Update Analysis

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Thomas Dehaeze 2019-10-25 12:33:08 +02:00
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@ -3,7 +3,7 @@
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2019-10-24 jeu. 17:44 --> <!-- 2019-10-25 ven. 12:32 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Simscape Uniaxial Model</title> <title>Simscape Uniaxial Model</title>
@ -246,6 +246,28 @@ for the JavaScript code in this tag.
} }
/*]]>*///--> /*]]>*///-->
</script> </script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
displayAlign: "center",
displayIndent: "0em",
"HTML-CSS": { scale: 100,
linebreaks: { automatic: "false" },
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</head> </head>
<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,51 +280,48 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orge60b193">1. Undamped System</a> <li><a href="#orgd9a890c">1. Simscape Model</a></li>
<li><a href="#orgeafc497">2. Undamped System</a>
<ul> <ul>
<li><a href="#org46cb925">1.1. Init</a></li> <li><a href="#org631c716">2.1. Init</a></li>
<li><a href="#orgbaff26c">1.2. Identification</a></li> <li><a href="#orgbbef650">2.2. Identification</a></li>
<li><a href="#orgf051d6b">1.3. Sensitivity to Disturbances</a></li> <li><a href="#orgb5102fd">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#org809a04d">1.4. Plant</a></li> <li><a href="#orgafe8970">2.4. Plant</a></li>
<li><a href="#orge7de64d">1.5. Save</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org0e4b7a2">2. Integral Force Feedback</a> <li><a href="#orgeab4870">3. Integral Force Feedback</a>
<ul> <ul>
<li><a href="#orge7eac97">2.1. Control Design</a></li> <li><a href="#org6cf62a2">3.1. Control Design</a></li>
<li><a href="#org1da475f">2.2. Identification</a></li> <li><a href="#orgf9a5f33">3.2. Identification</a></li>
<li><a href="#orgba751b8">2.3. Sensitivity to Disturbance</a></li> <li><a href="#org7a80859">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#org215411f">2.4. Damped Plant</a></li> <li><a href="#org7bab9e9">3.4. Damped Plant</a></li>
<li><a href="#org14fe313">2.5. Save</a></li> <li><a href="#orgaac01c0">3.5. Conclusion</a></li>
<li><a href="#org00d3320">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org6ef0786">3. Relative Motion Control</a> <li><a href="#org8d9b463">4. Relative Motion Control</a>
<ul> <ul>
<li><a href="#orgdcdfe4c">3.1. Control Design</a></li> <li><a href="#orgbf2540a">4.1. Control Design</a></li>
<li><a href="#orgc768160">3.2. Identification</a></li> <li><a href="#org1d106d7">4.2. Identification</a></li>
<li><a href="#org340b3bb">3.3. Sensitivity to Disturbance</a></li> <li><a href="#orgeb7d680">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#org67127eb">3.4. Damped Plant</a></li> <li><a href="#org573eda0">4.4. Damped Plant</a></li>
<li><a href="#org21a13ba">3.5. Save</a></li> <li><a href="#org02ca488">4.5. Conclusion</a></li>
<li><a href="#org6394f36">3.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org273e223">4. Direct Velocity Feedback</a> <li><a href="#org57948ea">5. Direct Velocity Feedback</a>
<ul> <ul>
<li><a href="#org254f765">4.1. Control Design</a></li> <li><a href="#org4b4d061">5.1. Control Design</a></li>
<li><a href="#org3f4f45f">4.2. Identification</a></li> <li><a href="#orgd4f4973">5.2. Identification</a></li>
<li><a href="#org580de8a">4.3. Sensitivity to Disturbance</a></li> <li><a href="#org6cfeae5">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#org5e7c1c3">4.4. Damped Plant</a></li> <li><a href="#org89e0408">5.4. Damped Plant</a></li>
<li><a href="#org0c0adf6">4.5. Save</a></li> <li><a href="#orgc27bce5">5.5. Conclusion</a></li>
<li><a href="#orgbbb2968">4.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org9720eac">5. Comparison of Active Damping Techniques</a> <li><a href="#org6dd07d9">6. Comparison of Active Damping Techniques</a>
<ul> <ul>
<li><a href="#org04bc1e0">5.1. Load the plants</a></li> <li><a href="#orgd62929a">6.1. Load the plants</a></li>
<li><a href="#orga979580">5.2. Sensitivity to Disturbance</a></li> <li><a href="#orgbd35b93">6.2. Sensitivity to Disturbance</a></li>
<li><a href="#orgc4c2c73">5.3. Damped Plant</a></li> <li><a href="#org72ab5fd">6.3. Damped Plant</a></li>
<li><a href="#org1c2b3da">5.4. Conclusion</a></li> <li><a href="#org2c43078">6.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -317,52 +336,102 @@ The idea is to use the same model as the full Simscape Model but to restrict the
This is done in order to more easily study the system and evaluate control techniques. This is done in order to more easily study the system and evaluate control techniques.
</p> </p>
<div id="outline-container-orge60b193" class="outline-2"> <div id="outline-container-orgd9a890c" class="outline-2">
<h2 id="orge60b193"><span class="section-number-2">1</span> Undamped System</h2> <h2 id="orgd9a890c"><span class="section-number-2">1</span> Simscape Model</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p>
A schematic of the uniaxial model used for simulations is represented in figure <a href="#org9234e2b">1</a>.
</p>
<p>
The perturbations \(w\) are:
</p>
<ul class="org-ul">
<li>\(F_s\): direct forces applied to the sample such as inertia forces and cable forces</li>
<li>\(F_{rz}\): parasitic forces due to the rotation of the spindle</li>
<li>\(F_{ty}\): parasitic forces due to scans with the translation stage</li>
<li>\(D_w\): ground motion</li>
</ul>
<p>
The quantity to \(z\) to control is:
</p>
<ul class="org-ul">
<li>\(D\): the position of the sample with respect to the granite</li>
</ul>
<p>
The measured quantities \(v\) are:
</p>
<ul class="org-ul">
<li>\(D\): the position of the sample with respect to the granite</li>
</ul>
<p>
We study the use of an additional sensor:
</p>
<ul class="org-ul">
<li>\(F_n\): a force sensor located in the nano-hexapod</li>
<li>\(v_n\): an absolute velocity sensor located on the top platform of the nano-hexapod</li>
<li>\(d_r\): a relative motion sensor located in the nano-hexapod</li>
</ul>
<p>
The control signal \(u\) is:
</p>
<ul class="org-ul">
<li>\(F\) the force applied by the nano-hexapod actuator</li>
</ul>
<div id="org9234e2b" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible.png" alt="uniaxial-model-nass-flexible.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Schematic of the uniaxial model used</p>
</div> </div>
<div id="outline-container-org46cb925" class="outline-3">
<h3 id="org46cb925"><span class="section-number-3">1.1</span> Init</h3>
<div class="outline-text-3" id="text-1-1"> <p>
Few active damping techniques will be compared in order to decide which sensor is to be included in the system.
Schematics of the active damping techniques are displayed in figure <a href="#org49f5486">2</a>.
</p>
<div id="org49f5486" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-active-damping.png" alt="uniaxial-model-nass-flexible-active-damping.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Comparison of used active damping techniques</p>
</div>
</div>
</div>
<div id="outline-container-orgeafc497" class="outline-2">
<h2 id="orgeafc497"><span class="section-number-2">2</span> Undamped System</h2>
<div class="outline-text-2" id="text-2">
<p>
Let's start by study the undamped system.
</p>
</div>
<div id="outline-container-org631c716" class="outline-3">
<h3 id="org631c716"><span class="section-number-3">2.1</span> Init</h3>
<div class="outline-text-3" id="text-2-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg. The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
</p> </p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p> <p>
All the controllers are set to 0. All the controllers are set to 0 (Open Loop).
</p> </p>
<div class="org-src-container">
<pre class="src src-matlab">K = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_iff = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_rmc = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
K_dvf = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div> </div>
</div> </div>
</div> <div id="outline-container-orgbbef650" class="outline-3">
<h3 id="orgbbef650"><span class="section-number-3">2.2</span> Identification</h3>
<div id="outline-container-orgbaff26c" class="outline-3"> <div class="outline-text-3" id="text-2-2">
<h3 id="orgbaff26c"><span class="section-number-3">1.2</span> Identification</h3> <p>
<div class="outline-text-3" id="text-1-2"> We identify the dynamics of the system.
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span> <pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
options = linearizeOptions; options = linearizeOptions;
@ -373,6 +442,9 @@ mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
</pre> </pre>
</div> </div>
<p>
The inputs and outputs are defined below and corresponds to the name of simulink blocks.
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span> <pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span> io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
@ -389,6 +461,9 @@ io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highligh
</pre> </pre>
</div> </div>
<p>
Finally, we use the <code>linearize</code> Matlab function to extract a state space model from the simscape model.
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span> <pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>; G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
@ -404,62 +479,79 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span> <span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre> </pre>
</div> </div>
</div>
</div>
<div id="outline-container-orgf051d6b" class="outline-3"> <p>
<h3 id="orgf051d6b"><span class="section-number-3">1.3</span> Sensitivity to Disturbances</h3> Finally, we save the identified system dynamics for further analysis.
<div class="outline-text-3" id="text-1-3">
<div id="org4bc7134" class="figure">
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-disturbances.pdf">pdf</a>)</p>
</div>
<div id="orga192bc9" class="figure">
<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-force-dist.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org809a04d" class="outline-3">
<h3 id="org809a04d"><span class="section-number-3">1.4</span> Plant</h3>
<div class="outline-text-3" id="text-1-4">
<div id="org1f07ded" class="figure">
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orge7de64d" class="outline-3">
<h3 id="orge7de64d"><span class="section-number-3">1.5</span> Save</h3>
<div class="outline-text-3" id="text-1-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgb5102fd" class="outline-3">
<h3 id="orgb5102fd"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We show several plots representing the sensitivity to disturbances:
</p>
<ul class="org-ul">
<li>in figure <a href="#orge3abf0f">3</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
<li>in figure <a href="#org25d95cb">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
</ul>
<div id="orge3abf0f" class="figure">
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-disturbances.pdf">pdf</a>)</p>
</div> </div>
<div id="outline-container-org0e4b7a2" class="outline-2">
<h2 id="org0e4b7a2"><span class="section-number-2">2</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-2"> <div id="org25d95cb" class="figure">
<p> <p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
<a id="org8efbd63"></a>
</p> </p>
<p><span class="figure-number">Figure 4: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-force-dist.pdf">pdf</a>)</p>
</div> </div>
<div id="outline-container-orge7eac97" class="outline-3"> </div>
<h3 id="orge7eac97"><span class="section-number-3">2.1</span> Control Design</h3> </div>
<div class="outline-text-3" id="text-2-1">
<div id="outline-container-orgafe8970" class="outline-3">
<h3 id="orgafe8970"><span class="section-number-3">2.4</span> Plant</h3>
<div class="outline-text-3" id="text-2-4">
<p>
The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#org62d1d12">5</a>.
It corresponds to the plant to control.
</p>
<div id="org62d1d12" class="figure">
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
</div>
</div>
</div>
</div>
<div id="outline-container-orgeab4870" class="outline-2">
<h2 id="orgeab4870"><span class="section-number-2">3</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org04c8f6e"></a>
</p>
<div id="orge50f87e" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Uniaxial IFF Control Schematic</p>
</div>
</div>
<div id="outline-container-org6cf62a2" class="outline-3">
<h3 id="org6cf62a2"><span class="section-number-3">3.1</span> Control Design</h3>
<div class="outline-text-3" id="text-3-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
@ -470,10 +562,10 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
</p> </p>
<div id="org07202e9" class="figure"> <div id="org26ea3c1" class="figure">
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" /> <p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 7: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p>
</div> </div>
<p> <p>
@ -485,17 +577,17 @@ The controller for each pair of actuator/sensor is:
</div> </div>
<div id="org4918c15" class="figure"> <div id="org27d1bb0" class="figure">
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" /> <p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 8: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1da475f" class="outline-3"> <div id="outline-container-orgf9a5f33" class="outline-3">
<h3 id="org1da475f"><span class="section-number-3">2.2</span> Identification</h3> <h3 id="orgf9a5f33"><span class="section-number-3">3.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
</p> </p>
@ -569,43 +661,7 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span> <span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre> </pre>
</div> </div>
</div>
</div>
<div id="outline-container-orgba751b8" class="outline-3">
<h3 id="orgba751b8"><span class="section-number-3">2.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-2-3">
<div id="org433ca31" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
</div>
<div id="org129b2c0" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org215411f" class="outline-3">
<h3 id="org215411f"><span class="section-number-3">2.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-2-4">
<div id="org9cbc1b3" class="figure">
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org14fe313" class="outline-3">
<h3 id="org14fe313"><span class="section-number-3">2.5</span> Save</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
@ -613,9 +669,40 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-org00d3320" class="outline-3"> <div id="outline-container-org7a80859" class="outline-3">
<h3 id="org00d3320"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org7a80859"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-3-3">
<div id="orgca12220" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
</div>
<div id="org19c25c8" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org7bab9e9" class="outline-3">
<h3 id="org7bab9e9"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-4">
<div id="org60ea1f1" class="figure">
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orgaac01c0" class="outline-3">
<h3 id="orgaac01c0"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5">
<div class="important"> <div class="important">
<p> <p>
Integral Force Feedback: Integral Force Feedback:
@ -626,19 +713,26 @@ Integral Force Feedback:
</div> </div>
</div> </div>
<div id="outline-container-org6ef0786" class="outline-2"> <div id="outline-container-org8d9b463" class="outline-2">
<h2 id="org6ef0786"><span class="section-number-2">3</span> Relative Motion Control</h2> <h2 id="org8d9b463"><span class="section-number-2">4</span> Relative Motion Control</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-4">
<p> <p>
<a id="orgd075f22"></a> <a id="orgdc4ae31"></a>
</p> </p>
<p> <p>
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input. In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
</p> </p>
<div id="org46f85ef" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Uniaxial RMC Control Schematic</p>
</div> </div>
<div id="outline-container-orgdcdfe4c" class="outline-3"> </div>
<h3 id="orgdcdfe4c"><span class="section-number-3">3.1</span> Control Design</h3> <div id="outline-container-orgbf2540a" class="outline-3">
<div class="outline-text-3" id="text-3-1"> <h3 id="orgbf2540a"><span class="section-number-3">4.1</span> Control Design</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
@ -649,10 +743,10 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
</p> </p>
<div id="orgd4c9455" class="figure"> <div id="orgc47e343" class="figure">
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" /> <p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 13: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p>
</div> </div>
<p> <p>
@ -665,17 +759,17 @@ A Low pass Filter is added to make the controller transfer function proper.
</div> </div>
<div id="orgde55454" class="figure"> <div id="org9c157b6" class="figure">
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" /> <p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 14: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgc768160" class="outline-3"> <div id="outline-container-org1d106d7" class="outline-3">
<h3 id="orgc768160"><span class="section-number-3">3.2</span> Identification</h3> <h3 id="org1d106d7"><span class="section-number-3">4.2</span> Identification</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-4-2">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
</p> </p>
@ -749,44 +843,7 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span> <span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre> </pre>
</div> </div>
</div>
</div>
<div id="outline-container-org340b3bb" class="outline-3">
<h3 id="org340b3bb"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-3-3">
<div id="orgc8a11d1" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
</div>
<div id="org919dd9d" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org67127eb" class="outline-3">
<h3 id="org67127eb"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-4">
<div id="org8490305" class="figure">
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org21a13ba" class="outline-3">
<h3 id="org21a13ba"><span class="section-number-3">3.5</span> Save</h3>
<div class="outline-text-3" id="text-3-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
@ -794,9 +851,41 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-org6394f36" class="outline-3">
<h3 id="org6394f36"><span class="section-number-3">3.6</span> Conclusion</h3> <div id="outline-container-orgeb7d680" class="outline-3">
<div class="outline-text-3" id="text-3-6"> <h3 id="orgeb7d680"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-4-3">
<div id="org7a8bd68" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
</div>
<div id="orgb8fed93" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org573eda0" class="outline-3">
<h3 id="org573eda0"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-4">
<div id="org1f8e935" class="figure">
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org02ca488" class="outline-3">
<h3 id="org02ca488"><span class="section-number-3">4.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-5">
<div class="important"> <div class="important">
<p> <p>
Relative Motion Control: Relative Motion Control:
@ -807,29 +896,36 @@ Relative Motion Control:
</div> </div>
</div> </div>
<div id="outline-container-org273e223" class="outline-2"> <div id="outline-container-org57948ea" class="outline-2">
<h2 id="org273e223"><span class="section-number-2">4</span> Direct Velocity Feedback</h2> <h2 id="org57948ea"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-5">
<p> <p>
<a id="org5a18f77"></a> <a id="orgdd11541"></a>
</p> </p>
<p> <p>
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input. In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
</p> </p>
<div id="org0fcd7e7" class="figure">
<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Uniaxial DVF Control Schematic</p>
</div> </div>
<div id="outline-container-org254f765" class="outline-3"> </div>
<h3 id="org254f765"><span class="section-number-3">4.1</span> Control Design</h3> <div id="outline-container-org4b4d061" class="outline-3">
<div class="outline-text-3" id="text-4-1"> <h3 id="org4b4d061"><span class="section-number-3">5.1</span> Control Design</h3>
<div class="outline-text-3" id="text-5-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="org505b157" class="figure"> <div id="orgbf7145f" class="figure">
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" /> <p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 19: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
@ -838,17 +934,17 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div> </div>
<div id="org3ef68bd" class="figure"> <div id="org1b6adf4" class="figure">
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" /> <p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 20: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org3f4f45f" class="outline-3"> <div id="outline-container-orgd4f4973" class="outline-3">
<h3 id="org3f4f45f"><span class="section-number-3">4.2</span> Identification</h3> <h3 id="orgd4f4973"><span class="section-number-3">5.2</span> Identification</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-5-2">
<p> <p>
Let's initialize the system prior to identification. Let's initialize the system prior to identification.
</p> </p>
@ -922,43 +1018,7 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span> <span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
</pre> </pre>
</div> </div>
</div>
</div>
<div id="outline-container-org580de8a" class="outline-3">
<h3 id="org580de8a"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-4-3">
<div id="orged4b1f3" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
</div>
<div id="org151dc83" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org5e7c1c3" class="outline-3">
<h3 id="org5e7c1c3"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-4">
<div id="orgfb4eb8b" class="figure">
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org0c0adf6" class="outline-3">
<h3 id="org0c0adf6"><span class="section-number-3">4.5</span> Save</h3>
<div class="outline-text-3" id="text-4-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
@ -966,9 +1026,40 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
</div> </div>
</div> </div>
<div id="outline-container-orgbbb2968" class="outline-3"> <div id="outline-container-org6cfeae5" class="outline-3">
<h3 id="orgbbb2968"><span class="section-number-3">4.6</span> Conclusion</h3> <h3 id="org6cfeae5"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-4-6"> <div class="outline-text-3" id="text-5-3">
<div id="org6fb6e94" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
</p>
<p><span class="figure-number">Figure 21: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
</div>
<div id="org6f13385" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
</p>
<p><span class="figure-number">Figure 22: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-org89e0408" class="outline-3">
<h3 id="org89e0408"><span class="section-number-3">5.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-4">
<div id="org7051238" class="figure">
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
</p>
<p><span class="figure-number">Figure 23: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orgc27bce5" class="outline-3">
<h3 id="orgc27bce5"><span class="section-number-3">5.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-5">
<div class="important"> <div class="important">
<p> <p>
Direct Velocity Feedback: Direct Velocity Feedback:
@ -978,16 +1069,16 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org9720eac" class="outline-2"> <div id="outline-container-org6dd07d9" class="outline-2">
<h2 id="org9720eac"><span class="section-number-2">5</span> Comparison of Active Damping Techniques</h2> <h2 id="org6dd07d9"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-6">
<p> <p>
<a id="org7404a5b"></a> <a id="org5272a4c"></a>
</p> </p>
</div> </div>
<div id="outline-container-org04bc1e0" class="outline-3"> <div id="outline-container-orgd62929a" class="outline-3">
<h3 id="org04bc1e0"><span class="section-number-3">5.1</span> Load the plants</h3> <h3 id="orgd62929a"><span class="section-number-3">6.1</span> Load the plants</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-6-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'G_dvf'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'G_dvf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
@ -995,44 +1086,126 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
<div id="outline-container-orga979580" class="outline-3"> <div id="outline-container-orgbd35b93" class="outline-3">
<h3 id="orga979580"><span class="section-number-3">5.2</span> Sensitivity to Disturbance</h3> <h3 id="orgbd35b93"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-6-2">
<div id="org076a7e7" class="figure"> <div id="org5eda09f" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_comp.png" alt="uniaxial_sensitivity_dist_comp.png" /> <p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
</p> </p>
<p><span class="figure-number">Figure 19: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_dist_comp.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_comp.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 24: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
</div> </div>
<div id="orgd0777da" class="figure">
<p><img src="figs/uniaxial_sensitivity_dist_stages_comp.png" alt="uniaxial_sensitivity_dist_stages_comp.png" /> <div id="org1fae0e7" class="figure">
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
</p> </p>
<p><span class="figure-number">Figure 20: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_dist_stages_comp.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_comp.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 25: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
</div>
<div id="orgb2bd39c" class="figure">
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
</p>
<p><span class="figure-number">Figure 26: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
</div>
<div id="org1f00826" class="figure">
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
</p>
<p><span class="figure-number">Figure 27: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgc4c2c73" class="outline-3"> <div id="outline-container-org72ab5fd" class="outline-3">
<h3 id="orgc4c2c73"><span class="section-number-3">5.3</span> Damped Plant</h3> <h3 id="org72ab5fd"><span class="section-number-3">6.3</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-6-3">
<div id="orge2efd1a" class="figure"> <div id="org0296cfa" class="figure">
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" /> <p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 21: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 28: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1c2b3da" class="outline-3">
<h3 id="org1c2b3da"><span class="section-number-3">5.4</span> Conclusion</h3> <div id="outline-container-org2c43078" class="outline-3">
<h3 id="org2c43078"><span class="section-number-3">6.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-6-4">
<table id="orga82a170" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Comparison of proposed active damping techniques</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-left">IFF</th>
<th scope="col" class="org-left">RMC</th>
<th scope="col" class="org-left">DVF</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Sensor Type</td>
<td class="org-left">Force sensor</td>
<td class="org-left">Relative Motion</td>
<td class="org-left">Inertial</td>
</tr>
<tr>
<td class="org-left">Guaranteed Stability</td>
<td class="org-left">+</td>
<td class="org-left">+</td>
<td class="org-left">-</td>
</tr>
<tr>
<td class="org-left">Sensitivity (\(D_w\))</td>
<td class="org-left">-</td>
<td class="org-left">+</td>
<td class="org-left">-</td>
</tr>
<tr>
<td class="org-left">Sensitivity (\(F_s\))</td>
<td class="org-left">- (at low freq)</td>
<td class="org-left">+</td>
<td class="org-left">+</td>
</tr>
<tr>
<td class="org-left">Sensitivity (\(F_{ty,rz}\))</td>
<td class="org-left">+</td>
<td class="org-left">-</td>
<td class="org-left">+</td>
</tr>
</tbody>
</table>
<div class="important">
<p>
The next step is to take into account the power spectral density of each disturbance.
</p>
</div>
</div>
</div> </div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-24 jeu. 17:44</p> <p class="date">Created: 2019-10-25 ven. 12:32</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>

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