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<title>Active Damping applied on the Simscape Model</title>
@@ -195,13 +194,13 @@
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@@ -261,9 +260,9 @@ for the JavaScript code in this tag.
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<a accesskey="h" href="../index.html"> UP </a>
<a accesskey="h" href="./index.html"> UP </a>
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</div><div id="content">
<h1 class="title">Active Damping applied on the Simscape Model</h1>
<div id="table-of-contents">
@@ -274,17 +273,17 @@ for the JavaScript code in this tag.
<ul>
<li><a href="#orga668d6d">1.1. Identification of the dynamics for Active Damping</a>
<ul>
<li><a href="#orgbaab9df">1.1.1. Identification</a></li>
<li><a href="#orgd1a656e">1.1.1. Identification</a></li>
<li><a href="#orge632d78">1.1.2. Obtained Plants for Active Damping</a></li>
</ul>
</li>
<li><a href="#orgacbac97">1.2. Identification of the dynamics for High Authority Control</a>
<ul>
<li><a href="#orgd1a656e">1.2.1. Identification</a></li>
<li><a href="#org9dde5ce">1.2.1. Identification</a></li>
<li><a href="#org245ebc9">1.2.2. Obtained Plants</a></li>
</ul>
</li>
<li><a href="#org072b32a">1.3. Tomography Experiment</a>
<li><a href="#orgc633a52">1.3. Tomography Experiment</a>
<ul>
<li><a href="#orgd2384a9">1.3.1. Simulation</a></li>
<li><a href="#orgd00d359">1.3.2. Results</a></li>
@@ -304,55 +303,55 @@ for the JavaScript code in this tag.
</li>
<li><a href="#org89179a2">2.4. Variation of the Tilt Angle</a></li>
<li><a href="#org701d7f3">2.5. Scans of the Translation Stage</a></li>
<li><a href="#orga697040">2.6. Conclusion</a></li>
<li><a href="#org1b61fb2">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org28bb8b8">3. Integral Force Feedback</a>
<ul>
<li><a href="#orga2142db">3.1. Control Design</a>
<li><a href="#org8147539">3.1. Control Design</a>
<ul>
<li><a href="#orgcf1bf17">3.1.1. Plant</a></li>
<li><a href="#orgaca3b16">3.1.2. Control Design</a></li>
<li><a href="#org39a3259">3.1.3. Diagonal Controller</a></li>
<li><a href="#org7579fa1">3.1.1. Plant</a></li>
<li><a href="#org1069779">3.1.2. Control Design</a></li>
<li><a href="#org0929a5f">3.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#orge945074">3.2. Tomography Experiment</a>
<li><a href="#org92b7e4a">3.2. Tomography Experiment</a>
<ul>
<li><a href="#orge827289">3.2.1. Simulation with IFF Controller</a></li>
<li><a href="#org0ca3dfa">3.2.2. Compare with Undamped system</a></li>
<li><a href="#org34c04f2">3.2.2. Compare with Undamped system</a></li>
</ul>
</li>
<li><a href="#orge036b39">3.3. Conclusion</a></li>
<li><a href="#orge208898">3.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#orge2515a1">4. Direct Velocity Feedback</a>
<ul>
<li><a href="#org7a0849a">4.1. Control Design</a>
<li><a href="#org2454b5d">4.1. Control Design</a>
<ul>
<li><a href="#org9a95e47">4.1.1. Plant</a></li>
<li><a href="#orgb9858c3">4.1.2. Control Design</a></li>
<li><a href="#orgb9638f1">4.1.3. Diagonal Controller</a></li>
<li><a href="#orgd36a459">4.1.1. Plant</a></li>
<li><a href="#orgf771969">4.1.2. Control Design</a></li>
<li><a href="#org1fa78ea">4.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#orgc633a52">4.2. Tomography Experiment</a>
<li><a href="#orgdc2cc7d">4.2. Tomography Experiment</a>
<ul>
<li><a href="#org4d239c9">4.2.1. Initialize the Simulation</a></li>
<li><a href="#org34c04f2">4.2.2. Compare with Undamped system</a></li>
<li><a href="#org315e901">4.2.1. Initialize the Simulation</a></li>
<li><a href="#orgbe122b9">4.2.2. Compare with Undamped system</a></li>
</ul>
</li>
<li><a href="#org24a50bf">4.3. Conclusion</a></li>
<li><a href="#org2edf5bd">4.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org5047e99">5. Inertial Control</a>
<ul>
<li><a href="#org1069779">5.1. Control Design</a>
<li><a href="#org5bec512">5.1. Control Design</a>
<ul>
<li><a href="#org7579fa1">5.1.1. Plant</a></li>
<li><a href="#orgc4c6a5a">5.1.2. Control Design</a></li>
<li><a href="#org0929a5f">5.1.3. Diagonal Controller</a></li>
<li><a href="#org16795b0">5.1.1. Plant</a></li>
<li><a href="#org9ce4e10">5.1.2. Control Design</a></li>
<li><a href="#org132c666">5.1.3. Diagonal Controller</a></li>
</ul>
</li>
<li><a href="#org1b61fb2">5.2. Conclusion</a></li>
<li><a href="#org408de58">5.2. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgd2a9c18">6. Comparison</a>
@@ -367,16 +366,16 @@ for the JavaScript code in this tag.
<ul>
<li><a href="#orgcf56890">7.1. prepareLinearizeIdentification</a>
<ul>
<li><a href="#org56ccd79">Function Description</a></li>
<li><a href="#orgdbd3a09">Optional Parameters</a></li>
<li><a href="#orgdd3adc1">Initialize the Simulation</a></li>
<li><a href="#org2b7c7da">Function Description</a></li>
<li><a href="#org6e16103">Optional Parameters</a></li>
<li><a href="#org552f1ca">Initialize the Simulation</a></li>
</ul>
</li>
<li><a href="#orgc2b4408">7.2. prepareTomographyExperiment</a>
<ul>
<li><a href="#org2b7c7da">Function Description</a></li>
<li><a href="#org6e16103">Optional Parameters</a></li>
<li><a href="#org315e901">Initialize the Simulation</a></li>
<li><a href="#org6dacc19">Function Description</a></li>
<li><a href="#org65022a7">Optional Parameters</a></li>
<li><a href="#orga0e6a80">Initialize the Simulation</a></li>
</ul>
</li>
</ul>
@@ -448,8 +447,8 @@ After that, a tomography experiment is simulation without any active damping tec
<h3 id="orga668d6d"><span class="section-number-3">1.1</span> Identification of the dynamics for Active Damping</h3>
<div class="outline-text-3" id="text-1-1">
</div>
<div id="outline-container-orgbaab9df" class="outline-4">
<h4 id="orgbaab9df"><span class="section-number-4">1.1.1</span> Identification</h4>
<div id="outline-container-orgd1a656e" class="outline-4">
<h4 id="orgd1a656e"><span class="section-number-4">1.1.1</span> Identification</h4>
<div class="outline-text-4" id="text-1-1-1">
<p>
We initialize all the stages with the default parameters.
@@ -542,8 +541,8 @@ And we save them for further analysis.
<h3 id="orgacbac97"><span class="section-number-3">1.2</span> Identification of the dynamics for High Authority Control</h3>
<div class="outline-text-3" id="text-1-2">
</div>
<div id="outline-container-orgd1a656e" class="outline-4">
<h4 id="orgd1a656e"><span class="section-number-4">1.2.1</span> Identification</h4>
<div id="outline-container-org9dde5ce" class="outline-4">
<h4 id="org9dde5ce"><span class="section-number-4">1.2.1</span> Identification</h4>
<div class="outline-text-4" id="text-1-2-1">
<p>
We initialize all the stages with the default parameters.
@@ -612,8 +611,8 @@ And we save them for further analysis.
</div>
</div>
<div id="outline-container-org072b32a" class="outline-3">
<h3 id="org072b32a"><span class="section-number-3">1.3</span> Tomography Experiment</h3>
<div id="outline-container-orgc633a52" class="outline-3">
<h3 id="orgc633a52"><span class="section-number-3">1.3</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-1-3">
</div>
<div id="outline-container-orgd2384a9" class="outline-4">
@@ -1001,8 +1000,8 @@ We identify the dynamics at different positions (times) when scanning with the T
</div>
</div>
<div id="outline-container-orga697040" class="outline-3">
<h3 id="orga697040"><span class="section-number-3">2.6</span> Conclusion</h3>
<div id="outline-container-org1b61fb2" class="outline-3">
<h3 id="org1b61fb2"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<table id="org664ed44" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Conclusion on the variability of the system dynamics for active damping</caption>
@@ -1093,12 +1092,12 @@ The control architecture is represented in figure <a href="#org03ecebf">29</a> w
</div>
</div>
<div id="outline-container-orga2142db" class="outline-3">
<h3 id="orga2142db"><span class="section-number-3">3.1</span> Control Design</h3>
<div id="outline-container-org8147539" class="outline-3">
<h3 id="org8147539"><span class="section-number-3">3.1</span> Control Design</h3>
<div class="outline-text-3" id="text-3-1">
</div>
<div id="outline-container-orgcf1bf17" class="outline-4">
<h4 id="orgcf1bf17"><span class="section-number-4">3.1.1</span> Plant</h4>
<div id="outline-container-org7579fa1" class="outline-4">
<h4 id="org7579fa1"><span class="section-number-4">3.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-3-1-1">
<p>
Let&rsquo;s load the previously identified undamped plant:
@@ -1122,8 +1121,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div>
</div>
<div id="outline-container-orgaca3b16" class="outline-4">
<h4 id="orgaca3b16"><span class="section-number-4">3.1.2</span> Control Design</h4>
<div id="outline-container-org1069779" class="outline-4">
<h4 id="org1069779"><span class="section-number-4">3.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-3-1-2">
<p>
The controller for each pair of actuator/sensor is:
@@ -1147,8 +1146,8 @@ The corresponding loop gains are shown in figure <a href="#orge32c0c8">31</a>.
</div>
</div>
<div id="outline-container-org39a3259" class="outline-4">
<h4 id="org39a3259"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4>
<div id="outline-container-org0929a5f" class="outline-4">
<h4 id="org0929a5f"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-3-1-3">
<p>
We create the diagonal controller and we add a minus sign as we have a positive
@@ -1170,8 +1169,8 @@ We save the controller for further analysis.
</div>
</div>
<div id="outline-container-orge945074" class="outline-3">
<h3 id="orge945074"><span class="section-number-3">3.2</span> Tomography Experiment</h3>
<div id="outline-container-org92b7e4a" class="outline-3">
<h3 id="org92b7e4a"><span class="section-number-3">3.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-3-2">
</div>
<div id="outline-container-orge827289" class="outline-4">
@@ -1223,8 +1222,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-org0ca3dfa" class="outline-4">
<h4 id="org0ca3dfa"><span class="section-number-4">3.2.2</span> Compare with Undamped system</h4>
<div id="outline-container-org34c04f2" class="outline-4">
<h4 id="org34c04f2"><span class="section-number-4">3.2.2</span> Compare with Undamped system</h4>
<div class="outline-text-4" id="text-3-2-2">
<div id="orgc83ffab" class="figure">
@@ -1250,8 +1249,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-orge036b39" class="outline-3">
<h3 id="orge036b39"><span class="section-number-3">3.3</span> Conclusion</h3>
<div id="outline-container-orge208898" class="outline-3">
<h3 id="orge208898"><span class="section-number-3">3.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-3">
<div class="important">
<p>
@@ -1286,12 +1285,12 @@ The actuator displacement can be measured with a capacitive sensor for instance.
</p>
</div>
<div id="outline-container-org7a0849a" class="outline-3">
<h3 id="org7a0849a"><span class="section-number-3">4.1</span> Control Design</h3>
<div id="outline-container-org2454b5d" class="outline-3">
<h3 id="org2454b5d"><span class="section-number-3">4.1</span> Control Design</h3>
<div class="outline-text-3" id="text-4-1">
</div>
<div id="outline-container-org9a95e47" class="outline-4">
<h4 id="org9a95e47"><span class="section-number-4">4.1.1</span> Plant</h4>
<div id="outline-container-orgd36a459" class="outline-4">
<h4 id="orgd36a459"><span class="section-number-4">4.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-4-1-1">
<p>
Let&rsquo;s load the undamped plant:
@@ -1315,8 +1314,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div>
</div>
<div id="outline-container-orgb9858c3" class="outline-4">
<h4 id="orgb9858c3"><span class="section-number-4">4.1.2</span> Control Design</h4>
<div id="outline-container-orgf771969" class="outline-4">
<h4 id="orgf771969"><span class="section-number-4">4.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-4-1-2">
<p>
The Direct Velocity Feedback is defined below.
@@ -1340,8 +1339,8 @@ The obtained loop gains are shown in figure <a href="#org713f5d4">36</a>.
</div>
</div>
<div id="outline-container-orgb9638f1" class="outline-4">
<h4 id="orgb9638f1"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4>
<div id="outline-container-org1fa78ea" class="outline-4">
<h4 id="org1fa78ea"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-4-1-3">
<p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@@ -1362,12 +1361,12 @@ We save the controller for further analysis.
</div>
</div>
<div id="outline-container-orgc633a52" class="outline-3">
<h3 id="orgc633a52"><span class="section-number-3">4.2</span> Tomography Experiment</h3>
<div id="outline-container-orgdc2cc7d" class="outline-3">
<h3 id="orgdc2cc7d"><span class="section-number-3">4.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-4-2">
</div>
<div id="outline-container-org4d239c9" class="outline-4">
<h4 id="org4d239c9"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4>
<div id="outline-container-org315e901" class="outline-4">
<h4 id="org315e901"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-4-2-1">
<p>
We initialize elements for the tomography experiment.
@@ -1415,8 +1414,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-org34c04f2" class="outline-4">
<h4 id="org34c04f2"><span class="section-number-4">4.2.2</span> Compare with Undamped system</h4>
<div id="outline-container-orgbe122b9" class="outline-4">
<h4 id="orgbe122b9"><span class="section-number-4">4.2.2</span> Compare with Undamped system</h4>
<div class="outline-text-4" id="text-4-2-2">
<div id="orge2d1a4a" class="figure">
@@ -1442,8 +1441,8 @@ save(<span class="org-string">'./active_damping/mat/tomo_exp.mat'</span>, <span
</div>
</div>
<div id="outline-container-org24a50bf" class="outline-3">
<h3 id="org24a50bf"><span class="section-number-3">4.3</span> Conclusion</h3>
<div id="outline-container-org2edf5bd" class="outline-3">
<h3 id="org2edf5bd"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3">
<div class="important">
<p>
@@ -1475,12 +1474,12 @@ In Inertial Control, a feedback is applied between the measured <b>absolute</b>
</p>
</div>
<div id="outline-container-org1069779" class="outline-3">
<h3 id="org1069779"><span class="section-number-3">5.1</span> Control Design</h3>
<div id="outline-container-org5bec512" class="outline-3">
<h3 id="org5bec512"><span class="section-number-3">5.1</span> Control Design</h3>
<div class="outline-text-3" id="text-5-1">
</div>
<div id="outline-container-org7579fa1" class="outline-4">
<h4 id="org7579fa1"><span class="section-number-4">5.1.1</span> Plant</h4>
<div id="outline-container-org16795b0" class="outline-4">
<h4 id="org16795b0"><span class="section-number-4">5.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-5-1-1">
<p>
Let&rsquo;s load the undamped plant:
@@ -1504,8 +1503,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div>
</div>
<div id="outline-container-orgc4c6a5a" class="outline-4">
<h4 id="orgc4c6a5a"><span class="section-number-4">5.1.2</span> Control Design</h4>
<div id="outline-container-org9ce4e10" class="outline-4">
<h4 id="org9ce4e10"><span class="section-number-4">5.1.2</span> Control Design</h4>
<div class="outline-text-4" id="text-5-1-2">
<p>
The controller is defined below and the obtained loop gain is shown in figure <a href="#org76d929a">41</a>.
@@ -1525,8 +1524,8 @@ The controller is defined below and the obtained loop gain is shown in figure <a
</div>
</div>
<div id="outline-container-org0929a5f" class="outline-4">
<h4 id="org0929a5f"><span class="section-number-4">5.1.3</span> Diagonal Controller</h4>
<div id="outline-container-org132c666" class="outline-4">
<h4 id="org132c666"><span class="section-number-4">5.1.3</span> Diagonal Controller</h4>
<div class="outline-text-4" id="text-5-1-3">
<p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@@ -1547,8 +1546,8 @@ We save the controller for further analysis.
</div>
</div>
<div id="outline-container-org1b61fb2" class="outline-3">
<h3 id="org1b61fb2"><span class="section-number-3">5.2</span> Conclusion</h3>
<div id="outline-container-org408de58" class="outline-3">
<h3 id="org408de58"><span class="section-number-3">5.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-2">
<div class="important">
<p>
@@ -1724,9 +1723,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
</p>
</div>
<div id="outline-container-org56ccd79" class="outline-4">
<h4 id="org56ccd79">Function Description</h4>
<div class="outline-text-4" id="text-org56ccd79">
<div id="outline-container-org2b7c7da" class="outline-4">
<h4 id="org2b7c7da">Function Description</h4>
<div class="outline-text-4" id="text-org2b7c7da">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">prepareLinearizeIdentification</span>(<span class="org-variable-name">args</span>)
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@@ -1734,9 +1733,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
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<h4 id="orgdbd3a09">Optional Parameters</h4>
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<h4 id="org6e16103">Optional Parameters</h4>
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<pre class="src src-matlab">arguments
args.nass_actuator char {mustBeMember(args.nass_actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
@@ -1747,9 +1746,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
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<h4 id="orgdd3adc1">Initialize the Simulation</h4>
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<h4 id="org552f1ca">Initialize the Simulation</h4>
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We initialize all the stages with the default parameters.
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@@ -1822,9 +1821,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
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<h4 id="org2b7c7da">Function Description</h4>
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<h4 id="org6dacc19">Function Description</h4>
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<pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[]</span> = <span class="org-function-name">prepareTomographyExperiment</span>(<span class="org-variable-name">args</span>)
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@@ -1832,9 +1831,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
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<h4 id="org6e16103">Optional Parameters</h4>
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<h4 id="org65022a7">Optional Parameters</h4>
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<pre class="src src-matlab">arguments
args.nass_actuator char {mustBeMember(args.nass_actuator,{<span class="org-string">'piezo'</span>, <span class="org-string">'lorentz'</span>})} = <span class="org-string">'piezo'</span>
@@ -1846,9 +1845,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
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<h4 id="org315e901">Initialize the Simulation</h4>
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<h4 id="orga0e6a80">Initialize the Simulation</h4>
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We initialize all the stages with the default parameters.
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@@ -1916,7 +1915,7 @@ We log the signals.
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<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:07</p>
<p class="date">Created: 2020-02-25 mar. 18:20</p>
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