in the task space</h3>
 <div class="outline-text-3" id="text-5-1">
 
-<div id="orgff7dfc6" class="figure">
+<div id="orge54ab8a" class="figure">
 <p><img src="figs/control_architecture_cascade_L.png" alt="control_architecture_cascade_L.png" />
 </p>
 <p><span class="figure-number">Figure 16: </span>Cascaded Control consisting of (from inner to outer loop): IFF, Linearization Loop, Tracking Control in the frame of the Legs</p>
@@ -491,11 +495,11 @@ The inner loop can be composed of the system controlled with the HAC-LAC topolog
 </div>
 </div>
 
-<div id="outline-container-org4353aca" class="outline-3">
-<h3 id="org4353aca"><span class="section-number-3">5.2</span> Cascade Control with HAC-LAC Inner Loop and Primary Controller in the joint space</h3>
+<div id="outline-container-org2f8d9f9" class="outline-3">
+<h3 id="org2f8d9f9"><span class="section-number-3">5.2</span> Cascade Control with HAC-LAC Inner Loop and Primary Controller in the joint space</h3>
 <div class="outline-text-3" id="text-5-2">
 
-<div id="org4bc4c4c" class="figure">
+<div id="orgdb3211a" class="figure">
 <p><img src="figs/control_architecture_cascade_X.png" alt="control_architecture_cascade_X.png" />
 </p>
 <p><span class="figure-number">Figure 17: </span>Cascaded Control consisting of (from inner to outer loop): IFF, Linearization Loop, Tracking Control in the Cartesian Frame</p>
@@ -504,8 +508,8 @@ The inner loop can be composed of the system controlled with the HAC-LAC topolog
 </div>
 </div>
 
-<div id="outline-container-org4ac6d11" class="outline-2">
-<h2 id="org4ac6d11"><span class="section-number-2">6</span> Force Control (<a href="control_force.html">link</a>)</h2>
+<div id="outline-container-org3a980c5" class="outline-2">
+<h2 id="org3a980c5"><span class="section-number-2">6</span> Force Control (<a href="control_force.html">link</a>)</h2>
 <div class="outline-text-2" id="text-6">
 <p>
 Signals:
@@ -517,41 +521,41 @@ Signals:
 </ul>
 
 
-<div class="figure">
+<div id="org17f57fd" class="figure">
 <p><img src="figs/control_architecture_force.png" alt="control_architecture_force.png" />
 </p>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org5840a0b" class="outline-2">
-<h2 id="org5840a0b"><span class="section-number-2">7</span> Other Control Architectures</h2>
+<div id="outline-container-org73661f1" class="outline-2">
+<h2 id="org73661f1"><span class="section-number-2">7</span> Other Control Architectures</h2>
 <div class="outline-text-2" id="text-7">
 </div>
-<div id="outline-container-org5be51f2" class="outline-3">
-<h3 id="org5be51f2"><span class="section-number-3">7.1</span> Control to force the nano-hexapod to not do any vertical rotation</h3>
+<div id="outline-container-org26f61ba" class="outline-3">
+<h3 id="org26f61ba"><span class="section-number-3">7.1</span> Control to force the nano-hexapod to not do any vertical rotation</h3>
 <div class="outline-text-3" id="text-7-1">
 <p>
 As the sample rotation around the vertical axis is not measure, the best we can do with the nano-hexapod is to not rotate around this same axis.
 </p>
 
 <p>
-One way to do it is shown in Figure <a href="#orga8781eb">19</a>.
+One way to do it is shown in Figure <a href="#org6559cc5">19</a>.
 </p>
 
 <p>
-The controller \(\bm{K}_{R_z}\) is decomposed as shown in Figure <a href="#org2f0522c">20</a>.
+The controller \(\bm{K}_{R_z}\) is decomposed as shown in Figure <a href="#org1d551e2">20</a>.
 </p>
 
 
-<div id="orga8781eb" class="figure">
+<div id="org6559cc5" class="figure">
 <p><img src="figs/control_architecture_fixed_rz.png" alt="control_architecture_fixed_rz.png" />
 </p>
 <p><span class="figure-number">Figure 19: </span>Figure caption</p>
 </div>
 
 
-<div id="org2f0522c" class="figure">
+<div id="org1d551e2" class="figure">
 <p><img src="figs/control_architecture_fixed_Krz.png" alt="control_architecture_fixed_Krz.png" />
 </p>
 <p><span class="figure-number">Figure 20: </span>Figure caption</p>
@@ -563,16 +567,18 @@ The controller \(\bm{K}_{R_z}\) is decomposed as shown in Figure <a href="#org2f
 
 <p>
 
-<h1 class='org-ref-bib-h1'>Bibliography</h1>
-<ul class='org-ref-bib'><li><a id="skogestad07_multiv_feedb_contr">[skogestad07_multiv_feedb_contr]</a> <a name="skogestad07_multiv_feedb_contr"></a>Skogestad & Postlethwaite, Multivariable Feedback Control: Analysis and Design, John Wiley (2007).</li>
-<li><a id="preumont18_vibrat_contr_activ_struc_fourt_edition">[preumont18_vibrat_contr_activ_struc_fourt_edition]</a> <a name="preumont18_vibrat_contr_activ_struc_fourt_edition"></a>Andre Preumont, Vibration Control of Active Structures - Fourth Edition, Springer International Publishing (2018).</li>
-<li><a id="taghirad13_paral">[taghirad13_paral]</a> <a name="taghirad13_paral"></a>Taghirad, Parallel robots : mechanics and control, CRC Press (2013).</li>
-</ul>
 </p>
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
+<div class="csl-bib-body">
+  <div class="csl-entry"><a name="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. <a href="https://doi.org/10.1007/978-3-319-72296-2">https://doi.org/10.1007/978-3-319-72296-2</a>.</div>
+  <div class="csl-entry"><a name="citeproc_bib_item_2"></a>Skogestad, Sigurd, and Ian Postlethwaite. 2007. <i>Multivariable Feedback Control: Analysis and Design</i>. John Wiley.</div>
+  <div class="csl-entry"><a name="citeproc_bib_item_3"></a>Taghirad, Hamid. 2013. <i>Parallel Robots : Mechanics and Control</i>. Boca Raton, FL: CRC Press.</div>
+</div>
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-04-17 ven. 09:35</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>

docs/control_cascade.html

@@ -1,75 +1,79 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
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- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Cascade Control applied on the Simscape Model</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org143e6e7">1. Initialization</a></li>
-<li><a href="#orga3bd04c">2. Low Authority Control - Integral Force Feedback \(\bm{K}_\text{IFF}\)</a>
+<li><a href="#org61c020f">1. Initialization</a></li>
+<li><a href="#orgabcff63">2. Low Authority Control - Integral Force Feedback \(\bm{K}_\text{IFF}\)</a>
 <ul>
-<li><a href="#org702c612">2.1. Identification</a></li>
-<li><a href="#org1eda739">2.2. Plant</a></li>
-<li><a href="#orgf33a40f">2.3. Root Locus</a></li>
-<li><a href="#orgd895b21">2.4. Controller and Loop Gain</a></li>
+<li><a href="#org340d5c4">2.1. Identification</a></li>
+<li><a href="#orga3a6bfe">2.2. Plant</a></li>
+<li><a href="#org08443b2">2.3. Root Locus</a></li>
+<li><a href="#orgfcc764a">2.4. Controller and Loop Gain</a></li>
 </ul>
 </li>
-<li><a href="#org101bfbc">3. High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</a>
+<li><a href="#org5f8f119">3. High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</a>
 <ul>
-<li><a href="#org259240d">3.1. Identification of the damped plant</a></li>
-<li><a href="#orgfc86b4c">3.2. Obtained Plant</a></li>
-<li><a href="#orgdea5e17">3.3. Controller Design and Loop Gain</a></li>
+<li><a href="#org4c8cb18">3.1. Identification of the damped plant</a></li>
+<li><a href="#org8ad1542">3.2. Obtained Plant</a></li>
+<li><a href="#orge39ae16">3.3. Controller Design and Loop Gain</a></li>
 </ul>
 </li>
-<li><a href="#org58f9f32">4. Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</a>
+<li><a href="#org11a22c2">4. Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</a>
 <ul>
-<li><a href="#org82ca884">4.1. Identification of the linearized plant</a></li>
-<li><a href="#org6f5b22e">4.2. Obtained Plant</a></li>
-<li><a href="#org839cdb3">4.3. Controller Design</a></li>
+<li><a href="#orgfc45f6f">4.1. Identification of the linearized plant</a></li>
+<li><a href="#org170c73f">4.2. Obtained Plant</a></li>
+<li><a href="#orge97b630">4.3. Controller Design</a></li>
 </ul>
 </li>
-<li><a href="#org3300911">5. Simulation</a></li>
-<li><a href="#org2943496">6. Results</a></li>
+<li><a href="#org07fbc52">5. Simulation</a></li>
+<li><a href="#org3e9cd70">6. Results</a></li>
 </ul>
 </div>
 </div>
 
 <p>
-The control architecture we wish here to study is shown in Figure <a href="#org19741db">1</a>.
+The control architecture we wish here to study is shown in Figure <a href="#orga0c68cb">1</a>.
 </p>
 
 
-<div id="org19741db" class="figure">
+<div id="orga0c68cb" class="figure">
 <p><img src="figs/cascade_control_architecture.png" alt="cascade_control_architecture.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Cascaded Control consisting of (from inner to outer loop): IFF, Linearization Loop, Tracking Control in the frame of the Legs</p>
@@ -79,28 +83,28 @@ The control architecture we wish here to study is shown in Figure <a href="#org1
 This cascade control is designed in three steps:
 </p>
 <ul class="org-ul">
-<li>In section <a href="#orga20c211">2</a>: an active damping controller is designed.
+<li>In section <a href="#orgbc2e2fd">2</a>: an active damping controller is designed.
 This is based on the Integral Force Feedback and applied in a decentralized way</li>
-<li>In section <a href="#org9367d49">3</a>: a decentralized tracking control is designed in the frame of the legs.
+<li>In section <a href="#orgd16580b">3</a>: a decentralized tracking control is designed in the frame of the legs.
 This controller is based on the displacement of each of the legs</li>
-<li>In section <a href="#orgdd883a0">4</a>: a controller is designed in the task space in order to follow the wanted reference path corresponding to the sample position with respect to the granite</li>
+<li>In section <a href="#org20bc645">4</a>: a controller is designed in the task space in order to follow the wanted reference path corresponding to the sample position with respect to the granite</li>
 </ul>
 
-<div id="outline-container-org143e6e7" class="outline-2">
-<h2 id="org143e6e7"><span class="section-number-2">1</span> Initialization</h2>
+<div id="outline-container-org61c020f" class="outline-2">
+<h2 id="org61c020f"><span class="section-number-2">1</span> Initialization</h2>
 <div class="outline-text-2" id="text-1">
 <p>
 We initialize all the stages with the default parameters.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
 </pre>
 </div>
 
@@ -108,8 +112,8 @@ initializeMirror();
 The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
-initializeSample(<span class="org-string">'mass'</span>, 1);
+<pre class="src src-matlab">  initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
+  initializeSample(<span class="org-string">'mass'</span>, 1);
 </pre>
 </div>
 
@@ -117,12 +121,12 @@ initializeSample(<span class="org-string">'mass'</span>, 1);
 We set the references that corresponds to a tomography experiment.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances();
+<pre class="src src-matlab">  initializeDisturbances();
 </pre>
 </div>
 
@@ -130,7 +134,7 @@ We set the references that corresponds to a tomography experiment.
 Open Loop.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'cascade-hac-lac'</span>);
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'cascade-hac-lac'</span>);
 </pre>
 </div>
 
@@ -138,7 +142,7 @@ Open Loop.
 And we put some gravity.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
+<pre class="src src-matlab">  initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
 </pre>
 </div>
 
@@ -146,55 +150,55 @@ And we put some gravity.
 We log the signals.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
+<pre class="src src-matlab">  initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">Kp = tf(zeros(6));
-Kl = tf(zeros(6));
-Kiff = tf(zeros(6));
+<pre class="src src-matlab">  Kp = tf(zeros(6));
+  Kl = tf(zeros(6));
+  Kiff = tf(zeros(6));
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orga3bd04c" class="outline-2">
-<h2 id="orga3bd04c"><span class="section-number-2">2</span> Low Authority Control - Integral Force Feedback \(\bm{K}_\text{IFF}\)</h2>
+<div id="outline-container-orgabcff63" class="outline-2">
+<h2 id="orgabcff63"><span class="section-number-2">2</span> Low Authority Control - Integral Force Feedback \(\bm{K}_\text{IFF}\)</h2>
 <div class="outline-text-2" id="text-2">
 <p>
-<a id="orga20c211"></a>
+<a id="orgbc2e2fd"></a>
 </p>
 </div>
-<div id="outline-container-org702c612" class="outline-3">
-<h3 id="org702c612"><span class="section-number-3">2.1</span> Identification</h3>
+<div id="outline-container-org340d5c4" class="outline-3">
+<h3 id="org340d5c4"><span class="section-number-3">2.1</span> Identification</h3>
 <div class="outline-text-3" id="text-2-1">
 <p>
 Let&rsquo;s first identify the plant for the IFF controller.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
-mdl = <span class="org-string">'nass_model'</span>;
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
-clear io; io_i = 1;
-io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],    1, <span class="org-string">'openinput'</span>);               io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
-io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Fnlm'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors</span>
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],    1, <span class="org-string">'openinput'</span>);               io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Fnlm'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors</span>
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
-G_iff = linearize(mdl, io, 0);
-G_iff.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
-G_iff.OutputName = {<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  G_iff = linearize(mdl, io, 0);
+  G_iff.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
+  G_iff.OutputName = {<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>};
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org1eda739" class="outline-3">
-<h3 id="org1eda739"><span class="section-number-3">2.2</span> Plant</h3>
+<div id="outline-container-orga3a6bfe" class="outline-3">
+<h3 id="orga3a6bfe"><span class="section-number-3">2.2</span> Plant</h3>
 <div class="outline-text-3" id="text-2-2">
 
-<div id="org366ff26" class="figure">
+<div id="orgdfa60cc" class="figure">
 <p><img src="figs/cascade_iff_plant.png" alt="cascade_iff_plant.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>IFF Plant (<a href="./figs/cascade_iff_plant.png">png</a>, <a href="./figs/cascade_iff_plant.pdf">pdf</a>)</p>
@@ -202,11 +206,11 @@ G_iff.OutputName = {<span class="org-string">'Fnlm1'</span>, <span class="org-st
 </div>
 </div>
 
-<div id="outline-container-orgf33a40f" class="outline-3">
-<h3 id="orgf33a40f"><span class="section-number-3">2.3</span> Root Locus</h3>
+<div id="outline-container-org08443b2" class="outline-3">
+<h3 id="org08443b2"><span class="section-number-3">2.3</span> Root Locus</h3>
 <div class="outline-text-3" id="text-2-3">
 
-<div id="orgdf7a93e" class="figure">
+<div id="org6320a7a" class="figure">
 <p><img src="figs/cascade_iff_root_locus.png" alt="cascade_iff_root_locus.png" />
 </p>
 <p><span class="figure-number">Figure 3: </span>Root Locus for the IFF control (<a href="./figs/cascade_iff_root_locus.png">png</a>, <a href="./figs/cascade_iff_root_locus.pdf">pdf</a>)</p>
@@ -218,21 +222,21 @@ The maximum damping is obtained for a control gain of \(\approx 3000\).
 </div>
 </div>
 
-<div id="outline-container-orgd895b21" class="outline-3">
-<h3 id="orgd895b21"><span class="section-number-3">2.4</span> Controller and Loop Gain</h3>
+<div id="outline-container-orgfcc764a" class="outline-3">
+<h3 id="orgfcc764a"><span class="section-number-3">2.4</span> Controller and Loop Gain</h3>
 <div class="outline-text-3" id="text-2-4">
 <p>
 We create the \(6 \times 6\) diagonal Integral Force Feedback controller.
-The obtained loop gain is shown in Figure <a href="#org7aaed92">4</a>.
+The obtained loop gain is shown in Figure <a href="#org59e605f">4</a>.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50;
-Kiff = <span class="org-type">-</span>3000<span class="org-type">/</span>s<span class="org-type">*</span>eye(6);
+<pre class="src src-matlab">  w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50;
+  Kiff = <span class="org-type">-</span>3000<span class="org-type">/</span>s<span class="org-type">*</span>eye(6);
 </pre>
 </div>
 
 
-<div id="org7aaed92" class="figure">
+<div id="org59e605f" class="figure">
 <p><img src="figs/cascade_iff_loop_gain.png" alt="cascade_iff_loop_gain.png" />
 </p>
 <p><span class="figure-number">Figure 4: </span>Obtained Loop gain the IFF Control (<a href="./figs/cascade_iff_loop_gain.png">png</a>, <a href="./figs/cascade_iff_loop_gain.pdf">pdf</a>)</p>
@@ -241,32 +245,32 @@ Kiff = <span class="org-type">-</span>3000<span class="org-type">/</span>s<span
 </div>
 </div>
 
-<div id="outline-container-org101bfbc" class="outline-2">
-<h2 id="org101bfbc"><span class="section-number-2">3</span> High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</h2>
+<div id="outline-container-org5f8f119" class="outline-2">
+<h2 id="org5f8f119"><span class="section-number-2">3</span> High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</h2>
 <div class="outline-text-2" id="text-3">
 <p>
-<a id="org9367d49"></a>
+<a id="orgd16580b"></a>
 </p>
 </div>
-<div id="outline-container-org259240d" class="outline-3">
-<h3 id="org259240d"><span class="section-number-3">3.1</span> Identification of the damped plant</h3>
+<div id="outline-container-org4c8cb18" class="outline-3">
+<h3 id="org4c8cb18"><span class="section-number-3">3.1</span> Identification of the damped plant</h3>
 <div class="outline-text-3" id="text-3-1">
 <p>
-We now identify the transfer function from \(\tau^\prime\) to \(d\bm{\mathcal{L}}\) as shown in Figure <a href="#org19741db">1</a>.
+We now identify the transfer function from \(\tau^\prime\) to \(d\bm{\mathcal{L}}\) as shown in Figure <a href="#orga0c68cb">1</a>.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
-mdl = <span class="org-string">'nass_model'</span>;
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
-clear io; io_i = 1;
-io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],    1, <span class="org-string">'input'</span>);               io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
-io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'output'</span>, [], <span class="org-string">'Dnlm'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg Displacement</span>
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],    1, <span class="org-string">'input'</span>);               io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'output'</span>, [], <span class="org-string">'Dnlm'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg Displacement</span>
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
-Gl = linearize(mdl, io, 0);
-Gl.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
-Gl.OutputName = {<span class="org-string">'Dnlm1'</span>, <span class="org-string">'Dnlm2'</span>, <span class="org-string">'Dnlm3'</span>, <span class="org-string">'Dnlm4'</span>, <span class="org-string">'Dnlm5'</span>, <span class="org-string">'Dnlm6'</span>};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  Gl = linearize(mdl, io, 0);
+  Gl.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
+  Gl.OutputName = {<span class="org-string">'Dnlm1'</span>, <span class="org-string">'Dnlm2'</span>, <span class="org-string">'Dnlm3'</span>, <span class="org-string">'Dnlm4'</span>, <span class="org-string">'Dnlm5'</span>, <span class="org-string">'Dnlm6'</span>};
 </pre>
 </div>
 
@@ -275,19 +279,19 @@ There are some unstable poles in the Plant with very small imaginary parts.
 These unstable poles are probably not physical, and they disappear when taking the minimum realization of the plant.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">isstable(Gl)
-Gl = minreal(Gl);
-isstable(Gl)
+<pre class="src src-matlab">  isstable(Gl)
+  Gl = minreal(Gl);
+  isstable(Gl)
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgfc86b4c" class="outline-3">
-<h3 id="orgfc86b4c"><span class="section-number-3">3.2</span> Obtained Plant</h3>
+<div id="outline-container-org8ad1542" class="outline-3">
+<h3 id="org8ad1542"><span class="section-number-3">3.2</span> Obtained Plant</h3>
 <div class="outline-text-3" id="text-3-2">
 <p>
-The obtain plant is shown in Figure <a href="#org455eb07">5</a>.
+The obtain plant is shown in Figure <a href="#org5030d6d">5</a>.
 </p>
 
 <p>
@@ -295,7 +299,7 @@ We can see that the plant is quite well decoupled.
 </p>
 
 
-<div id="org455eb07" class="figure">
+<div id="org5030d6d" class="figure">
 <p><img src="figs/cascade_hac_joint_plant.png" alt="cascade_hac_joint_plant.png" />
 </p>
 <p><span class="figure-number">Figure 5: </span>Plant for the High Authority Control in the Joint Space (<a href="./figs/cascade_hac_joint_plant.png">png</a>, <a href="./figs/cascade_hac_joint_plant.pdf">pdf</a>)</p>
@@ -304,8 +308,8 @@ We can see that the plant is quite well decoupled.
 </div>
 
 
-<div id="outline-container-orgdea5e17" class="outline-3">
-<h3 id="orgdea5e17"><span class="section-number-3">3.3</span> Controller Design and Loop Gain</h3>
+<div id="outline-container-orge39ae16" class="outline-3">
+<h3 id="orge39ae16"><span class="section-number-3">3.3</span> Controller Design and Loop Gain</h3>
 <div class="outline-text-3" id="text-3-3">
 <p>
 The controller consists of:
@@ -318,20 +322,20 @@ The controller consists of:
 </ul>
 
 <div class="org-src-container">
-<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>400; <span class="org-comment">% Bandwidth Bandwidth [rad/s]</span>
+<pre class="src src-matlab">  wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>400; <span class="org-comment">% Bandwidth Bandwidth [rad/s]</span>
 
-h = 2; <span class="org-comment">% Lead parameter</span>
+  h = 2; <span class="org-comment">% Lead parameter</span>
 
-<span class="org-comment">% Kl = (1/h) * (1 + s/wc*h)/(1 + s/wc/h) * wc/s * ((s/wc*2 + 1)/(s/wc*2)) * (1/(1 + s/wc/2));</span>
-Kl = (1<span class="org-type">/</span>h) <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> (1<span class="org-type">/</span>h) <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> wc<span class="org-type">/</span>s;
+  <span class="org-comment">% Kl = (1/h) * (1 + s/wc*h)/(1 + s/wc/h) * wc/s * ((s/wc*2 + 1)/(s/wc*2)) * (1/(1 + s/wc/2));</span>
+  Kl = (1<span class="org-type">/</span>h) <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> (1<span class="org-type">/</span>h) <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> wc<span class="org-type">/</span>s;
 
-<span class="org-comment">% Normalization of the gain of have a loop gain of 1 at frequency wc</span>
-Kl = Kl<span class="org-type">.*</span>diag(1<span class="org-type">./</span>diag(abs(freqresp(Gl<span class="org-type">*</span>Kl, wc))));
+  <span class="org-comment">% Normalization of the gain of have a loop gain of 1 at frequency wc</span>
+  Kl = Kl<span class="org-type">.*</span>diag(1<span class="org-type">./</span>diag(abs(freqresp(Gl<span class="org-type">*</span>Kl, wc))));
 </pre>
 </div>
 
 
-<div id="org3dd0142" class="figure">
+<div id="org3b106c4" class="figure">
 <p><img src="figs/cascade_hac_joint_loop_gain.png" alt="cascade_hac_joint_loop_gain.png" />
 </p>
 <p><span class="figure-number">Figure 6: </span>Loop Gain for the High Autority Control in the joint space (<a href="./figs/cascade_hac_joint_loop_gain.png">png</a>, <a href="./figs/cascade_hac_joint_loop_gain.pdf">pdf</a>)</p>
@@ -340,32 +344,32 @@ Kl = Kl<span class="org-type">.*</span>diag(1<span class="org-type">./</span>dia
 </div>
 </div>
 
-<div id="outline-container-org58f9f32" class="outline-2">
-<h2 id="org58f9f32"><span class="section-number-2">4</span> Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</h2>
+<div id="outline-container-org11a22c2" class="outline-2">
+<h2 id="org11a22c2"><span class="section-number-2">4</span> Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</h2>
 <div class="outline-text-2" id="text-4">
 <p>
-<a id="orgdd883a0"></a>
+<a id="org20bc645"></a>
 </p>
 </div>
-<div id="outline-container-org82ca884" class="outline-3">
-<h3 id="org82ca884"><span class="section-number-3">4.1</span> Identification of the linearized plant</h3>
+<div id="outline-container-orgfc45f6f" class="outline-3">
+<h3 id="orgfc45f6f"><span class="section-number-3">4.1</span> Identification of the linearized plant</h3>
 <div class="outline-text-3" id="text-4-1">
 <p>
 We know identify the dynamics between \(\bm{r}_{\mathcal{X}_n}\) and \(\bm{r}_\mathcal{X}\).
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
-mdl = <span class="org-string">'nass_model'</span>;
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
-clear io; io_i = 1;
-io(io_i) = linio([mdl, <span class="org-string">'/Controller/Cascade-HAC-LAC/Kp'</span>],  1, <span class="org-string">'input'</span>); io_i = io_i <span class="org-type">+</span> 1;
-io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'output'</span>, [], <span class="org-string">'En'</span>);      io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position Errror</span>
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller/Cascade-HAC-LAC/Kp'</span>],  1, <span class="org-string">'input'</span>); io_i = io_i <span class="org-type">+</span> 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'output'</span>, [], <span class="org-string">'En'</span>);      io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position Errror</span>
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
-Gx = linearize(mdl, io, 0);
-Gx.InputName  = {<span class="org-string">'rL1'</span>, <span class="org-string">'rL2'</span>, <span class="org-string">'rL3'</span>, <span class="org-string">'rL4'</span>, <span class="org-string">'rL5'</span>, <span class="org-string">'rL6'</span>};
-Gx.OutputName = {<span class="org-string">'Ex'</span>, <span class="org-string">'Ey'</span>, <span class="org-string">'Ez'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  Gx = linearize(mdl, io, 0);
+  Gx.InputName  = {<span class="org-string">'rL1'</span>, <span class="org-string">'rL2'</span>, <span class="org-string">'rL3'</span>, <span class="org-string">'rL4'</span>, <span class="org-string">'rL5'</span>, <span class="org-string">'rL6'</span>};
+  Gx.OutputName = {<span class="org-string">'Ex'</span>, <span class="org-string">'Ey'</span>, <span class="org-string">'Ez'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
 </pre>
 </div>
 
@@ -373,19 +377,19 @@ Gx.OutputName = {<span class="org-string">'Ex'</span>, <span class="org-string">
 As before, we take the minimum realization.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">isstable(Gx)
-Gx = minreal(Gx);
-isstable(Gx)
+<pre class="src src-matlab">  isstable(Gx)
+  Gx = minreal(Gx);
+  isstable(Gx)
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org6f5b22e" class="outline-3">
-<h3 id="org6f5b22e"><span class="section-number-3">4.2</span> Obtained Plant</h3>
+<div id="outline-container-org170c73f" class="outline-3">
+<h3 id="org170c73f"><span class="section-number-3">4.2</span> Obtained Plant</h3>
 <div class="outline-text-3" id="text-4-2">
 
-<div id="orge364e46" class="figure">
+<div id="org9c2e85a" class="figure">
 <p><img src="figs/cascade_primary_plant.png" alt="cascade_primary_plant.png" />
 </p>
 <p><span class="figure-number">Figure 7: </span>Plant for the Primary Controller (<a href="./figs/cascade_primary_plant.png">png</a>, <a href="./figs/cascade_primary_plant.pdf">pdf</a>)</p>
@@ -393,23 +397,23 @@ isstable(Gx)
 </div>
 </div>
 
-<div id="outline-container-org839cdb3" class="outline-3">
-<h3 id="org839cdb3"><span class="section-number-3">4.3</span> Controller Design</h3>
+<div id="outline-container-orge97b630" class="outline-3">
+<h3 id="orge97b630"><span class="section-number-3">4.3</span> Controller Design</h3>
 <div class="outline-text-3" id="text-4-3">
 <div class="org-src-container">
-<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>10; <span class="org-comment">% Bandwidth Bandwidth [rad/s]</span>
+<pre class="src src-matlab">  wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>10; <span class="org-comment">% Bandwidth Bandwidth [rad/s]</span>
 
-h = 2; <span class="org-comment">% Lead parameter</span>
+  h = 2; <span class="org-comment">% Lead parameter</span>
 
-Kp = (1<span class="org-type">/</span>h) <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> wc<span class="org-type">/</span>s <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>5)<span class="org-type">/</span>s <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>20);
+  Kp = (1<span class="org-type">/</span>h) <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> wc<span class="org-type">/</span>s <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>5)<span class="org-type">/</span>s <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>20);
 
-<span class="org-comment">% Normalization of the gain of have a loop gain of 1 at frequency wc</span>
-Kp = Kp<span class="org-type">.*</span>diag(1<span class="org-type">./</span>diag(abs(freqresp(Gx<span class="org-type">*</span>Kp, wc))));
+  <span class="org-comment">% Normalization of the gain of have a loop gain of 1 at frequency wc</span>
+  Kp = Kp<span class="org-type">.*</span>diag(1<span class="org-type">./</span>diag(abs(freqresp(Gx<span class="org-type">*</span>Kp, wc))));
 </pre>
 </div>
 
 
-<div id="orgb9d3971" class="figure">
+<div id="org37a2534" class="figure">
 <p><img src="figs/cascade_primary_loop_gain.png" alt="cascade_primary_loop_gain.png" />
 </p>
 <p><span class="figure-number">Figure 8: </span>Loop Gain for the primary controller (outer loop) (<a href="./figs/cascade_primary_loop_gain.png">png</a>, <a href="./figs/cascade_primary_loop_gain.pdf">pdf</a>)</p>
@@ -418,12 +422,12 @@ Kp = Kp<span class="org-type">.*</span>diag(1<span class="org-type">./</span>dia
 </div>
 </div>
 
-<div id="outline-container-org3300911" class="outline-2">
-<h2 id="org3300911"><span class="section-number-2">5</span> Simulation</h2>
+<div id="outline-container-org07fbc52" class="outline-2">
+<h2 id="org07fbc52"><span class="section-number-2">5</span> Simulation</h2>
 <div class="outline-text-2" id="text-5">
 <div class="org-src-container">
-<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
-<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
+<pre class="src src-matlab">  load(<span class="org-string">'mat/conf_simulink.mat'</span>);
+  <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
 </pre>
 </div>
 
@@ -431,58 +435,58 @@ Kp = Kp<span class="org-type">.*</span>diag(1<span class="org-type">./</span>dia
 And we simulate the system.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">cascade_hac_lac = simout;
-save(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="org-string">'cascade_hac_lac'</span>);
+<pre class="src src-matlab">  cascade_hac_lac = simout;
+  save(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="org-string">'cascade_hac_lac'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org2943496" class="outline-2">
-<h2 id="org2943496"><span class="section-number-2">6</span> Results</h2>
+<div id="outline-container-org3e9cd70" class="outline-2">
+<h2 id="org3e9cd70"><span class="section-number-2">6</span> Results</h2>
 <div class="outline-text-2" id="text-6">
 <div class="org-src-container">
-<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
-load(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="org-string">'cascade_hac_lac'</span>);
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
+  load(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="org-string">'cascade_hac_lac'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">n_av = 4;
-han_win = hanning(ceil(length(cascade_hac_lac.Em.En.Data(<span class="org-type">:</span>,1))<span class="org-type">/</span>n_av));
+<pre class="src src-matlab">  n_av = 4;
+  han_win = hanning(ceil(length(cascade_hac_lac.Em.En.Data(<span class="org-type">:</span>,1))<span class="org-type">/</span>n_av));
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">t = cascade_hac_lac.Em.En.Time;
-Ts = t(2)<span class="org-type">-</span>t(1);
+<pre class="src src-matlab">  t = cascade_hac_lac.Em.En.Time;
+  Ts = t(2)<span class="org-type">-</span>t(1);
 
-[pxx_ol, f] = pwelch(tomo_align_dist.Em.En.Data, han_win, [], [], 1<span class="org-type">/</span>Ts);
-[pxx_ca, <span class="org-type">~</span>] = pwelch(cascade_hac_lac.Em.En.Data, han_win, [], [], 1<span class="org-type">/</span>Ts);
+  [pxx_ol, f] = pwelch(tomo_align_dist.Em.En.Data, han_win, [], [], 1<span class="org-type">/</span>Ts);
+  [pxx_ca, <span class="org-type">~</span>] = pwelch(cascade_hac_lac.Em.En.Data, han_win, [], [], 1<span class="org-type">/</span>Ts);
 </pre>
 </div>
 
 
-<div id="org11aa945" class="figure">
+<div id="orgb068123" class="figure">
 <p><img src="figs/cascade_hac_lac_tomography_psd.png" alt="cascade_hac_lac_tomography_psd.png" />
 </p>
 <p><span class="figure-number">Figure 9: </span>ASD of the position error (<a href="./figs/cascade_hac_lac_tomography_psd.png">png</a>, <a href="./figs/cascade_hac_lac_tomography_psd.pdf">pdf</a>)</p>
 </div>
 
 
-<div id="org845b982" class="figure">
+<div id="orgb10044c" class="figure">
 <p><img src="figs/cascade_hac_lac_tomography_cas.png" alt="cascade_hac_lac_tomography_cas.png" />
 </p>
 <p><span class="figure-number">Figure 10: </span>Cumulative Amplitude Spectrum of the position error (<a href="./figs/cascade_hac_lac_tomography_cas.png">png</a>, <a href="./figs/cascade_hac_lac_tomography_cas.pdf">pdf</a>)</p>
 </div>
 
 
-<div id="org0151895" class="figure">
+<div id="orgd639abb" class="figure">
 <p><img src="figs/cascade_hac_lac_tomography.png" alt="cascade_hac_lac_tomography.png" />
 </p>
 <p><span class="figure-number">Figure 11: </span>Results of the Tomography Experiment (<a href="./figs/cascade_hac_lac_tomography.png">png</a>, <a href="./figs/cascade_hac_lac_tomography.pdf">pdf</a>)</p>
@@ -492,7 +496,7 @@ Ts = t(2)<span class="org-type">-</span>t(1);
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-04-17 ven. 09:35</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>

docs/control_decentralized.html

@@ -1,65 +1,69 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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+<!-- 2021-02-20 sam. 23:08 -->
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 <title>Control in the Frame of the Legs applied on the Simscape Model</title>
 <meta name="generator" content="Org mode" />
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 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Control in the Frame of the Legs applied on the Simscape Model</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org1f22cdb">1. Decentralized Control</a>
+<li><a href="#org1a08332">1. Decentralized Control</a>
 <ul>
-<li><a href="#org01937c0">1.1. Control Schematic</a></li>
-<li><a href="#orgc9e3b66">1.2. Initialize the Simscape Model</a></li>
-<li><a href="#org42afc36">1.3. Identification of the plant</a></li>
-<li><a href="#org871560e">1.4. Plant Analysis</a></li>
-<li><a href="#org296e3de">1.5. Controller Design</a></li>
-<li><a href="#orgb7afa1e">1.6. Simulation</a></li>
-<li><a href="#orgbb1dc16">1.7. Results</a></li>
+<li><a href="#org88b6ca3">1.1. Control Schematic</a></li>
+<li><a href="#org9041934">1.2. Initialize the Simscape Model</a></li>
+<li><a href="#org78bce32">1.3. Identification of the plant</a></li>
+<li><a href="#org3a56a98">1.4. Plant Analysis</a></li>
+<li><a href="#org36df689">1.5. Controller Design</a></li>
+<li><a href="#orgac5ea1c">1.6. Simulation</a></li>
+<li><a href="#orga044079">1.7. Results</a></li>
 </ul>
 </li>
-<li><a href="#orgfa4be92">2. HAC-LAC (IFF) Decentralized Control</a>
+<li><a href="#orgeeaa041">2. HAC-LAC (IFF) Decentralized Control</a>
 <ul>
-<li><a href="#orgbc4af09">2.1. Control Schematic</a></li>
-<li><a href="#org5ac6c37">2.2. Initialize the Simscape Model</a></li>
-<li><a href="#org0903106">2.3. Initialization</a></li>
-<li><a href="#orge739f61">2.4. Identification for IFF</a></li>
-<li><a href="#org08b6a99">2.5. Integral Force Feedback Controller</a></li>
-<li><a href="#org06b5c75">2.6. Identification of the damped plant</a></li>
-<li><a href="#org85a0730">2.7. Controller Design</a></li>
-<li><a href="#org58ffd80">2.8. Simulation</a></li>
-<li><a href="#orga01ccc6">2.9. Results</a></li>
+<li><a href="#orge42dfda">2.1. Control Schematic</a></li>
+<li><a href="#org790d1db">2.2. Initialize the Simscape Model</a></li>
+<li><a href="#org110a4e9">2.3. Initialization</a></li>
+<li><a href="#org8f68ab2">2.4. Identification for IFF</a></li>
+<li><a href="#orgbe68cd0">2.5. Integral Force Feedback Controller</a></li>
+<li><a href="#orgca29231">2.6. Identification of the damped plant</a></li>
+<li><a href="#org95df29b">2.7. Controller Design</a></li>
+<li><a href="#org8b5710f">2.8. Simulation</a></li>
+<li><a href="#org791c2a5">2.9. Results</a></li>
 </ul>
 </li>
-<li><a href="#org21a9294">3. Conclusion</a></li>
+<li><a href="#orgf9b95b3">3. Conclusion</a></li>
 </ul>
 </div>
 </div>
@@ -68,15 +72,15 @@
 In this document, we apply some decentralized control to the NASS and see what level of performance can be obtained.
 </p>
 
-<div id="outline-container-org1f22cdb" class="outline-2">
-<h2 id="org1f22cdb"><span class="section-number-2">1</span> Decentralized Control</h2>
+<div id="outline-container-org1a08332" class="outline-2">
+<h2 id="org1a08332"><span class="section-number-2">1</span> Decentralized Control</h2>
 <div class="outline-text-2" id="text-1">
 </div>
-<div id="outline-container-org01937c0" class="outline-3">
-<h3 id="org01937c0"><span class="section-number-3">1.1</span> Control Schematic</h3>
+<div id="outline-container-org88b6ca3" class="outline-3">
+<h3 id="org88b6ca3"><span class="section-number-3">1.1</span> Control Schematic</h3>
 <div class="outline-text-3" id="text-1-1">
 <p>
-The control architecture is shown in Figure <a href="#org5b9133f">1</a>.
+The control architecture is shown in Figure <a href="#orgd4d73cb">1</a>.
 </p>
 
 <p>
@@ -92,7 +96,7 @@ The signals are:
 </ul>
 
 
-<div id="org5b9133f" class="figure">
+<div id="orgd4d73cb" class="figure">
 <p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Decentralized control for reference tracking</p>
@@ -100,21 +104,21 @@ The signals are:
 </div>
 </div>
 
-<div id="outline-container-orgc9e3b66" class="outline-3">
-<h3 id="orgc9e3b66"><span class="section-number-3">1.2</span> Initialize the Simscape Model</h3>
+<div id="outline-container-org9041934" class="outline-3">
+<h3 id="org9041934"><span class="section-number-3">1.2</span> Initialize the Simscape Model</h3>
 <div class="outline-text-3" id="text-1-2">
 <p>
 We initialize all the stages with the default parameters.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
 </pre>
 </div>
 
@@ -122,8 +126,8 @@ initializeMirror();
 The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
-initializeSample(<span class="org-string">'mass'</span>, 1);
+<pre class="src src-matlab">  initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
+  initializeSample(<span class="org-string">'mass'</span>, 1);
 </pre>
 </div>
 
@@ -131,12 +135,12 @@ initializeSample(<span class="org-string">'mass'</span>, 1);
 We set the references that corresponds to a tomography experiment.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances();
+<pre class="src src-matlab">  initializeDisturbances();
 </pre>
 </div>
 
@@ -144,8 +148,8 @@ We set the references that corresponds to a tomography experiment.
 Open Loop.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
-Kl = tf(zeros(6));
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
+  Kl = tf(zeros(6));
 </pre>
 </div>
 
@@ -153,7 +157,7 @@ Kl = tf(zeros(6));
 And we put some gravity.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
+<pre class="src src-matlab">  initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
 </pre>
 </div>
 
@@ -161,41 +165,41 @@ And we put some gravity.
 We log the signals.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
+<pre class="src src-matlab">  initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org42afc36" class="outline-3">
-<h3 id="org42afc36"><span class="section-number-3">1.3</span> Identification of the plant</h3>
+<div id="outline-container-org78bce32" class="outline-3">
+<h3 id="org78bce32"><span class="section-number-3">1.3</span> Identification of the plant</h3>
 <div class="outline-text-3" id="text-1-3">
 <p>
 Let&rsquo;s identify the transfer function from \(\bm{\tau}\) to \(\bm{\mathcal{L}}\).
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
-mdl = <span class="org-string">'nass_model'</span>;
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
-clear io; io_i = 1;
-io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],                          1, <span class="org-string">'openinput'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
-io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],                          1, <span class="org-string">'openinput'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
-G = linearize(mdl, io, 0);
-G.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
-G.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  G = linearize(mdl, io, 0);
+  G.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
+  G.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org871560e" class="outline-3">
-<h3 id="org871560e"><span class="section-number-3">1.4</span> Plant Analysis</h3>
+<div id="outline-container-org3a56a98" class="outline-3">
+<h3 id="org3a56a98"><span class="section-number-3">1.4</span> Plant Analysis</h3>
 <div class="outline-text-3" id="text-1-4">
 <p>
-The diagonal and off-diagonal terms of the plant are shown in Figure <a href="#org68ea839">2</a>.
+The diagonal and off-diagonal terms of the plant are shown in Figure <a href="#orgbc5977b">2</a>.
 </p>
 
 <p>
@@ -207,7 +211,7 @@ We can see that:
 </ul>
 
 
-<div id="org68ea839" class="figure">
+<div id="orgbc5977b" class="figure">
 <p><img src="figs/decentralized_control_plant_L.png" alt="decentralized_control_plant_L.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Transfer Functions from forces applied in each actuator \(\tau_i\) to the relative motion of each leg \(d\mathcal{L}_i\) (<a href="./figs/decentralized_control_plant_L.png">png</a>, <a href="./figs/decentralized_control_plant_L.pdf">pdf</a>)</p>
@@ -215,8 +219,8 @@ We can see that:
 </div>
 </div>
 
-<div id="outline-container-org296e3de" class="outline-3">
-<h3 id="org296e3de"><span class="section-number-3">1.5</span> Controller Design</h3>
+<div id="outline-container-org36df689" class="outline-3">
+<h3 id="org36df689"><span class="section-number-3">1.5</span> Controller Design</h3>
 <div class="outline-text-3" id="text-1-5">
 <p>
 The controller consists of:
@@ -229,14 +233,14 @@ The controller consists of:
 </ul>
 
 <p>
-The obtained loop gains corresponding to the diagonal elements are shown in Figure <a href="#org3bd29d4">3</a>.
+The obtained loop gains corresponding to the diagonal elements are shown in Figure <a href="#org0e9c3e8">3</a>.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20;
-h = 1.5;
+<pre class="src src-matlab">  wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>20;
+  h = 1.5;
 
-Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span class="org-type">*</span> ...
+  Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span class="org-type">*</span> ...
        wc<span class="org-type">/</span>s <span class="org-type">*</span> ...<span class="org-comment"> % Pure Integrator</span>
        ((s<span class="org-type">/</span>wc<span class="org-type">*</span>2 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>wc<span class="org-type">*</span>2)) <span class="org-type">*</span> ...<span class="org-comment"> % Integrator up to wc/2</span>
        1<span class="org-type">/</span>h <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> ...<span class="org-comment"> % Lead</span>
@@ -246,7 +250,7 @@ Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span cla
 </div>
 
 
-<div id="org3bd29d4" class="figure">
+<div id="org0e9c3e8" class="figure">
 <p><img src="figs/decentralized_control_L_loop_gain.png" alt="decentralized_control_L_loop_gain.png" />
 </p>
 <p><span class="figure-number">Figure 3: </span>Obtained Loop Gain (<a href="./figs/decentralized_control_L_loop_gain.png">png</a>, <a href="./figs/decentralized_control_L_loop_gain.pdf">pdf</a>)</p>
@@ -256,54 +260,54 @@ Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(G, wc)))) <span cla
 We add a minus sign to the controller as it is not included in the Simscape model.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">Kl = <span class="org-type">-</span>Kl;
+<pre class="src src-matlab">  Kl = <span class="org-type">-</span>Kl;
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgb7afa1e" class="outline-3">
-<h3 id="orgb7afa1e"><span class="section-number-3">1.6</span> Simulation</h3>
+<div id="outline-container-orgac5ea1c" class="outline-3">
+<h3 id="orgac5ea1c"><span class="section-number-3">1.6</span> Simulation</h3>
 <div class="outline-text-3" id="text-1-6">
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
-<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
+<pre class="src src-matlab">  load(<span class="org-string">'mat/conf_simulink.mat'</span>);
+  <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">decentralized_L = simout;
-save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>, <span class="org-string">'-append'</span>);
+<pre class="src src-matlab">  decentralized_L = simout;
+  save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgbb1dc16" class="outline-3">
-<h3 id="orgbb1dc16"><span class="section-number-3">1.7</span> Results</h3>
+<div id="outline-container-orga044079" class="outline-3">
+<h3 id="orga044079"><span class="section-number-3">1.7</span> Results</h3>
 <div class="outline-text-3" id="text-1-7">
 <p>
-The reference path and the position of the mobile platform are shown in Figure <a href="#org247b3a0">4</a>.
+The reference path and the position of the mobile platform are shown in Figure <a href="#org5b1621d">4</a>.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
-load(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>);
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
+  load(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_L'</span>);
 </pre>
 </div>
 
 
-<div id="org247b3a0" class="figure">
+<div id="org5b1621d" class="figure">
 <p><img src="figs/decentralized_L_position_errors.png" alt="decentralized_L_position_errors.png" />
 </p>
 <p><span class="figure-number">Figure 4: </span>Position Errors when using the Decentralized Control Architecture (<a href="./figs/decentralized_L_position_errors.png">png</a>, <a href="./figs/decentralized_L_position_errors.pdf">pdf</a>)</p>
@@ -312,19 +316,19 @@ load(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span cl
 </div>
 </div>
 
-<div id="outline-container-orgfa4be92" class="outline-2">
-<h2 id="orgfa4be92"><span class="section-number-2">2</span> HAC-LAC (IFF) Decentralized Control</h2>
+<div id="outline-container-orgeeaa041" class="outline-2">
+<h2 id="orgeeaa041"><span class="section-number-2">2</span> HAC-LAC (IFF) Decentralized Control</h2>
 <div class="outline-text-2" id="text-2">
 <p>
 We here add an Active Damping Loop (Integral Force Feedback) prior to using the Decentralized control architecture using \(\bm{\mathcal{L}}\).
 </p>
 </div>
 
-<div id="outline-container-orgbc4af09" class="outline-3">
-<h3 id="orgbc4af09"><span class="section-number-3">2.1</span> Control Schematic</h3>
+<div id="outline-container-orge42dfda" class="outline-3">
+<h3 id="orge42dfda"><span class="section-number-3">2.1</span> Control Schematic</h3>
 <div class="outline-text-3" id="text-2-1">
 <p>
-The control architecture is shown in Figure <a href="#org5b9133f">1</a>.
+The control architecture is shown in Figure <a href="#orgd4d73cb">1</a>.
 </p>
 
 <p>
@@ -340,7 +344,7 @@ The signals are:
 </ul>
 
 
-<div id="org657383b" class="figure">
+<div id="org9b33c60" class="figure">
 <p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" />
 </p>
 <p><span class="figure-number">Figure 5: </span>Decentralized control for reference tracking</p>
@@ -348,21 +352,21 @@ The signals are:
 </div>
 </div>
 
-<div id="outline-container-org5ac6c37" class="outline-3">
-<h3 id="org5ac6c37"><span class="section-number-3">2.2</span> Initialize the Simscape Model</h3>
+<div id="outline-container-org790d1db" class="outline-3">
+<h3 id="org790d1db"><span class="section-number-3">2.2</span> Initialize the Simscape Model</h3>
 <div class="outline-text-3" id="text-2-2">
 <p>
 We initialize all the stages with the default parameters.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
 </pre>
 </div>
 
@@ -370,8 +374,8 @@ initializeMirror();
 The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
-initializeSample(<span class="org-string">'mass'</span>, 1);
+<pre class="src src-matlab">  initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
+  initializeSample(<span class="org-string">'mass'</span>, 1);
 </pre>
 </div>
 
@@ -379,12 +383,12 @@ initializeSample(<span class="org-string">'mass'</span>, 1);
 We set the references that corresponds to a tomography experiment.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances();
+<pre class="src src-matlab">  initializeDisturbances();
 </pre>
 </div>
 
@@ -392,8 +396,8 @@ We set the references that corresponds to a tomography experiment.
 Open Loop.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
-Kl = tf(zeros(6));
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
+  Kl = tf(zeros(6));
 </pre>
 </div>
 
@@ -401,7 +405,7 @@ Kl = tf(zeros(6));
 And we put some gravity.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
+<pre class="src src-matlab">  initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
 </pre>
 </div>
 
@@ -409,90 +413,90 @@ And we put some gravity.
 We log the signals.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
+<pre class="src src-matlab">  initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org0903106" class="outline-3">
-<h3 id="org0903106"><span class="section-number-3">2.3</span> Initialization</h3>
+<div id="outline-container-org110a4e9" class="outline-3">
+<h3 id="org110a4e9"><span class="section-number-3">2.3</span> Initialization</h3>
 <div class="outline-text-3" id="text-2-3">
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
-K_iff = tf(zeros(6));
-Kl = tf(zeros(6));
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
+  K_iff = tf(zeros(6));
+  Kl = tf(zeros(6));
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orge739f61" class="outline-3">
-<h3 id="orge739f61"><span class="section-number-3">2.4</span> Identification for IFF</h3>
+<div id="outline-container-org8f68ab2" class="outline-3">
+<h3 id="org8f68ab2"><span class="section-number-3">2.4</span> Identification for IFF</h3>
 <div class="outline-text-3" id="text-2-4">
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
-mdl = <span class="org-string">'nass_model'</span>;
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
-clear io; io_i = 1;
-io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],                              1, <span class="org-string">'openinput'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
-io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Fnlm'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors</span>
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],                              1, <span class="org-string">'openinput'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Fnlm'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Force Sensors</span>
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
-G_iff = linearize(mdl, io, 0);
-G_iff.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
-G_iff.OutputName = {<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  G_iff = linearize(mdl, io, 0);
+  G_iff.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
+  G_iff.OutputName = {<span class="org-string">'Fnlm1'</span>, <span class="org-string">'Fnlm2'</span>, <span class="org-string">'Fnlm3'</span>, <span class="org-string">'Fnlm4'</span>, <span class="org-string">'Fnlm5'</span>, <span class="org-string">'Fnlm6'</span>};
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org08b6a99" class="outline-3">
-<h3 id="org08b6a99"><span class="section-number-3">2.5</span> Integral Force Feedback Controller</h3>
+<div id="outline-container-orgbe68cd0" class="outline-3">
+<h3 id="orgbe68cd0"><span class="section-number-3">2.5</span> Integral Force Feedback Controller</h3>
 <div class="outline-text-3" id="text-2-5">
 <div class="org-src-container">
-<pre class="src src-matlab">w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50;
-K_iff = <span class="org-type">-</span>5000<span class="org-type">/</span>s <span class="org-type">*</span> (s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>w0) <span class="org-type">*</span> eye(6);
+<pre class="src src-matlab">  w0 = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50;
+  K_iff = <span class="org-type">-</span>5000<span class="org-type">/</span>s <span class="org-type">*</span> (s<span class="org-type">/</span>w0)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>w0) <span class="org-type">*</span> eye(6);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">K_iff = <span class="org-type">-</span>K_iff;
+<pre class="src src-matlab">  K_iff = <span class="org-type">-</span>K_iff;
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org06b5c75" class="outline-3">
-<h3 id="org06b5c75"><span class="section-number-3">2.6</span> Identification of the damped plant</h3>
+<div id="outline-container-orgca29231" class="outline-3">
+<h3 id="orgca29231"><span class="section-number-3">2.6</span> Identification of the damped plant</h3>
 <div class="outline-text-3" id="text-2-6">
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink  DehaezeFile</span></span>
-mdl = <span class="org-string">'nass_model'</span>;
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink  DehaezeFile</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
-clear io; io_i = 1;
-io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],                              1, <span class="org-string">'input'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
-io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-IFF-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],                              1, <span class="org-string">'input'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller/Reference-Tracking-IFF-L/Sum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Leg length error</span>
 
-<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
-Gd = linearize(mdl, io, 0);
-Gd.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
-Gd.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  Gd = linearize(mdl, io, 0);
+  Gd.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
+  Gd.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string">'El2'</span>, <span class="org-string">'El3'</span>, <span class="org-string">'El4'</span>, <span class="org-string">'El5'</span>, <span class="org-string">'El6'</span>};
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org85a0730" class="outline-3">
-<h3 id="org85a0730"><span class="section-number-3">2.7</span> Controller Design</h3>
+<div id="outline-container-org95df29b" class="outline-3">
+<h3 id="org95df29b"><span class="section-number-3">2.7</span> Controller Design</h3>
 <div class="outline-text-3" id="text-2-7">
 <div class="org-src-container">
-<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
-h = 3;
+<pre class="src src-matlab">  wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
+  h = 3;
 
-Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gd, wc)))) <span class="org-type">*</span> ...
+  Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gd, wc)))) <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>20) <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>20))) <span class="org-type">*</span> ...<span class="org-comment"> % Pure Integrator</span>
        ((s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>50) <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>50))) <span class="org-type">*</span> ...<span class="org-comment"> % Integrator up to wc/2</span>
        1<span class="org-type">/</span>h <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> ...
@@ -502,56 +506,56 @@ Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gd, wc)))) <span cl
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">isstable(feedback(Gd<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
+<pre class="src src-matlab">  isstable(feedback(Gd<span class="org-type">*</span>Kl, eye(6), <span class="org-type">-</span>1))
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">Kl = <span class="org-type">-</span>Kl;
+<pre class="src src-matlab">  Kl = <span class="org-type">-</span>Kl;
 </pre>
 </div>
 </div>
 </div>
 
 
-<div id="outline-container-org58ffd80" class="outline-3">
-<h3 id="org58ffd80"><span class="section-number-3">2.8</span> Simulation</h3>
+<div id="outline-container-org8b5710f" class="outline-3">
+<h3 id="org8b5710f"><span class="section-number-3">2.8</span> Simulation</h3>
 <div class="outline-text-3" id="text-2-8">
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
-<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
+<pre class="src src-matlab">  load(<span class="org-string">'mat/conf_simulink.mat'</span>);
+  <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">decentralized_iff_L = simout;
-save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_iff_L'</span>, <span class="org-string">'-append'</span>);
+<pre class="src src-matlab">  decentralized_iff_L = simout;
+  save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span class="org-string">'decentralized_iff_L'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orga01ccc6" class="outline-3">
-<h3 id="orga01ccc6"><span class="section-number-3">2.9</span> Results</h3>
+<div id="outline-container-org791c2a5" class="outline-3">
+<h3 id="org791c2a5"><span class="section-number-3">2.9</span> Results</h3>
 </div>
 </div>
-<div id="outline-container-org21a9294" class="outline-2">
-<h2 id="org21a9294"><span class="section-number-2">3</span> Conclusion</h2>
+<div id="outline-container-orgf9b95b3" class="outline-2">
+<h2 id="orgf9b95b3"><span class="section-number-2">3</span> Conclusion</h2>
 </div>
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-04-17 ven. 09:35</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>

docs/control_force.html

@@ -1,34 +1,38 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "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. 09:35 -->
+<!-- 2021-02-20 sam. 23:08 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Force Control applied on the Simscape Model</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
-<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
-<script src="./js/jquery.min.js"></script>
-<script src="./js/bootstrap.min.js"></script>
-<script src="./js/jquery.stickytableheaders.min.js"></script>
-<script src="./js/readtheorg.js"></script>
-<script>MathJax = {
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
+<script>
+           MathJax = {
+             svg: {
+               scale: 1,
+               fontCache: "global"
+             },
              tex: {
-            tags: 'ams',
-            macros: {bm: ["\\boldsymbol{#1}",1],}
+               tags: "ams",
+               multlineWidth: "%MULTLINEWIDTH",
+               tagSide: "right",
+                       macros: {bm: ["\\boldsymbol{#1}",1],},
+               tagIndent: ".8em"
              }
            };
            </script>
-          <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+           <script id="MathJax-script" async
+             src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Force Control applied on the Simscape Model</h1>
 <p>
@@ -47,20 +51,20 @@ Ideas:
 </ul>
 
 
-<div class="figure">
+<div id="org517d735" class="figure">
 <p><img src="figs/control_cascade_force_F.png" alt="control_cascade_force_F.png" />
 </p>
 </div>
 
 
-<div class="figure">
+<div id="org05e43e1" class="figure">
 <p><img src="figs/control_cascade_force_tau.png" alt="control_cascade_force_tau.png" />
 </p>
 </div>
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-04-17 ven. 09:35</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>

docs/control_hac_lac.html

@@ -1,58 +1,62 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2020-05-05 mar. 10:34 -->
+<!-- 2021-02-20 sam. 23:08 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>HAC-LAC applied on the Simscape Model</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
-<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
-<script src="./js/jquery.min.js"></script>
-<script src="./js/bootstrap.min.js"></script>
-<script src="./js/jquery.stickytableheaders.min.js"></script>
-<script src="./js/readtheorg.js"></script>
-<script>MathJax = {
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
+<script>
+           MathJax = {
+             svg: {
+               scale: 1,
+               fontCache: "global"
+             },
              tex: {
-            tags: 'ams',
-            macros: {bm: ["\\boldsymbol{#1}",1],}
+               tags: "ams",
+               multlineWidth: "%MULTLINEWIDTH",
+               tagSide: "right",
+                       macros: {bm: ["\\boldsymbol{#1}",1],},
+               tagIndent: ".8em"
              }
            };
            </script>
-          <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+           <script id="MathJax-script" async
+             src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">HAC-LAC applied on the Simscape Model</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org1fe8594">1. Initialization</a></li>
-<li><a href="#orgfd54447">2. Low Authority Control - Direct Velocity Feedback \(\bm{K}_\mathcal{L}\)</a>
+<li><a href="#org689cb19">1. Initialization</a></li>
+<li><a href="#org24d1d7f">2. Low Authority Control - Direct Velocity Feedback \(\bm{K}_\mathcal{L}\)</a>
 <ul>
-<li><a href="#orga860160">2.1. Identification</a></li>
-<li><a href="#org7a2c131">2.2. Plant</a></li>
-<li><a href="#org46eb79b">2.3. Root Locus</a></li>
-<li><a href="#orgafbd7d0">2.4. Controller and Loop Gain</a></li>
+<li><a href="#org68cbbe7">2.1. Identification</a></li>
+<li><a href="#org7c1c629">2.2. Plant</a></li>
+<li><a href="#org719e252">2.3. Root Locus</a></li>
+<li><a href="#org2c42b90">2.4. Controller and Loop Gain</a></li>
 </ul>
 </li>
-<li><a href="#org73445c2">3. Uncertainty Improvements thanks to the LAC control</a></li>
-<li><a href="#orged12a17">4. High Authority Control - \(\bm{K}_\mathcal{X}\)</a>
+<li><a href="#org195a29c">3. Uncertainty Improvements thanks to the LAC control</a></li>
+<li><a href="#org81738ac">4. High Authority Control - \(\bm{K}_\mathcal{X}\)</a>
 <ul>
-<li><a href="#orgc22e2f2">4.1. Identification of the damped plant</a></li>
-<li><a href="#org6bca8e2">4.2. Controller Design</a></li>
+<li><a href="#org94cb2c9">4.1. Identification of the damped plant</a></li>
+<li><a href="#org2a269d5">4.2. Controller Design</a></li>
 </ul>
 </li>
-<li><a href="#orgb7ffa65">5. Simulation</a></li>
-<li><a href="#org448f335">6. Results</a></li>
+<li><a href="#org1171960">5. Simulation</a></li>
+<li><a href="#orgad3e1c7">6. Results</a></li>
 </ul>
 </div>
 </div>
@@ -66,27 +70,27 @@ It is then compare to the wanted position of the Sample \(\bm{r}_\mathcal{X}\) i
 </p>
 
 
-<div id="orgb987aa6" class="figure">
+<div id="org270f668" class="figure">
 <p><img src="figs/hac_lac_control_schematic.png" alt="hac_lac_control_schematic.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>HAC-LAC Control Architecture used for the Control of the NASS</p>
 </div>
 
-<div id="outline-container-org1fe8594" class="outline-2">
-<h2 id="org1fe8594"><span class="section-number-2">1</span> Initialization</h2>
+<div id="outline-container-org689cb19" class="outline-2">
+<h2 id="org689cb19"><span class="section-number-2">1</span> Initialization</h2>
 <div class="outline-text-2" id="text-1">
 <p>
 We initialize all the stages with the default parameters.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
 </pre>
 </div>
 
@@ -94,8 +98,8 @@ initializeMirror();
 The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeNanoHexapod('actuator', 'piezo');
-initializeSample('mass', 1);
+<pre class="src src-matlab">  initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
+  initializeSample(<span class="org-string">'mass'</span>, 1);
 </pre>
 </div>
 
@@ -103,12 +107,12 @@ initializeSample('mass', 1);
 We set the references that corresponds to a tomography experiment.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances();
+<pre class="src src-matlab">  initializeDisturbances();
 </pre>
 </div>
 
@@ -116,7 +120,7 @@ We set the references that corresponds to a tomography experiment.
 Open Loop.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController('type', 'open-loop');
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
 </pre>
 </div>
 
@@ -124,7 +128,7 @@ Open Loop.
 And we put some gravity.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeSimscapeConfiguration('gravity', true);
+<pre class="src src-matlab">  initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
 </pre>
 </div>
 
@@ -132,14 +136,14 @@ And we put some gravity.
 We log the signals.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeLoggingConfiguration('log', 'all');
+<pre class="src src-matlab">  initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgfd54447" class="outline-2">
-<h2 id="orgfd54447"><span class="section-number-2">2</span> Low Authority Control - Direct Velocity Feedback \(\bm{K}_\mathcal{L}\)</h2>
+<div id="outline-container-org24d1d7f" class="outline-2">
+<h2 id="org24d1d7f"><span class="section-number-2">2</span> Low Authority Control - Direct Velocity Feedback \(\bm{K}_\mathcal{L}\)</h2>
 <div class="outline-text-2" id="text-2">
 <p>
 The first loop closed corresponds to a direct velocity feedback loop.
@@ -150,106 +154,106 @@ The design of the associated decentralized controller is explained in <a href="c
 </p>
 </div>
 
-<div id="outline-container-orga860160" class="outline-3">
-<h3 id="orga860160"><span class="section-number-3">2.1</span> Identification</h3>
+<div id="outline-container-org68cbbe7" class="outline-3">
+<h3 id="org68cbbe7"><span class="section-number-3">2.1</span> Identification</h3>
 <div class="outline-text-3" id="text-2-1">
 <div class="org-src-container">
-<pre class="src src-matlab">%% Name of the Simulink File
-mdl = 'nass_model';
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-%% Input/Output definition
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Controller'],    1, 'openinput');               io_i = io_i + 1; % Actuator Inputs
-io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm');  io_i = io_i + 1; % Relative Motion Outputs
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],    1, <span class="org-string">'openinput'</span>);               io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station'</span>], 3, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'Dnlm'</span>);  io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Motion Outputs</span>
 
-%% Run the linearization
-G_dvf = linearize(mdl, io, 0);
-G_dvf.InputName  = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
-G_dvf.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  G_dvf = linearize(mdl, io, 0);
+  G_dvf.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
+  G_dvf.OutputName = {<span class="org-string">'Dnlm1'</span>, <span class="org-string">'Dnlm2'</span>, <span class="org-string">'Dnlm3'</span>, <span class="org-string">'Dnlm4'</span>, <span class="org-string">'Dnlm5'</span>, <span class="org-string">'Dnlm6'</span>};
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org7a2c131" class="outline-3">
-<h3 id="org7a2c131"><span class="section-number-3">2.2</span> Plant</h3>
+<div id="outline-container-org7c1c629" class="outline-3">
+<h3 id="org7c1c629"><span class="section-number-3">2.2</span> Plant</h3>
 </div>
-<div id="outline-container-org46eb79b" class="outline-3">
-<h3 id="org46eb79b"><span class="section-number-3">2.3</span> Root Locus</h3>
+<div id="outline-container-org719e252" class="outline-3">
+<h3 id="org719e252"><span class="section-number-3">2.3</span> Root Locus</h3>
 </div>
-<div id="outline-container-orgafbd7d0" class="outline-3">
-<h3 id="orgafbd7d0"><span class="section-number-3">2.4</span> Controller and Loop Gain</h3>
+<div id="outline-container-org2c42b90" class="outline-3">
+<h3 id="org2c42b90"><span class="section-number-3">2.4</span> Controller and Loop Gain</h3>
 <div class="outline-text-3" id="text-2-4">
 <div class="org-src-container">
-<pre class="src src-matlab">K_dvf = s*15000/(1 + s/2/pi/10000);
+<pre class="src src-matlab">  K_dvf = s<span class="org-type">*</span>15000<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>10000);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">K_dvf = -K_dvf*eye(6);
+<pre class="src src-matlab">  K_dvf = <span class="org-type">-</span>K_dvf<span class="org-type">*</span>eye(6);
 </pre>
 </div>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org73445c2" class="outline-2">
-<h2 id="org73445c2"><span class="section-number-2">3</span> Uncertainty Improvements thanks to the LAC control</h2>
+<div id="outline-container-org195a29c" class="outline-2">
+<h2 id="org195a29c"><span class="section-number-2">3</span> Uncertainty Improvements thanks to the LAC control</h2>
 <div class="outline-text-2" id="text-3">
 <div class="org-src-container">
-<pre class="src src-matlab">K_dvf_backup = K_dvf;
-initializeController('type', 'hac-dvf');
+<pre class="src src-matlab">  K_dvf_backup = K_dvf;
+  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-dvf'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">masses = [1, 10, 50]; % [kg]
+<pre class="src src-matlab">  masses = [1, 10, 50]; <span class="org-comment">% [kg]</span>
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">%% Name of the Simulink File
-mdl = 'nass_model';
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-%% Input/Output definition
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Controller'],     1, 'input');            io_i = io_i + 1; % Actuator Inputs
-io(io_i) = linio([mdl, '/Tracking Error'], 1, 'output', [], 'En'); io_i = io_i + 1; % Position Errror
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],     1, <span class="org-string">'input'</span>);            io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'output'</span>, [], <span class="org-string">'En'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position Errror</span>
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orged12a17" class="outline-2">
-<h2 id="orged12a17"><span class="section-number-2">4</span> High Authority Control - \(\bm{K}_\mathcal{X}\)</h2>
+<div id="outline-container-org81738ac" class="outline-2">
+<h2 id="org81738ac"><span class="section-number-2">4</span> High Authority Control - \(\bm{K}_\mathcal{X}\)</h2>
 <div class="outline-text-2" id="text-4">
 </div>
-<div id="outline-container-orgc22e2f2" class="outline-3">
-<h3 id="orgc22e2f2"><span class="section-number-3">4.1</span> Identification of the damped plant</h3>
+<div id="outline-container-org94cb2c9" class="outline-3">
+<h3 id="org94cb2c9"><span class="section-number-3">4.1</span> Identification of the damped plant</h3>
 <div class="outline-text-3" id="text-4-1">
 <div class="org-src-container">
-<pre class="src src-matlab">Kx = tf(zeros(6));
+<pre class="src src-matlab">  Kx = tf(zeros(6));
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController('type', 'hac-dvf');
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-dvf'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">%% Name of the Simulink File
-mdl = 'nass_model';
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-%% Input/Output definition
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Controller'],     1, 'input');            io_i = io_i + 1; % Actuator Inputs
-io(io_i) = linio([mdl, '/Tracking Error'], 1, 'output', [], 'En'); io_i = io_i + 1; % Position Errror
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>],     1, <span class="org-string">'input'</span>);            io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Inputs</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Tracking Error'</span>], 1, <span class="org-string">'output'</span>, [], <span class="org-string">'En'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position Errror</span>
 
-%% Run the linearization
-G = linearize(mdl, io, 0);
-G.InputName  = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'};
-G.OutputName = {'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
+  G = linearize(mdl, io, 0);
+  G.InputName  = {<span class="org-string">'Fnl1'</span>, <span class="org-string">'Fnl2'</span>, <span class="org-string">'Fnl3'</span>, <span class="org-string">'Fnl4'</span>, <span class="org-string">'Fnl5'</span>, <span class="org-string">'Fnl6'</span>};
+  G.OutputName = {<span class="org-string">'Ex'</span>, <span class="org-string">'Ey'</span>, <span class="org-string">'Ez'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
 </pre>
 </div>
 
@@ -257,17 +261,17 @@ G.OutputName = {'Ex', 'Ey', 'Ez', 'Erx', 'Ery', 'Erz'};
 The minus sine is put here because there is already a minus sign included due to the computation of the position error.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">load('mat/stages.mat', 'nano_hexapod');
+<pre class="src src-matlab">  load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
 
-Gx = -G*inv(nano_hexapod.kinematics.J');
-Gx.InputName  = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
+  Gx = <span class="org-type">-</span>G<span class="org-type">*</span>inv(nano_hexapod.kinematics.J<span class="org-type">'</span>);
+  Gx.InputName  = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org6bca8e2" class="outline-3">
-<h3 id="org6bca8e2"><span class="section-number-3">4.2</span> Controller Design</h3>
+<div id="outline-container-org2a269d5" class="outline-3">
+<h3 id="org2a269d5"><span class="section-number-3">4.2</span> Controller Design</h3>
 <div class="outline-text-3" id="text-4-2">
 <p>
 The controller consists of:
@@ -280,41 +284,41 @@ The controller consists of:
 </ul>
 
 <div class="org-src-container">
-<pre class="src src-matlab">wc = 2*pi*15; % Bandwidth Bandwidth [rad/s]
+<pre class="src src-matlab">  wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>15; <span class="org-comment">% Bandwidth Bandwidth [rad/s]</span>
 
-h = 1.5; % Lead parameter
+  h = 1.5; <span class="org-comment">% Lead parameter</span>
 
-Kx = (1/h) * (1 + s/wc*h)/(1 + s/wc/h) * wc/s * ((s/wc*2 + 1)/(s/wc*2)) * (1/(1 + s/wc/2));
+  Kx = (1<span class="org-type">/</span>h) <span class="org-type">*</span> (1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">*</span>h)<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>h) <span class="org-type">*</span> wc<span class="org-type">/</span>s <span class="org-type">*</span> ((s<span class="org-type">/</span>wc<span class="org-type">*</span>2 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>wc<span class="org-type">*</span>2)) <span class="org-type">*</span> (1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>wc<span class="org-type">/</span>2));
 
-% Normalization of the gain of have a loop gain of 1 at frequency wc
-Kx = Kx.*diag(1./diag(abs(freqresp(Gx*Kx, wc))));
+  <span class="org-comment">% Normalization of the gain of have a loop gain of 1 at frequency wc</span>
+  Kx = Kx<span class="org-type">.*</span>diag(1<span class="org-type">./</span>diag(abs(freqresp(Gx<span class="org-type">*</span>Kx, wc))));
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">isstable(feedback(Gx*Kx, eye(6), -1))
+<pre class="src src-matlab">  isstable(feedback(Gx<span class="org-type">*</span>Kx, eye(6), <span class="org-type">-</span>1))
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">Kx = inv(nano_hexapod.kinematics.J')*Kx;
+<pre class="src src-matlab">  Kx = inv(nano_hexapod.kinematics.J<span class="org-type">'</span>)<span class="org-type">*</span>Kx;
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">isstable(feedback(G*Kx, eye(6), 1))
+<pre class="src src-matlab">  isstable(feedback(G<span class="org-type">*</span>Kx, eye(6), 1))
 </pre>
 </div>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgb7ffa65" class="outline-2">
-<h2 id="orgb7ffa65"><span class="section-number-2">5</span> Simulation</h2>
+<div id="outline-container-org1171960" class="outline-2">
+<h2 id="org1171960"><span class="section-number-2">5</span> Simulation</h2>
 <div class="outline-text-2" id="text-5">
 <div class="org-src-container">
-<pre class="src src-matlab">load('mat/conf_simulink.mat');
-set_param(conf_simulink, 'StopTime', '2');
+<pre class="src src-matlab">  load(<span class="org-string">'mat/conf_simulink.mat'</span>);
+  <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
 </pre>
 </div>
 
@@ -322,27 +326,27 @@ set_param(conf_simulink, 'StopTime', '2');
 And we simulate the system.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">sim('nass_model');
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">hac_dvf = simout;
-save('./mat/tomo_exp_hac_lac.mat', 'hac_dvf');
+<pre class="src src-matlab">  hac_dvf = simout;
+  save(<span class="org-string">'./mat/tomo_exp_hac_lac.mat'</span>, <span class="org-string">'hac_dvf'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org448f335" class="outline-2">
-<h2 id="org448f335"><span class="section-number-2">6</span> Results</h2>
+<div id="outline-container-orgad3e1c7" class="outline-2">
+<h2 id="orgad3e1c7"><span class="section-number-2">6</span> Results</h2>
 <div class="outline-text-2" id="text-6">
 <p>
 Let&rsquo;s load the simulation when no control is applied.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_align_dist');
-load('./mat/tomo_exp_hac_lac.mat', 'hac_dvf');
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
+  load(<span class="org-string">'./mat/tomo_exp_hac_lac.mat'</span>, <span class="org-string">'hac_dvf'</span>);
 </pre>
 </div>
 </div>
@@ -350,7 +354,7 @@ load('./mat/tomo_exp_hac_lac.mat', 'hac_dvf');
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-05-05 mar. 10:34</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>

docs/control_virtual_mass.html

@@ -1,78 +1,82 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2020-05-05 mar. 10:34 -->
+<!-- 2021-02-20 sam. 23:09 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Decentralize control to add virtual mass</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
-<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
-<script src="./js/jquery.min.js"></script>
-<script src="./js/bootstrap.min.js"></script>
-<script src="./js/jquery.stickytableheaders.min.js"></script>
-<script src="./js/readtheorg.js"></script>
-<script>MathJax = {
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
+<script>
+           MathJax = {
+             svg: {
+               scale: 1,
+               fontCache: "global"
+             },
              tex: {
-            tags: 'ams',
-            macros: {bm: ["\\boldsymbol{#1}",1],}
+               tags: "ams",
+               multlineWidth: "%MULTLINEWIDTH",
+               tagSide: "right",
+                       macros: {bm: ["\\boldsymbol{#1}",1],},
+               tagIndent: ".8em"
              }
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            </script>
-          <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+           <script id="MathJax-script" async
+             src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Decentralize control to add virtual mass</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org982b263">1. Initialization</a></li>
-<li><a href="#org35a3822">2. Identification</a></li>
-<li><a href="#orgd6fc719">3. Adding Virtual Mass in the Leg&rsquo;s Space</a>
+<li><a href="#org48b52bd">1. Initialization</a></li>
+<li><a href="#org157dc5d">2. Identification</a></li>
+<li><a href="#orgd072386">3. Adding Virtual Mass in the Leg&rsquo;s Space</a>
 <ul>
-<li><a href="#orga27c9a0">3.1. Plant</a></li>
-<li><a href="#orgcbce41a">3.2. Controller Design</a></li>
-<li><a href="#orgca1f525">3.3. Identification of the Primary Plant</a></li>
+<li><a href="#org147b003">3.1. Plant</a></li>
+<li><a href="#orgacd4421">3.2. Controller Design</a></li>
+<li><a href="#org4c460cf">3.3. Identification of the Primary Plant</a></li>
 </ul>
 </li>
-<li><a href="#orgc9131d0">4. Adding Virtual Mass in the Task Space</a>
+<li><a href="#org3c74924">4. Adding Virtual Mass in the Task Space</a>
 <ul>
-<li><a href="#orgdbe6a25">4.1. Plant</a></li>
-<li><a href="#org571922f">4.2. Controller Design</a></li>
-<li><a href="#org4960701">4.3. Identification of the Primary Plant</a></li>
+<li><a href="#org3b61568">4.1. Plant</a></li>
+<li><a href="#orgf37b1c0">4.2. Controller Design</a></li>
+<li><a href="#orgcd22c9f">4.3. Identification of the Primary Plant</a></li>
 </ul>
 </li>
 </ul>
 </div>
 </div>
 
-<div id="outline-container-org982b263" class="outline-2">
-<h2 id="org982b263"><span class="section-number-2">1</span> Initialization</h2>
+<div id="outline-container-org48b52bd" class="outline-2">
+<h2 id="org48b52bd"><span class="section-number-2">1</span> Initialization</h2>
 <div class="outline-text-2" id="text-1">
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
 
-initializeSimscapeConfiguration();
-initializeDisturbances('enable', false);
-initializeLoggingConfiguration('log', 'none');
+  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>);
 
-initializeController('type', 'hac-dvf');
+  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-dvf'</span>);
 </pre>
 </div>
 
@@ -80,7 +84,7 @@ initializeController('type', 'hac-dvf');
 The nano-hexapod has the following leg&rsquo;s stiffness and damping.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeNanoHexapod('k', 1e5, 'c', 2e2);
+<pre class="src src-matlab">  initializeNanoHexapod(<span class="org-string">'k'</span>, 1e5, <span class="org-string">'c'</span>, 2e2);
 </pre>
 </div>
 
@@ -88,20 +92,20 @@ The nano-hexapod has the following leg&rsquo;s stiffness and damping.
 We set the stiffness of the payload fixation:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">Kp = 1e8; % [N/m]
+<pre class="src src-matlab">  Kp = 1e8; <span class="org-comment">% [N/m]</span>
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org35a3822" class="outline-2">
-<h2 id="org35a3822"><span class="section-number-2">2</span> Identification</h2>
+<div id="outline-container-org157dc5d" class="outline-2">
+<h2 id="org157dc5d"><span class="section-number-2">2</span> Identification</h2>
 <div class="outline-text-2" id="text-2">
 <p>
 We identify the system for the following payload masses:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">Ms = [1, 10, 50];
+<pre class="src src-matlab">  Ms = [1, 10, 50];
 </pre>
 </div>
 
@@ -111,15 +115,15 @@ Identification of the Primary plant without virtual add of mass
 </p>
 </div>
 </div>
-<div id="outline-container-orgd6fc719" class="outline-2">
-<h2 id="orgd6fc719"><span class="section-number-2">3</span> Adding Virtual Mass in the Leg&rsquo;s Space</h2>
+<div id="outline-container-orgd072386" class="outline-2">
+<h2 id="orgd072386"><span class="section-number-2">3</span> Adding Virtual Mass in the Leg&rsquo;s Space</h2>
 <div class="outline-text-2" id="text-3">
 </div>
-<div id="outline-container-orga27c9a0" class="outline-3">
-<h3 id="orga27c9a0"><span class="section-number-3">3.1</span> Plant</h3>
+<div id="outline-container-org147b003" class="outline-3">
+<h3 id="org147b003"><span class="section-number-3">3.1</span> Plant</h3>
 <div class="outline-text-3" id="text-3-1">
 
-<div id="org98e7ba8" class="figure">
+<div id="org74dce28" class="figure">
 <p><img src="figs/virtual_mass_plant_L.png" alt="virtual_mass_plant_L.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Transfer function from \(\tau_i\) to \(d\mathcal{L}_i\) for three payload masses</p>
@@ -127,16 +131,16 @@ Identification of the Primary plant without virtual add of mass
 </div>
 </div>
 
-<div id="outline-container-orgcbce41a" class="outline-3">
-<h3 id="orgcbce41a"><span class="section-number-3">3.2</span> Controller Design</h3>
+<div id="outline-container-orgacd4421" class="outline-3">
+<h3 id="orgacd4421"><span class="section-number-3">3.2</span> Controller Design</h3>
 <div class="outline-text-3" id="text-3-2">
 <div class="org-src-container">
-<pre class="src src-matlab">Kdvf = 10*s^2/(1+s/2/pi/500)^2*eye(6);
+<pre class="src src-matlab">  Kdvf = 10<span class="org-type">*</span>s<span class="org-type">^</span>2<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>500)<span class="org-type">^</span>2<span class="org-type">*</span>eye(6);
 </pre>
 </div>
 
 
-<div id="orgccb3b9e" class="figure">
+<div id="orgdf2df59" class="figure">
 <p><img src="figs/virtual_mass_loop_gain_L.png" alt="virtual_mass_loop_gain_L.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Loop Gain for the addition of virtual mass in the leg&rsquo;s space</p>
@@ -144,18 +148,18 @@ Identification of the Primary plant without virtual add of mass
 </div>
 </div>
 
-<div id="outline-container-orgca1f525" class="outline-3">
-<h3 id="orgca1f525"><span class="section-number-3">3.3</span> Identification of the Primary Plant</h3>
+<div id="outline-container-org4c460cf" class="outline-3">
+<h3 id="org4c460cf"><span class="section-number-3">3.3</span> Identification of the Primary Plant</h3>
 <div class="outline-text-3" id="text-3-3">
 
-<div id="orgd49505e" class="figure">
+<div id="org29e9333" class="figure">
 <p><img src="figs/virtual_mass_L_primary_plant_X.png" alt="virtual_mass_L_primary_plant_X.png" />
 </p>
 <p><span class="figure-number">Figure 3: </span>Comparison of the transfer function from \(\mathcal{F}_{x,y,z}\) to \(\mathcal{X}_{x,y,z}\) with and without the virtual addition of mass in the leg&rsquo;s space</p>
 </div>
 
 
-<div id="org2281744" class="figure">
+<div id="orgd96256a" class="figure">
 <p><img src="figs/virtual_mass_L_primary_plant_L.png" alt="virtual_mass_L_primary_plant_L.png" />
 </p>
 <p><span class="figure-number">Figure 4: </span>Comparison of the transfer function from \(\tau_i\) to \(\mathcal{L}_{i}\) with and without the virtual addition of mass in the leg&rsquo;s space</p>
@@ -164,12 +168,12 @@ Identification of the Primary plant without virtual add of mass
 </div>
 </div>
 
-<div id="outline-container-orgc9131d0" class="outline-2">
-<h2 id="orgc9131d0"><span class="section-number-2">4</span> Adding Virtual Mass in the Task Space</h2>
+<div id="outline-container-org3c74924" class="outline-2">
+<h2 id="org3c74924"><span class="section-number-2">4</span> Adding Virtual Mass in the Task Space</h2>
 <div class="outline-text-2" id="text-4">
 </div>
-<div id="outline-container-orgdbe6a25" class="outline-3">
-<h3 id="orgdbe6a25"><span class="section-number-3">4.1</span> Plant</h3>
+<div id="outline-container-org3b61568" class="outline-3">
+<h3 id="org3b61568"><span class="section-number-3">4.1</span> Plant</h3>
 <div class="outline-text-3" id="text-4-1">
 <p>
 Let&rsquo;s look at the transfer function from \(\bm{\mathcal{F}}\) to \(d\bm{\mathcal{X}}\):
@@ -177,7 +181,7 @@ Let&rsquo;s look at the transfer function from \(\bm{\mathcal{F}}\) to \(d\bm{\m
 </p>
 
 
-<div id="org6488b4c" class="figure">
+<div id="orgb509352" class="figure">
 <p><img src="figs/virtual_mass_plant_X.png" alt="virtual_mass_plant_X.png" />
 </p>
 <p><span class="figure-number">Figure 5: </span>Dynamics from \(\mathcal{F}_{x,y,z}\) to \(\mathcal{X}_{x,y,z}\) used for virtual mass addition in the task space</p>
@@ -185,40 +189,40 @@ Let&rsquo;s look at the transfer function from \(\bm{\mathcal{F}}\) to \(d\bm{\m
 </div>
 </div>
 
-<div id="outline-container-org571922f" class="outline-3">
-<h3 id="org571922f"><span class="section-number-3">4.2</span> Controller Design</h3>
+<div id="outline-container-orgf37b1c0" class="outline-3">
+<h3 id="orgf37b1c0"><span class="section-number-3">4.2</span> Controller Design</h3>
 <div class="outline-text-3" id="text-4-2">
 <div class="org-src-container">
-<pre class="src src-matlab">KmX = (s^2*1/(1+s/2/pi/500)^2*diag([1 1 50 0 0 0]));
+<pre class="src src-matlab">  KmX = (s<span class="org-type">^</span>2<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>500)<span class="org-type">^</span>2<span class="org-type">*</span>diag([1 1 50 0 0 0]));
 </pre>
 </div>
 
 
-<div id="orgf411330" class="figure">
+<div id="org18b3b14" class="figure">
 <p><img src="figs/virtual_mass_loop_gain_X.png" alt="virtual_mass_loop_gain_X.png" />
 </p>
 <p><span class="figure-number">Figure 6: </span>Loop gain for virtual mass addition in the task space</p>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">Kdvf = inv(nano_hexapod.kinematics.J')*KmX*inv(nano_hexapod.kinematics.J);
+<pre class="src src-matlab">  Kdvf = inv(nano_hexapod.kinematics.J<span class="org-type">'</span>)<span class="org-type">*</span>KmX<span class="org-type">*</span>inv(nano_hexapod.kinematics.J);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org4960701" class="outline-3">
-<h3 id="org4960701"><span class="section-number-3">4.3</span> Identification of the Primary Plant</h3>
+<div id="outline-container-orgcd22c9f" class="outline-3">
+<h3 id="orgcd22c9f"><span class="section-number-3">4.3</span> Identification of the Primary Plant</h3>
 <div class="outline-text-3" id="text-4-3">
 
-<div id="orge1df87b" class="figure">
+<div id="orgfde1133" class="figure">
 <p><img src="figs/virtual_mass_X_primary_plant_X.png" alt="virtual_mass_X_primary_plant_X.png" />
 </p>
 <p><span class="figure-number">Figure 7: </span>Comparison of the transfer function from \(\mathcal{F}_{x,y,z}\) to \(\mathcal{X}_{x,y,z}\) with and without the virtual addition of mass in the task space</p>
 </div>
 
 
-<div id="org647b748" class="figure">
+<div id="org095b9cd" class="figure">
 <p><img src="figs/virtual_mass_X_primary_plant_L.png" alt="virtual_mass_X_primary_plant_L.png" />
 </p>
 <p><span class="figure-number">Figure 8: </span>Comparison of the transfer function from \(\tau_i\) to \(\mathcal{L}_{i}\) with and without the virtual addition of mass in the task space</p>
@@ -229,7 +233,7 @@ Let&rsquo;s look at the transfer function from \(\bm{\mathcal{F}}\) to \(d\bm{\m
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-05-05 mar. 10:34</p>
+<p class="date">Created: 2021-02-20 sam. 23:09</p>
 </div>
 </body>
 </html>

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docs/disturbances.html

@@ -3,31 +3,36 @@
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2020-09-01 mar. 13:48 -->
+<!-- 2021-02-20 sam. 23:08 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Identification of the disturbances</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
-<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
-<script src="./js/jquery.min.js"></script>
-<script src="./js/bootstrap.min.js"></script>
-<script src="./js/jquery.stickytableheaders.min.js"></script>
-<script src="./js/readtheorg.js"></script>
-<script>MathJax = {
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
+<script>
+           MathJax = {
+             svg: {
+               scale: 1,
+               fontCache: "global"
+             },
              tex: {
-            tags: 'ams',
-            macros: {bm: ["\\boldsymbol{#1}",1],}
+               tags: "ams",
+               multlineWidth: "%MULTLINEWIDTH",
+               tagSide: "right",
+                       macros: {bm: ["\\boldsymbol{#1}",1],},
+               tagIndent: ".8em"
              }
            };
            </script>
-          <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+           <script id="MathJax-script" async
+             src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Identification of the disturbances</h1>
 <div id="table-of-contents">
@@ -41,12 +46,12 @@
 <li><a href="#Compute-the-Power-Spectral-Density-of-the-disturbance-force">5. Compute the Power Spectral Density of the disturbance force</a></li>
 <li><a href="#Noise-Budget">6. Noise Budget</a></li>
 <li><a href="#Save">7. Save</a></li>
-<li><a href="#orgd564a58">8. Time Domain Disturbances</a></li>
-<li><a href="#org8212830">9. Time Domain Effect of Disturbances</a>
+<li><a href="#orgca3331b">8. Time Domain Disturbances</a></li>
+<li><a href="#orgbbaf1e8">9. Time Domain Effect of Disturbances</a>
 <ul>
-<li><a href="#org76c96f4">9.1. Initialization of the Experiment</a></li>
-<li><a href="#orgf9c1ad9">9.2. Simulations</a></li>
-<li><a href="#org8107e0b">9.3. Comparison</a></li>
+<li><a href="#org44ce5e0">9.1. Initialization of the Experiment</a></li>
+<li><a href="#org6eb944e">9.2. Simulations</a></li>
+<li><a href="#org0e0c592">9.3. Comparison</a></li>
 </ul>
 </li>
 </ul>
@@ -58,7 +63,7 @@ The goal here is to extract the Power Spectral Density of the sources of perturb
 </p>
 
 <p>
-The sources of perturbations are (schematically shown in figure <a href="#org3b8025c">1</a>):
+The sources of perturbations are (schematically shown in figure <a href="#orgd508b9c">1</a>):
 </p>
 <ul class="org-ul">
 <li>\(D_w\): Ground Motion</li>
@@ -67,11 +72,11 @@ These forces can be due to imperfect guiding for instance.</li>
 </ul>
 
 <p>
-Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure <a href="#org3b8025c">1</a>) and then, using a model, compute the forces that induced such velocity.
+Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones, \(D\) on figure <a href="#orgd508b9c">1</a>) and then, using a model, compute the forces that induced such velocity.
 </p>
 
 
-<div id="org3b8025c" class="figure">
+<div id="orgd508b9c" class="figure">
 <p><img src="figs/uniaxial-model-micro-station.png" alt="uniaxial-model-micro-station.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>Schematic of the Micro Station and the sources of disturbance</p>
@@ -82,19 +87,19 @@ Because we cannot measure directly the perturbation forces, we have the measure
 This file is divided in the following sections:
 </p>
 <ul class="org-ul">
-<li>Section <a href="#org7cdab70">1</a>: the simscape model used here is presented</li>
-<li>Section <a href="#org43ec76b">2</a>: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup</li>
-<li>Section <a href="#org5636fee">3</a>: the bode plot of those transfer functions are shown</li>
-<li>Section <a href="#org40a7e4e">4</a>: the measured PSD of the effect of the disturbances are shown</li>
-<li>Section <a href="#orgd113ba5">5</a>: from the model and the measured PSD, the PSD of the disturbance forces are computed</li>
-<li>Section <a href="#org71da6bd">6</a>: with the computed PSD, the noise budget of the system is done</li>
+<li>Section <a href="#orga31fad3">1</a>: the simscape model used here is presented</li>
+<li>Section <a href="#org6a358d2">2</a>: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup</li>
+<li>Section <a href="#orgaf4acdc">3</a>: the bode plot of those transfer functions are shown</li>
+<li>Section <a href="#org01aa3d0">4</a>: the measured PSD of the effect of the disturbances are shown</li>
+<li>Section <a href="#org5b257d4">5</a>: from the model and the measured PSD, the PSD of the disturbance forces are computed</li>
+<li>Section <a href="#org0e0f7ed">6</a>: with the computed PSD, the noise budget of the system is done</li>
 </ul>
 
 <div id="outline-container-Simscape-Model" class="outline-2">
 <h2 id="Simscape-Model"><span class="section-number-2">1</span> Simscape Model</h2>
 <div class="outline-text-2" id="text-Simscape-Model">
 <p>
-<a id="org7cdab70"></a>
+<a id="orga31fad3"></a>
 </p>
 
 <p>
@@ -111,8 +116,8 @@ Also, we measure the absolute displacement of the granite and of the top platfor
 We load the configuration and we set a small <code>StopTime</code>.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">load('mat/conf_simulink.mat');
-set_param(conf_simulink, 'StopTime', '0.5');
+<pre class="src src-matlab">  load(<span class="org-string">'mat/conf_simulink.mat'</span>);
+  <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.5'</span>);
 </pre>
 </div>
 
@@ -121,16 +126,16 @@ We initialize all the stages without the sample nor the nano-hexapod.
 The obtained system corresponds to the status micro-station when the vibration measurements were conducted.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite('type', 'modal-analysis');
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod('type', 'modal-analysis');
-initializeAxisc('type', 'none');
-initializeMirror('type', 'none');
-initializeNanoHexapod('type', 'none');
-initializeSample('type', 'none');
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite(<span class="org-string">'type'</span>, <span class="org-string">'modal-analysis'</span>);
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod(<span class="org-string">'type'</span>, <span class="org-string">'modal-analysis'</span>);
+  initializeAxisc(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
+  initializeMirror(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
+  initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
+  initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
 </pre>
 </div>
 
@@ -138,7 +143,7 @@ initializeSample('type', 'none');
 Open Loop Control.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController('type', 'open-loop');
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
 </pre>
 </div>
 
@@ -146,7 +151,7 @@ Open Loop Control.
 We don&rsquo;t need gravity here.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeSimscapeConfiguration('gravity', false);
+<pre class="src src-matlab">  initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
 </pre>
 </div>
 
@@ -154,7 +159,7 @@ We don&rsquo;t need gravity here.
 We log the signals.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeLoggingConfiguration('log', 'all');
+<pre class="src src-matlab">  initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
 </pre>
 </div>
 </div>
@@ -164,25 +169,25 @@ We log the signals.
 <h2 id="Identification"><span class="section-number-2">2</span> Identification</h2>
 <div class="outline-text-2" id="text-Identification">
 <p>
-<a id="org43ec76b"></a>
+<a id="org6a358d2"></a>
 The transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup with the code below.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-matlab">%% Name of the Simulink File
-mdl = 'nass_model';
+<pre class="src src-matlab">  <span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
+  mdl = <span class="org-string">'nass_model'</span>;
 
-%% Micro-Hexapod
-clear io; io_i = 1;
-io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Dwz'); io_i = io_i + 1; % Vertical Ground Motion
-io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Fty_z'); io_i = io_i + 1; % Parasitic force Ty
-io(io_i) = linio([mdl, '/Disturbances'], 1, 'openinput', [], 'Frz_z'); io_i = io_i + 1; % Parasitic force Rz
+  <span class="org-matlab-cellbreak"><span class="org-comment">%% Micro-Hexapod</span></span>
+  clear io; io_i = 1;
+  io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Dwz'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Vertical Ground Motion</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Fty_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Ty</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <span class="org-string">'openinput'</span>, [], <span class="org-string">'Frz_z'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Parasitic force Rz</span>
 
-io(io_i) = linio([mdl, '/Micro-Station/Granite/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1; % Absolute motion - Granite
-io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'],  1, 'openoutput'); io_i = io_i + 1; % Absolute Motion - Hexapod
+  io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Granite/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute motion - Granite</span>
+  io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'</span>],  1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion - Hexapod</span>
 
-% Run the linearization
-G = linearize(mdl, io, 0);
+  <span class="org-comment">% Run the linearization</span>
+  G = linearize(mdl, io, 0);
 </pre>
 </div>
 
@@ -190,11 +195,11 @@ G = linearize(mdl, io, 0);
 We Take only the outputs corresponding to the vertical acceleration.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">G = G([3,9], :);
+<pre class="src src-matlab">  G = G([3,9], <span class="org-type">:</span>);
 
-% Input/Output names
-G.InputName  = {'Dw', 'Fty', 'Frz'};
-G.OutputName = {'Agm', 'Ahm'};
+  <span class="org-comment">% Input/Output names</span>
+  G.InputName  = {<span class="org-string">'Dw'</span>, <span class="org-string">'Fty'</span>, <span class="org-string">'Frz'</span>};
+  G.OutputName = {<span class="org-string">'Agm'</span>, <span class="org-string">'Ahm'</span>};
 </pre>
 </div>
 
@@ -202,11 +207,11 @@ G.OutputName = {'Agm', 'Ahm'};
 We integrate 1 time the output to have the velocity and we substract the absolute velocities to have the relative velocity.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">G = (1/s)*tf([-1, 1])*G;
+<pre class="src src-matlab">  G = (1<span class="org-type">/</span>s)<span class="org-type">*</span>tf([<span class="org-type">-</span>1, 1])<span class="org-type">*</span>G;
 
-% Input/Output names
-G.InputName  = {'Dw', 'Fty', 'Frz'};
-G.OutputName = {'Vm'};
+  <span class="org-comment">% Input/Output names</span>
+  G.InputName  = {<span class="org-string">'Dw'</span>, <span class="org-string">'Fty'</span>, <span class="org-string">'Frz'</span>};
+  G.OutputName = {<span class="org-string">'Vm'</span>};
 </pre>
 </div>
 </div>
@@ -216,19 +221,19 @@ G.OutputName = {'Vm'};
 <h2 id="Sensitivity-to-Disturbances"><span class="section-number-2">3</span> Sensitivity to Disturbances</h2>
 <div class="outline-text-2" id="text-Sensitivity-to-Disturbances">
 <p>
-<a id="org5636fee"></a>
+<a id="orgaf4acdc"></a>
 </p>
 
 <p>
 The obtained sensitivity to disturbances are shown bellow:
 </p>
 <ul class="org-ul">
-<li>The transfer function from vertical ground motion \(D_w\) to the vertical relative displacement from the micro-hexapod to the granite \(D\) is shown in Figure <a href="#org7fe296c">2</a></li>
-<li>The sensitive from vertical forces applied in the Translation stage is shown in Figure <a href="#orgce9715c">3</a></li>
+<li>The transfer function from vertical ground motion \(D_w\) to the vertical relative displacement from the micro-hexapod to the granite \(D\) is shown in Figure <a href="#org0ff7b6f">2</a></li>
+<li>The sensitive from vertical forces applied in the Translation stage is shown in Figure <a href="#org6cdcb5f">3</a></li>
 </ul>
 
 
-<div id="org7fe296c" class="figure">
+<div id="org0ff7b6f" class="figure">
 <p><img src="figs/sensitivity_dist_gm.png" alt="sensitivity_dist_gm.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>Sensitivity to Ground Motion (<a href="./figs/sensitivity_dist_gm.png">png</a>, <a href="./figs/sensitivity_dist_gm.pdf">pdf</a>)</p>
@@ -236,7 +241,7 @@ The obtained sensitivity to disturbances are shown bellow:
 
 
 
-<div id="orgce9715c" class="figure">
+<div id="org6cdcb5f" class="figure">
 <p><img src="figs/sensitivity_dist_fty.png" alt="sensitivity_dist_fty.png" />
 </p>
 <p><span class="figure-number">Figure 3: </span>Sensitivity to vertical forces applied by the Ty stage (<a href="./figs/sensitivity_dist_fty.png">png</a>, <a href="./figs/sensitivity_dist_fty.pdf">pdf</a>)</p>
@@ -244,7 +249,7 @@ The obtained sensitivity to disturbances are shown bellow:
 
 
 
-<div id="orga3e6fbc" class="figure">
+<div id="orgef9814b" class="figure">
 <p><img src="figs/sensitivity_dist_frz.png" alt="sensitivity_dist_frz.png" />
 </p>
 <p><span class="figure-number">Figure 4: </span>Sensitivity to vertical forces applied by the Rz stage (<a href="./figs/sensitivity_dist_frz.png">png</a>, <a href="./figs/sensitivity_dist_frz.pdf">pdf</a>)</p>
@@ -256,7 +261,7 @@ The obtained sensitivity to disturbances are shown bellow:
 <h2 id="Power-Spectral-Density-of-the-effect-of-the-disturbances"><span class="section-number-2">4</span> Power Spectral Density of the effect of the disturbances</h2>
 <div class="outline-text-2" id="text-Power-Spectral-Density-of-the-effect-of-the-disturbances">
 <p>
-<a id="org40a7e4e"></a>
+<a id="org01aa3d0"></a>
 </p>
 
 <p>
@@ -272,10 +277,10 @@ Also, the Ground Motion is measured.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-matlab">gm  = load('./mat/psd_gm.mat', 'f', 'psd_gm');
-rz  = load('./mat/pxsp_r.mat', 'f', 'pxsp_r');
-tyz = load('./mat/pxz_ty_r.mat', 'f', 'pxz_ty_r');
-tyx = load('./mat/pxe_ty_r.mat', 'f', 'pxe_ty_r');
+<pre class="src src-matlab">  gm  = load(<span class="org-string">'./mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>);
+  rz  = load(<span class="org-string">'./mat/pxsp_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxsp_r'</span>);
+  tyz = load(<span class="org-string">'./mat/pxz_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxz_ty_r'</span>);
+  tyx = load(<span class="org-string">'./mat/pxe_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxe_ty_r'</span>);
 </pre>
 </div>
 
@@ -283,11 +288,11 @@ tyx = load('./mat/pxe_ty_r.mat', 'f', 'pxe_ty_r');
 Because some 50Hz and harmonics were present in the ground motion measurement, we remove these peaks with the following code:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">f0s = [50, 100, 150, 200, 250, 350, 450];
-for f0 = f0s
-    i = find(gm.f &gt; f0-0.5 &amp; gm.f &lt; f0+0.5);
-    gm.psd_gm(i) = linspace(gm.psd_gm(i(1)), gm.psd_gm(i(end)), length(i));
-end
+<pre class="src src-matlab">  f0s = [50, 100, 150, 200, 250, 350, 450];
+  <span class="org-keyword">for</span> <span class="org-variable-name">f0</span> = <span class="org-constant">f0s</span>
+      <span class="org-constant">i</span> = find(gm.f <span class="org-type">&gt;</span> f0<span class="org-type">-</span>0.5 <span class="org-type">&amp;</span> gm.f <span class="org-type">&lt;</span> f0<span class="org-type">+</span>0.5);
+      gm.psd_gm(<span class="org-constant">i</span>) = linspace(gm.psd_gm(<span class="org-constant">i</span>(1)), gm.psd_gm(<span class="org-constant">i</span>(end)), length(<span class="org-constant">i</span>));
+  <span class="org-keyword">end</span>
 </pre>
 </div>
 
@@ -295,20 +300,20 @@ end
 We now compute the relative velocity between the hexapod and the granite due to ground motion.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2;
+<pre class="src src-matlab">  gm.psd_rv = gm.psd_gm<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Dw'</span>), gm.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
 </pre>
 </div>
 
 <p>
-The Power Spectral Density of the relative motion and velocity of the hexapod with respect to the granite are shown in figures <a href="#orgb815ef2">5</a> and <a href="#org4c2c215">6</a>.
+The Power Spectral Density of the relative motion and velocity of the hexapod with respect to the granite are shown in figures <a href="#orge9a5c6c">5</a> and <a href="#org179679e">6</a>.
 </p>
 
 <p>
-The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a href="#orgaf910f1">7</a>.
+The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a href="#orgdd992d9">7</a>.
 </p>
 
 
-<div id="orgb815ef2" class="figure">
+<div id="orge9a5c6c" class="figure">
 <p><img src="figs/dist_effect_relative_velocity.png" alt="dist_effect_relative_velocity.png" />
 </p>
 <p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_velocity.png">png</a>, <a href="./figs/dist_effect_relative_velocity.pdf">pdf</a>)</p>
@@ -316,22 +321,22 @@ The Cumulative Amplitude Spectrum of the relative motion is shown in figure <a h
 
 
 
-<div id="org4c2c215" class="figure">
+<div id="org179679e" class="figure">
 <p><img src="figs/dist_effect_relative_motion.png" alt="dist_effect_relative_motion.png" />
 </p>
 <p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the relative displacement of the hexapod with respect to the granite due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion.png">png</a>, <a href="./figs/dist_effect_relative_motion.pdf">pdf</a>)</p>
 </div>
 
 
-<div id="orgaf910f1" class="figure">
+<div id="orgdd992d9" class="figure">
 <p><img src="figs/dist_effect_relative_motion_cas.png" alt="dist_effect_relative_motion_cas.png" />
 </p>
 <p><span class="figure-number">Figure 7: </span>Cumulative Amplitude Spectrum of the relative motion due to different sources of perturbation (<a href="./figs/dist_effect_relative_motion_cas.png">png</a>, <a href="./figs/dist_effect_relative_motion_cas.pdf">pdf</a>)</p>
 </div>
 
-<div class="important">
+<div class="important" id="org211b9ec">
 <p>
-From Figure <a href="#orgaf910f1">7</a>, we can see that the translation stage and the rotation stage have almost the same effect on the position error.
+From Figure <a href="#orgdd992d9">7</a>, we can see that the translation stage and the rotation stage have almost the same effect on the position error.
 Also, the ground motion has a relatively negligible effect on the position error.
 </p>
 
@@ -343,28 +348,28 @@ Also, the ground motion has a relatively negligible effect on the position error
 <h2 id="Compute-the-Power-Spectral-Density-of-the-disturbance-force"><span class="section-number-2">5</span> Compute the Power Spectral Density of the disturbance force</h2>
 <div class="outline-text-2" id="text-Compute-the-Power-Spectral-Density-of-the-disturbance-force">
 <p>
-<a id="orgd113ba5"></a>
+<a id="org5b257d4"></a>
 </p>
 
 <p>
-Using the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section <a href="#org5636fee">3</a>) and using the measured PSD of the relative motion (section <a href="#org40a7e4e">4</a>), we can compute the PSD of the disturbance force.
+Using the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section <a href="#orgaf4acdc">3</a>) and using the measured PSD of the relative motion (section <a href="#org01aa3d0">4</a>), we can compute the PSD of the disturbance force.
 </p>
 
 <p>
 This is done below.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">rz.psd_f  = rz.pxsp_r./abs(squeeze(freqresp(G('Vm', 'Frz'), rz.f, 'Hz'))).^2;
-tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G('Vm', 'Fty'), tyz.f, 'Hz'))).^2;
+<pre class="src src-matlab">  rz.psd_f  = rz.pxsp_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Frz'</span>), rz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
+  tyz.psd_f = tyz.pxz_ty_r<span class="org-type">./</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Fty'</span>), tyz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
 </pre>
 </div>
 
 <p>
-The obtained amplitude spectral densities of the disturbance forces are shown in Figure <a href="#org45cf35c">8</a>.
+The obtained amplitude spectral densities of the disturbance forces are shown in Figure <a href="#org7843e80">8</a>.
 </p>
 
 
-<div id="org45cf35c" class="figure">
+<div id="org7843e80" class="figure">
 <p><img src="figs/dist_force_psd.png" alt="dist_force_psd.png" />
 </p>
 <p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the disturbance force (<a href="./figs/dist_force_psd.png">png</a>, <a href="./figs/dist_force_psd.pdf">pdf</a>)</p>
@@ -376,7 +381,7 @@ The obtained amplitude spectral densities of the disturbance forces are shown in
 <h2 id="Noise-Budget"><span class="section-number-2">6</span> Noise Budget</h2>
 <div class="outline-text-2" id="text-Noise-Budget">
 <p>
-<a id="org71da6bd"></a>
+<a id="org0e0f7ed"></a>
 </p>
 
 <p>
@@ -389,18 +394,18 @@ This is done in order to verify that this is coherent with the measurements.
 </p>
 
 <p>
-The power spectral density of the relative motion is computed below and the result is shown in Figure <a href="#orgcacf809">9</a>.
-We can see that this is exactly the same as the Figure <a href="#org4c2c215">6</a>.
+The power spectral density of the relative motion is computed below and the result is shown in Figure <a href="#orga081bb2">9</a>.
+We can see that this is exactly the same as the Figure <a href="#org179679e">6</a>.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">psd_gm_d = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw')/s, gm.f, 'Hz'))).^2;
-psd_ty_d = tyz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Fty')/s, tyz.f, 'Hz'))).^2;
-psd_rz_d = rz.psd_f.*abs(squeeze(freqresp(G('Vm', 'Frz')/s, rz.f, 'Hz'))).^2;
+<pre class="src src-matlab">  psd_gm_d = gm.psd_gm<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Dw'</span>)<span class="org-type">/</span>s, gm.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
+  psd_ty_d = tyz.psd_f<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Fty'</span>)<span class="org-type">/</span>s, tyz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
+  psd_rz_d = rz.psd_f<span class="org-type">.*</span>abs(squeeze(freqresp(G(<span class="org-string">'Vm'</span>, <span class="org-string">'Frz'</span>)<span class="org-type">/</span>s, rz.f, <span class="org-string">'Hz'</span>)))<span class="org-type">.^</span>2;
 </pre>
 </div>
 
 
-<div id="orgcacf809" class="figure">
+<div id="orga081bb2" class="figure">
 <p><img src="figs/psd_effect_dist_verif.png" alt="psd_effect_dist_verif.png" />
 </p>
 <p><span class="figure-number">Figure 9: </span>Computed Effect of the disturbances on the relative displacement hexapod/granite (<a href="./figs/psd_effect_dist_verif.png">png</a>, <a href="./figs/psd_effect_dist_verif.pdf">pdf</a>)</p>
@@ -416,38 +421,38 @@ The PSD of the disturbance force are now saved for further analysis.
 </p>
 
 <div class="org-src-container">
-<pre class="src src-matlab">dist_f = struct();
+<pre class="src src-matlab">  dist_f = struct();
 
-dist_f.f = gm.f; % Frequency Vector [Hz]
+  dist_f.f = gm.f; <span class="org-comment">% Frequency Vector [Hz]</span>
 
-dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m^2/Hz]
-dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz]
-dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz]
+  dist_f.psd_gm = gm.psd_gm; <span class="org-comment">% Power Spectral Density of the Ground Motion [m^2/Hz]</span>
+  dist_f.psd_ty = tyz.psd_f; <span class="org-comment">% Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz]</span>
+  dist_f.psd_rz = rz.psd_f; <span class="org-comment">% Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz]</span>
 
-save('./mat/dist_psd.mat', 'dist_f');
+  save(<span class="org-string">'./mat/dist_psd.mat'</span>, <span class="org-string">'dist_f'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgd564a58" class="outline-2">
-<h2 id="orgd564a58"><span class="section-number-2">8</span> Time Domain Disturbances</h2>
+<div id="outline-container-orgca3331b" class="outline-2">
+<h2 id="orgca3331b"><span class="section-number-2">8</span> Time Domain Disturbances</h2>
 <div class="outline-text-2" id="text-8">
 <p>
 Let&rsquo;s initialize the time domain disturbances and load them.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances();
-dist = load('nass_disturbances.mat');
+<pre class="src src-matlab">  initializeDisturbances();
+  dist = load(<span class="org-string">'nass_disturbances.mat'</span>);
 </pre>
 </div>
 
 <p>
-The time domain disturbance signals are shown in Figure <a href="#org3ff859b">10</a>.
+The time domain disturbance signals are shown in Figure <a href="#orgc58b665">10</a>.
 </p>
 
 
-<div id="org3ff859b" class="figure">
+<div id="orgc58b665" class="figure">
 <p><img src="figs/disturbances_time_domain.png" alt="disturbances_time_domain.png" />
 </p>
 <p><span class="figure-number">Figure 10: </span>Disturbances in the Time Domain (<a href="./figs/disturbances_time_domain.png">png</a>, <a href="./figs/disturbances_time_domain.pdf">pdf</a>)</p>
@@ -455,25 +460,25 @@ The time domain disturbance signals are shown in Figure <a href="#org3ff859b">10
 </div>
 </div>
 
-<div id="outline-container-org8212830" class="outline-2">
-<h2 id="org8212830"><span class="section-number-2">9</span> Time Domain Effect of Disturbances</h2>
+<div id="outline-container-orgbbaf1e8" class="outline-2">
+<h2 id="orgbbaf1e8"><span class="section-number-2">9</span> Time Domain Effect of Disturbances</h2>
 <div class="outline-text-2" id="text-9">
 </div>
-<div id="outline-container-org76c96f4" class="outline-3">
-<h3 id="org76c96f4"><span class="section-number-3">9.1</span> Initialization of the Experiment</h3>
+<div id="outline-container-org44ce5e0" class="outline-3">
+<h3 id="org44ce5e0"><span class="section-number-3">9.1</span> Initialization of the Experiment</h3>
 <div class="outline-text-3" id="text-9-1">
 <p>
 We initialize all the stages with the default parameters.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
 </pre>
 </div>
 
@@ -481,37 +486,37 @@ initializeMirror();
 The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeNanoHexapod('type', 'rigid');
-initializeSample('mass', 1);
+<pre class="src src-matlab">  initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
+  initializeSample(<span class="org-string">'mass'</span>, 1);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences();
-initializeController('type', 'open-loop');
-initializeSimscapeConfiguration('gravity', false);
-initializeLoggingConfiguration('log', 'all');
+<pre class="src src-matlab">  initializeReferences();
+  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
+  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>);
 </pre>
 </div>
 
 <div class="org-src-container">
-<pre class="src src-matlab">load('mat/conf_simulink.mat');
-set_param(conf_simulink, 'StopTime', '2');
+<pre class="src src-matlab">  load(<span class="org-string">'mat/conf_simulink.mat'</span>);
+  <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgf9c1ad9" class="outline-3">
-<h3 id="orgf9c1ad9"><span class="section-number-3">9.2</span> Simulations</h3>
+<div id="outline-container-org6eb944e" class="outline-3">
+<h3 id="org6eb944e"><span class="section-number-3">9.2</span> Simulations</h3>
 <div class="outline-text-3" id="text-9-2">
 <p>
 No disturbances:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances('enable', false);
-sim('nass_model');
-sim_no = simout;
+<pre class="src src-matlab">  initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
+  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
+  sim_no = simout;
 </pre>
 </div>
 
@@ -519,9 +524,9 @@ sim_no = simout;
 Ground Motion:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances('Fty_x', false, 'Fty_z', false, 'Frz_z', false);
-sim('nass_model');
-sim_gm = simout;
+<pre class="src src-matlab">  initializeDisturbances(<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, <span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span>);
+  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
+  sim_gm = simout;
 </pre>
 </div>
 
@@ -529,9 +534,9 @@ sim_gm = simout;
 Translation Stage Vibrations:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances('Dwx', false, 'Dwy', false, 'Dwz', false, 'Frz_z', false);
-sim('nass_model');
-sim_ty = simout;
+<pre class="src src-matlab">  initializeDisturbances(<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, <span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span>);
+  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
+  sim_ty = simout;
 </pre>
 </div>
 
@@ -539,23 +544,23 @@ sim_ty = simout;
 Rotation Stage Vibrations:
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances('Dwx', false, 'Dwy', false, 'Dwz', false, 'Fty_x', false, 'Fty_z', false);
-sim('nass_model');
-sim_rz = simout;
+<pre class="src src-matlab">  initializeDisturbances(<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, <span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, <span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>);
+  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
+  sim_rz = simout;
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org8107e0b" class="outline-3">
-<h3 id="org8107e0b"><span class="section-number-3">9.3</span> Comparison</h3>
+<div id="outline-container-org0e0c592" class="outline-3">
+<h3 id="org0e0c592"><span class="section-number-3">9.3</span> Comparison</h3>
 <div class="outline-text-3" id="text-9-3">
 <p>
-Let&rsquo;s now compare the effect of those perturbations on the position error of the sample (Figure <a href="#orgee898d4">11</a>)
+Let&rsquo;s now compare the effect of those perturbations on the position error of the sample (Figure <a href="#orgfbe77be">11</a>)
 </p>
 
 
-<div id="orgee898d4" class="figure">
+<div id="orgfbe77be" class="figure">
 <p><img src="figs/effect_disturbances_position_error.png" alt="effect_disturbances_position_error.png" />
 </p>
 <p><span class="figure-number">Figure 11: </span>Effect of Perturbations on the position error (<a href="./figs/effect_disturbances_position_error.png">png</a>, <a href="./figs/effect_disturbances_position_error.pdf">pdf</a>)</p>
@@ -566,7 +571,7 @@ Let&rsquo;s now compare the effect of those perturbations on the position error
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-09-01 mar. 13:48</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>

docs/experiments.html

@@ -1,66 +1,61 @@
 <?xml version="1.0" encoding="utf-8"?>
-<?xml version="1.0" encoding="utf-8"?>
 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
 "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
 <head>
-<!-- 2020-05-05 mar. 10:34 -->
+<!-- 2021-02-20 sam. 23:08 -->
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
 <title>Simulation of Scientific Experiments</title>
 <meta name="generator" content="Org mode" />
 <meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
-<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
-<script src="./js/jquery.min.js"></script>
-<script src="./js/bootstrap.min.js"></script>
-<script src="./js/jquery.stickytableheaders.min.js"></script>
-<script src="./js/readtheorg.js"></script>
+<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
+<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
 </head>
 <body>
 <div id="org-div-home-and-up">
  <a accesskey="h" href="./index.html"> UP </a>
  |
- <a accesskey="H" href="./index.html"> HOME </a>
+ <a accesskey="H" href="../../index.html"> HOME </a>
 </div><div id="content">
 <h1 class="title">Simulation of Scientific Experiments</h1>
 <div id="table-of-contents">
 <h2>Table of Contents</h2>
 <div id="text-table-of-contents">
 <ul>
-<li><a href="#org03b2a76">1. Simscape Model</a></li>
-<li><a href="#org6ed78a0">2. Tomography Experiment with no disturbances</a>
+<li><a href="#org5e41cbf">1. Simscape Model</a></li>
+<li><a href="#orge687eef">2. Tomography Experiment with no disturbances</a>
 <ul>
-<li><a href="#orge3f0741">2.1. Simulation Setup</a></li>
-<li><a href="#org1836f98">2.2. Analysis</a></li>
-<li><a href="#org8cf54cb">2.3. Conclusion</a></li>
+<li><a href="#orgd7be9f9">2.1. Simulation Setup</a></li>
+<li><a href="#org3cc37e4">2.2. Analysis</a></li>
+<li><a href="#org635d5aa">2.3. Conclusion</a></li>
 </ul>
 </li>
-<li><a href="#org16d8e58">3. Tomography Experiment with included perturbations</a>
+<li><a href="#orgbaff4a2">3. Tomography Experiment with included perturbations</a>
 <ul>
-<li><a href="#org9d04c8b">3.1. Simulation Setup</a></li>
-<li><a href="#org746ee08">3.2. Analysis</a></li>
-<li><a href="#org42ba456">3.3. Conclusion</a></li>
+<li><a href="#org2adb412">3.1. Simulation Setup</a></li>
+<li><a href="#org0574e3b">3.2. Analysis</a></li>
+<li><a href="#orga01299f">3.3. Conclusion</a></li>
 </ul>
 </li>
-<li><a href="#org7202245">4. Tomography Experiment with Ty raster scans</a>
+<li><a href="#org2e6a61c">4. Tomography Experiment with Ty raster scans</a>
 <ul>
-<li><a href="#org0b606be">4.1. Simulation Setup</a></li>
-<li><a href="#org2e0557a">4.2. Analysis</a></li>
-<li><a href="#org6c8cc28">4.3. Conclusion</a></li>
+<li><a href="#orgea8ee40">4.1. Simulation Setup</a></li>
+<li><a href="#org10c7f76">4.2. Analysis</a></li>
+<li><a href="#org9121d09">4.3. Conclusion</a></li>
 </ul>
 </li>
-<li><a href="#org72f01ab">5. Tomography when the micro-hexapod is not centered</a>
+<li><a href="#orgfc40faa">5. Tomography when the micro-hexapod is not centered</a>
 <ul>
-<li><a href="#org98d14be">5.1. Simulation Setup</a></li>
-<li><a href="#org6dc8ae4">5.2. Analysis</a></li>
-<li><a href="#orgb632268">5.3. Conclusion</a></li>
+<li><a href="#orgbab9ef9">5.1. Simulation Setup</a></li>
+<li><a href="#org012e268">5.2. Analysis</a></li>
+<li><a href="#org75b29bc">5.3. Conclusion</a></li>
 </ul>
 </li>
-<li><a href="#org8fa1632">6. Raster Scans with the translation stage</a>
+<li><a href="#org3ba6838">6. Raster Scans with the translation stage</a>
 <ul>
-<li><a href="#orgdd9a5de">6.1. Simulation Setup</a></li>
-<li><a href="#orgad49d2c">6.2. Analysis</a></li>
-<li><a href="#org57c774f">6.3. Conclusion</a></li>
+<li><a href="#org5f4e508">6.1. Simulation Setup</a></li>
+<li><a href="#orgf069548">6.2. Analysis</a></li>
+<li><a href="#org3446ba0">6.3. Conclusion</a></li>
 </ul>
 </li>
 </ul>
@@ -85,26 +80,26 @@ This has several goals:
 The document in organized as follow:
 </p>
 <ul class="org-ul">
-<li>In section <a href="#orgfc7d050">1</a> the Simscape model is initialized</li>
-<li>In section <a href="#org3effbb8">2</a> a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included</li>
-<li>In section <a href="#org4e7f626">3</a>, the same is done but with disturbance included</li>
-<li>In section <a href="#orgb31e3fb">5</a> the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included</li>
-<li>In section <a href="#org6aaeb53">6</a>, scans with the translation stage are simulated with no perturbation included</li>
+<li>In section <a href="#org5180d92">1</a> the Simscape model is initialized</li>
+<li>In section <a href="#org141b5a6">2</a> a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included</li>
+<li>In section <a href="#org95498dc">3</a>, the same is done but with disturbance included</li>
+<li>In section <a href="#orgd1d4e24">5</a> the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included</li>
+<li>In section <a href="#orgeec7f3c">6</a>, scans with the translation stage are simulated with no perturbation included</li>
 </ul>
 
-<div id="outline-container-org03b2a76" class="outline-2">
-<h2 id="org03b2a76"><span class="section-number-2">1</span> Simscape Model</h2>
+<div id="outline-container-org5e41cbf" class="outline-2">
+<h2 id="org5e41cbf"><span class="section-number-2">1</span> Simscape Model</h2>
 <div class="outline-text-2" id="text-1">
 <p>
-<a id="orgfc7d050"></a>
+<a id="org5180d92"></a>
 </p>
 
 <p>
 We load the shared simulink configuration and we set the <code>StopTime</code>.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">load('mat/conf_simulink.mat');
-set_param(conf_simulink, 'StopTime', '2');
+<pre class="src src-matlab">  load(<span class="org-string">'mat/conf_simulink.mat'</span>);
+  <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'2'</span>);
 </pre>
 </div>
 
@@ -113,16 +108,16 @@ We first initialize all the stages.
 The nano-hexapod is considered to be a rigid body.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
-initializeNanoHexapod('type', 'rigid');
-initializeSample('mass', 1);
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
+  initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
+  initializeSample(<span class="org-string">'mass'</span>, 1);
 </pre>
 </div>
 
@@ -130,7 +125,7 @@ initializeSample('mass', 1);
 No controller is used (Open Loop).
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeController('type', 'open-loop');
+<pre class="src src-matlab">  initializeController(<span class="org-string">'type'</span>, <span class="org-string">'open-loop'</span>);
 </pre>
 </div>
 
@@ -138,7 +133,7 @@ No controller is used (Open Loop).
 We don&rsquo;t gravity.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeSimscapeConfiguration('gravity', false);
+<pre class="src src-matlab">  initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
 </pre>
 </div>
 
@@ -146,37 +141,37 @@ We don&rsquo;t gravity.
 We log the signals for further analysis.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeLoggingConfiguration('log', 'all');
+<pre class="src src-matlab">  initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org6ed78a0" class="outline-2">
-<h2 id="org6ed78a0"><span class="section-number-2">2</span> Tomography Experiment with no disturbances</h2>
+<div id="outline-container-orge687eef" class="outline-2">
+<h2 id="orge687eef"><span class="section-number-2">2</span> Tomography Experiment with no disturbances</h2>
 <div class="outline-text-2" id="text-2">
 <p>
-<a id="org3effbb8"></a>
+<a id="org141b5a6"></a>
 </p>
 <p>
 In this section, a tomography experiment is performed with the sample aligned with the rotation axis.
 No disturbance is included.
 </p>
 </div>
-<div id="outline-container-orge3f0741" class="outline-3">
-<h3 id="orge3f0741"><span class="section-number-3">2.1</span> Simulation Setup</h3>
+<div id="outline-container-orgd7be9f9" class="outline-3">
+<h3 id="orgd7be9f9"><span class="section-number-3">2.1</span> Simulation Setup</h3>
 <div class="outline-text-3" id="text-2-1">
 <p>
 And we initialize the disturbances to be equal to zero.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances(...
-    'Dwx', false, ... % Ground Motion - X direction
-    'Dwy', false, ... % Ground Motion - Y direction
-    'Dwz', false, ... % Ground Motion - Z direction
-    'Fty_x', false, ... % Translation Stage - X direction
-    'Fty_z', false, ... % Translation Stage - Z direction
-    'Frz_z', false  ... % Spindle - Z direction
+<pre class="src src-matlab">  initializeDisturbances(...
+      <span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
+      <span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
+      <span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
+      <span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
+      <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
+      <span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span>  ...<span class="org-comment"> % Spindle - Z direction</span>
       );
 </pre>
 </div>
@@ -186,7 +181,7 @@ We initialize the reference path for all the stages.
 All stage is set to its zero position except the Spindle which is rotating at 60rpm.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
@@ -194,7 +189,7 @@ All stage is set to its zero position except the Spindle which is rotating at 60
 We simulate the model.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">sim('nass_model');
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
@@ -202,23 +197,23 @@ We simulate the model.
 And we save the obtained data.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">tomo_align_no_dist = simout;
-save('./mat/experiment_tomography.mat', 'tomo_align_no_dist', '-append');
+<pre class="src src-matlab">  tomo_align_no_dist = simout;
+  save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org1836f98" class="outline-3">
-<h3 id="org1836f98"><span class="section-number-3">2.2</span> Analysis</h3>
+<div id="outline-container-org3cc37e4" class="outline-3">
+<h3 id="org3cc37e4"><span class="section-number-3">2.2</span> Analysis</h3>
 <div class="outline-text-3" id="text-2-2">
 <div class="org-src-container">
-<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_align_no_dist');
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
 </pre>
 </div>
 
 
-<div id="orgfcc6055" class="figure">
+<div id="org3dd3ed3" class="figure">
 <p><img src="figs/exp_tomo_without_dist.png" alt="exp_tomo_without_dist.png" />
 </p>
 <p><span class="figure-number">Figure 1: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_without_dist.png">png</a>, <a href="./figs/exp_tomo_without_dist.pdf">pdf</a>)</p>
@@ -226,10 +221,10 @@ save('./mat/experiment_tomography.mat', 'tomo_align_no_dist', '-append');
 </div>
 </div>
 
-<div id="outline-container-org8cf54cb" class="outline-3">
-<h3 id="org8cf54cb"><span class="section-number-3">2.3</span> Conclusion</h3>
+<div id="outline-container-org635d5aa" class="outline-3">
+<h3 id="org635d5aa"><span class="section-number-3">2.3</span> Conclusion</h3>
 <div class="outline-text-3" id="text-2-3">
-<div class="important">
+<div class="important" id="orgbee0f3e">
 <p>
 When everything is aligned, the resulting error motion is very small (nm range) and is quite negligible with respect to the error when disturbances are included.
 This residual error motion probably comes from a small misalignment somewhere.
@@ -240,31 +235,31 @@ This residual error motion probably comes from a small misalignment somewhere.
 </div>
 </div>
 
-<div id="outline-container-org16d8e58" class="outline-2">
-<h2 id="org16d8e58"><span class="section-number-2">3</span> Tomography Experiment with included perturbations</h2>
+<div id="outline-container-orgbaff4a2" class="outline-2">
+<h2 id="orgbaff4a2"><span class="section-number-2">3</span> Tomography Experiment with included perturbations</h2>
 <div class="outline-text-2" id="text-3">
 <p>
-<a id="org4e7f626"></a>
+<a id="org95498dc"></a>
 </p>
 <p>
 In this section, we also perform a tomography experiment with the sample&rsquo;s center of mass aligned with the rotation axis.
 However this time, we include perturbations such as ground motion and stage vibrations.
 </p>
 </div>
-<div id="outline-container-org9d04c8b" class="outline-3">
-<h3 id="org9d04c8b"><span class="section-number-3">3.1</span> Simulation Setup</h3>
+<div id="outline-container-org2adb412" class="outline-3">
+<h3 id="org2adb412"><span class="section-number-3">3.1</span> Simulation Setup</h3>
 <div class="outline-text-3" id="text-3-1">
 <p>
 We now activate the disturbances.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances(...
-    'Dwx', true, ... % Ground Motion - X direction
-    'Dwy', true, ... % Ground Motion - Y direction
-    'Dwz', true, ... % Ground Motion - Z direction
-    'Fty_x', false, ... % Translation Stage - X direction
-    'Fty_z', false, ... % Translation Stage - Z direction
-    'Frz_z', true  ... % Spindle - Z direction
+<pre class="src src-matlab">  initializeDisturbances(...
+      <span class="org-string">'Dwx'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
+      <span class="org-string">'Dwy'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
+      <span class="org-string">'Dwz'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
+      <span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
+      <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
+      <span class="org-string">'Frz_z'</span>, <span class="org-constant">true</span>  ...<span class="org-comment"> % Spindle - Z direction</span>
       );
 </pre>
 </div>
@@ -274,7 +269,7 @@ We initialize the reference path for all the stages.
 All stage is set to its zero position except the Spindle which is rotating at 60rpm.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
@@ -282,7 +277,7 @@ All stage is set to its zero position except the Spindle which is rotating at 60
 We simulate the model.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">sim('nass_model');
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
@@ -290,23 +285,23 @@ We simulate the model.
 And we save the obtained data.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">tomo_align_dist = simout;
-save('./mat/experiment_tomography.mat', 'tomo_align_dist', '-append');
+<pre class="src src-matlab">  tomo_align_dist = simout;
+  save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org746ee08" class="outline-3">
-<h3 id="org746ee08"><span class="section-number-3">3.2</span> Analysis</h3>
+<div id="outline-container-org0574e3b" class="outline-3">
+<h3 id="org0574e3b"><span class="section-number-3">3.2</span> Analysis</h3>
 <div class="outline-text-3" id="text-3-2">
 <div class="org-src-container">
-<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_align_dist', 'tomo_align_no_dist');
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
 </pre>
 </div>
 
 
-<div id="org8030dba" class="figure">
+<div id="org7188a2d" class="figure">
 <p><img src="figs/exp_tomo_dist.png" alt="exp_tomo_dist.png" />
 </p>
 <p><span class="figure-number">Figure 2: </span>X-Y-Z translations and rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist.png">png</a>, <a href="./figs/exp_tomo_dist.pdf">pdf</a>)</p>
@@ -314,10 +309,10 @@ save('./mat/experiment_tomography.mat', 'tomo_align_dist', '-append');
 </div>
 </div>
 
-<div id="outline-container-org42ba456" class="outline-3">
-<h3 id="org42ba456"><span class="section-number-3">3.3</span> Conclusion</h3>
+<div id="outline-container-orga01299f" class="outline-3">
+<h3 id="orga01299f"><span class="section-number-3">3.3</span> Conclusion</h3>
 <div class="outline-text-3" id="text-3-3">
-<div class="important">
+<div class="important" id="org2449de1">
 <p>
 Here, no vibration is included in the X and Y directions.
 </p>
@@ -327,31 +322,31 @@ Here, no vibration is included in the X and Y directions.
 </div>
 </div>
 
-<div id="outline-container-org7202245" class="outline-2">
-<h2 id="org7202245"><span class="section-number-2">4</span> Tomography Experiment with Ty raster scans</h2>
+<div id="outline-container-org2e6a61c" class="outline-2">
+<h2 id="org2e6a61c"><span class="section-number-2">4</span> Tomography Experiment with Ty raster scans</h2>
 <div class="outline-text-2" id="text-4">
 <p>
-<a id="orgd4f0240"></a>
+<a id="org4907e7b"></a>
 </p>
 <p>
 In this section, we also perform a tomography experiment with scans of the Translation stage.
 All the perturbations are included.
 </p>
 </div>
-<div id="outline-container-org0b606be" class="outline-3">
-<h3 id="org0b606be"><span class="section-number-3">4.1</span> Simulation Setup</h3>
+<div id="outline-container-orgea8ee40" class="outline-3">
+<h3 id="orgea8ee40"><span class="section-number-3">4.1</span> Simulation Setup</h3>
 <div class="outline-text-3" id="text-4-1">
 <p>
 We now activate the disturbances.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances(...
-    'Dwx', true, ... % Ground Motion - X direction
-    'Dwy', true, ... % Ground Motion - Y direction
-    'Dwz', true, ... % Ground Motion - Z direction
-    'Fty_x', true, ... % Translation Stage - X direction
-    'Fty_z', true, ... % Translation Stage - Z direction
-    'Frz_z', true  ... % Spindle - Z direction
+<pre class="src src-matlab">  initializeDisturbances(...
+      <span class="org-string">'Dwx'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
+      <span class="org-string">'Dwy'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
+      <span class="org-string">'Dwz'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
+      <span class="org-string">'Fty_x'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
+      <span class="org-string">'Fty_z'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
+      <span class="org-string">'Frz_z'</span>, <span class="org-constant">true</span>  ...<span class="org-comment"> % Spindle - Z direction</span>
       );
 </pre>
 </div>
@@ -362,7 +357,7 @@ The Spindle which is rotating at 60rpm and the translation stage not moving as i
 However, vibrations of the Ty stage are included.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
@@ -370,7 +365,7 @@ However, vibrations of the Ty stage are included.
 We simulate the model.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">sim('nass_model');
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
@@ -378,23 +373,23 @@ We simulate the model.
 And we save the obtained data.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">scans_rz_align_dist = simout;
-save('./mat/experiment_tomography.mat', 'scans_rz_align_dist', '-append');
+<pre class="src src-matlab">  scans_rz_align_dist = simout;
+  save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'scans_rz_align_dist'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org2e0557a" class="outline-3">
-<h3 id="org2e0557a"><span class="section-number-3">4.2</span> Analysis</h3>
+<div id="outline-container-org10c7f76" class="outline-3">
+<h3 id="org10c7f76"><span class="section-number-3">4.2</span> Analysis</h3>
 <div class="outline-text-3" id="text-4-2">
 <div class="org-src-container">
-<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'scans_rz_align_dist');
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'scans_rz_align_dist'</span>);
 </pre>
 </div>
 
 
-<div id="org38e229c" class="figure">
+<div id="org125e802" class="figure">
 <p><img src="figs/exp_scans_rz_dist.png" alt="exp_scans_rz_dist.png" />
 </p>
 <p><span class="figure-number">Figure 3: </span>X-Y-Z translations and rotations of the sample w.r.t. the granite when performing tomography experiment and scans with the translation stage at the same time</p>
@@ -402,16 +397,16 @@ save('./mat/experiment_tomography.mat', 'scans_rz_align_dist', '-append');
 </div>
 </div>
 
-<div id="outline-container-org6c8cc28" class="outline-3">
-<h3 id="org6c8cc28"><span class="section-number-3">4.3</span> Conclusion</h3>
+<div id="outline-container-org9121d09" class="outline-3">
+<h3 id="org9121d09"><span class="section-number-3">4.3</span> Conclusion</h3>
 </div>
 </div>
 
-<div id="outline-container-org72f01ab" class="outline-2">
-<h2 id="org72f01ab"><span class="section-number-2">5</span> Tomography when the micro-hexapod is not centered</h2>
+<div id="outline-container-orgfc40faa" class="outline-2">
+<h2 id="orgfc40faa"><span class="section-number-2">5</span> Tomography when the micro-hexapod is not centered</h2>
 <div class="outline-text-2" id="text-5">
 <p>
-<a id="orgb31e3fb"></a>
+<a id="orgd1d4e24"></a>
 </p>
 <p>
 In this section, the sample&rsquo;s center of mass is not aligned with the rotation axis anymore.
@@ -422,14 +417,14 @@ This is due to the fact that the micro-hexapod has performed some displacement.
 No disturbances are included.
 </p>
 </div>
-<div id="outline-container-org98d14be" class="outline-3">
-<h3 id="org98d14be"><span class="section-number-3">5.1</span> Simulation Setup</h3>
+<div id="outline-container-orgbab9ef9" class="outline-3">
+<h3 id="orgbab9ef9"><span class="section-number-3">5.1</span> Simulation Setup</h3>
 <div class="outline-text-3" id="text-5-1">
 <p>
 We first set the wanted translation of the Micro Hexapod.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">P_micro_hexapod = [0.01; 0; 0]; % [m]
+<pre class="src src-matlab">  P_micro_hexapod = [0.01; 0; 0]; <span class="org-comment">% [m]</span>
 </pre>
 </div>
 
@@ -437,7 +432,7 @@ We first set the wanted translation of the Micro Hexapod.
 We initialize the reference path.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Dh_pos'</span>, [P_micro_hexapod; 0; 0; 0], <span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
 </pre>
 </div>
 
@@ -445,7 +440,7 @@ We initialize the reference path.
 We initialize the stages.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeMicroHexapod('AP', P_micro_hexapod);
+<pre class="src src-matlab">  initializeMicroHexapod(<span class="org-string">'AP'</span>, P_micro_hexapod);
 </pre>
 </div>
 
@@ -453,13 +448,13 @@ We initialize the stages.
 And we initialize the disturbances to zero.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances(...
-    'Dwx', false, ... % Ground Motion - X direction
-    'Dwy', false, ... % Ground Motion - Y direction
-    'Dwz', false, ... % Ground Motion - Z direction
-    'Fty_x', false, ... % Translation Stage - X direction
-    'Fty_z', false, ... % Translation Stage - Z direction
-    'Frz_z', false  ... % Spindle - Z direction
+<pre class="src src-matlab">  initializeDisturbances(...
+      <span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
+      <span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
+      <span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
+      <span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
+      <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
+      <span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span>  ...<span class="org-comment"> % Spindle - Z direction</span>
       );
 </pre>
 </div>
@@ -468,7 +463,7 @@ And we initialize the disturbances to zero.
 We simulate the model.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">sim('nass_model');
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
@@ -476,23 +471,23 @@ We simulate the model.
 And we save the obtained data.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">tomo_not_align = simout;
-save('./mat/experiment_tomography.mat', 'tomo_not_align', '-append');
+<pre class="src src-matlab">  tomo_not_align = simout;
+  save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_not_align'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-org6dc8ae4" class="outline-3">
-<h3 id="org6dc8ae4"><span class="section-number-3">5.2</span> Analysis</h3>
+<div id="outline-container-org012e268" class="outline-3">
+<h3 id="org012e268"><span class="section-number-3">5.2</span> Analysis</h3>
 <div class="outline-text-3" id="text-5-2">
 <div class="org-src-container">
-<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_not_align', 'tomo_align_no_dist');
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_not_align'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
 </pre>
 </div>
 
 
-<div id="orgb824a01" class="figure">
+<div id="orge17b520" class="figure">
 <p><img src="figs/exp_tomo_offset.png" alt="exp_tomo_offset.png" />
 </p>
 <p><span class="figure-number">Figure 4: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset.png">png</a>, <a href="./figs/exp_tomo_offset.pdf">pdf</a>)</p>
@@ -500,10 +495,10 @@ save('./mat/experiment_tomography.mat', 'tomo_not_align', '-append');
 </div>
 </div>
 
-<div id="outline-container-orgb632268" class="outline-3">
-<h3 id="orgb632268"><span class="section-number-3">5.3</span> Conclusion</h3>
+<div id="outline-container-org75b29bc" class="outline-3">
+<h3 id="org75b29bc"><span class="section-number-3">5.3</span> Conclusion</h3>
 <div class="outline-text-3" id="text-5-3">
-<div class="important">
+<div class="important" id="org970013d">
 <p>
 The main motion error are 1Hz X-Y translations and constant Ry error.
 This is mainly due to finite stiffness of the elements.
@@ -514,33 +509,33 @@ This is mainly due to finite stiffness of the elements.
 </div>
 </div>
 
-<div id="outline-container-org8fa1632" class="outline-2">
-<h2 id="org8fa1632"><span class="section-number-2">6</span> Raster Scans with the translation stage</h2>
+<div id="outline-container-org3ba6838" class="outline-2">
+<h2 id="org3ba6838"><span class="section-number-2">6</span> Raster Scans with the translation stage</h2>
 <div class="outline-text-2" id="text-6">
 <p>
-<a id="org6aaeb53"></a>
+<a id="orgeec7f3c"></a>
 </p>
 <p>
 In this section, scans with the translation stage are performed.
 </p>
 </div>
-<div id="outline-container-orgdd9a5de" class="outline-3">
-<h3 id="orgdd9a5de"><span class="section-number-3">6.1</span> Simulation Setup</h3>
+<div id="outline-container-org5f4e508" class="outline-3">
+<h3 id="org5f4e508"><span class="section-number-3">6.1</span> Simulation Setup</h3>
 <div class="outline-text-3" id="text-6-1">
 <p>
 We initialize the stages.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeGround();
-initializeGranite();
-initializeTy();
-initializeRy();
-initializeRz();
-initializeMicroHexapod();
-initializeAxisc();
-initializeMirror();
-initializeNanoHexapod('type', 'rigid');
-initializeSample('mass', 1);
+<pre class="src src-matlab">  initializeGround();
+  initializeGranite();
+  initializeTy();
+  initializeRy();
+  initializeRz();
+  initializeMicroHexapod();
+  initializeAxisc();
+  initializeMirror();
+  initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
+  initializeSample(<span class="org-string">'mass'</span>, 1);
 </pre>
 </div>
 
@@ -548,13 +543,13 @@ initializeSample('mass', 1);
 And we initialize the disturbances to zero.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeDisturbances(...
-    'Dwx', false, ... % Ground Motion - X direction
-    'Dwy', false, ... % Ground Motion - Y direction
-    'Dwz', false, ... % Ground Motion - Z direction
-    'Fty_x', false, ... % Translation Stage - X direction
-    'Fty_z', false, ... % Translation Stage - Z direction
-    'Frz_z', false  ... % Spindle - Z direction
+<pre class="src src-matlab">  initializeDisturbances(...
+      <span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
+      <span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
+      <span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
+      <span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
+      <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
+      <span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span>  ...<span class="org-comment"> % Spindle - Z direction</span>
       );
 </pre>
 </div>
@@ -563,7 +558,7 @@ And we initialize the disturbances to zero.
 We set the reference path to be a triangular signal for the Translation Stage.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Dy_type'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'Dy_amplitude'</span>, 10e<span class="org-type">-</span>3, <span class="org-string">'Dy_period'</span>, 1);
 </pre>
 </div>
 
@@ -571,7 +566,7 @@ We set the reference path to be a triangular signal for the Translation Stage.
 We simulate the model.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">sim('nass_model');
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
@@ -579,8 +574,8 @@ We simulate the model.
 And we save the obtained data.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">ty_scan_triangle = simout;
-save('./mat/experiment_tomography.mat', 'ty_scan_triangle', '-append');
+<pre class="src src-matlab">  ty_scan_triangle = simout;
+  save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'ty_scan_triangle'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 
@@ -588,7 +583,7 @@ save('./mat/experiment_tomography.mat', 'ty_scan_triangle', '-append');
 We now set the reference path to be a sinusoidal signal for the Translation Stage.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">initializeReferences('Dy_type', 'sinusoidal', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
+<pre class="src src-matlab">  initializeReferences(<span class="org-string">'Dy_type'</span>, <span class="org-string">'sinusoidal'</span>, <span class="org-string">'Dy_amplitude'</span>, 10e<span class="org-type">-</span>3, <span class="org-string">'Dy_period'</span>, 1);
 </pre>
 </div>
 
@@ -596,7 +591,7 @@ We now set the reference path to be a sinusoidal signal for the Translation Stag
 We simulate the model.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">sim('nass_model');
+<pre class="src src-matlab">  <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
 </pre>
 </div>
 
@@ -604,23 +599,23 @@ We simulate the model.
 And we save the obtained data.
 </p>
 <div class="org-src-container">
-<pre class="src src-matlab">ty_scan_sinus = simout;
-save('./mat/experiment_tomography.mat', 'ty_scan_sinus', '-append');
+<pre class="src src-matlab">  ty_scan_sinus = simout;
+  save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'ty_scan_sinus'</span>, <span class="org-string">'-append'</span>);
 </pre>
 </div>
 </div>
 </div>
 
-<div id="outline-container-orgad49d2c" class="outline-3">
-<h3 id="orgad49d2c"><span class="section-number-3">6.2</span> Analysis</h3>
+<div id="outline-container-orgf069548" class="outline-3">
+<h3 id="orgf069548"><span class="section-number-3">6.2</span> Analysis</h3>
 <div class="outline-text-3" id="text-6-2">
 <div class="org-src-container">
-<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'ty_scan_triangle', 'ty_scan_sinus');
+<pre class="src src-matlab">  load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'ty_scan_triangle'</span>, <span class="org-string">'ty_scan_sinus'</span>);
 </pre>
 </div>
 
 
-<div id="org888f0bf" class="figure">
+<div id="orgebbbb99" class="figure">
 <p><img src="figs/exp_ty_scan.png" alt="exp_ty_scan.png" />
 </p>
 <p><span class="figure-number">Figure 5: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan.png">png</a>, <a href="./figs/exp_ty_scan.pdf">pdf</a>)</p>
@@ -628,10 +623,10 @@ save('./mat/experiment_tomography.mat', 'ty_scan_sinus', '-append');
 </div>
 </div>
 
-<div id="outline-container-org57c774f" class="outline-3">
-<h3 id="org57c774f"><span class="section-number-3">6.3</span> Conclusion</h3>
+<div id="outline-container-org3446ba0" class="outline-3">
+<h3 id="org3446ba0"><span class="section-number-3">6.3</span> Conclusion</h3>
 <div class="outline-text-3" id="text-6-3">
-<div class="important">
+<div class="important" id="orgf5f4292">
 <p>
 Scans with the translation stage induces some errors in the Y direction and Rx translations.
 </p>
@@ -648,7 +643,7 @@ Thus, this should be preferred.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-05-05 mar. 10:34</p>
+<p class="date">Created: 2021-02-20 sam. 23:08</p>
 </div>
 </body>
 </html>