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<title>Active Damping applied on the Simscape Model</title>
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<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>)
</pre>
@ -1734,9 +1733,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
</div>
</div>
<div id="outline-container-orgdbd3a09" class="outline-4">
<h4 id="orgdbd3a09">Optional Parameters</h4>
<div class="outline-text-4" id="text-orgdbd3a09">
<div id="outline-container-org6e16103" class="outline-4">
<h4 id="org6e16103">Optional Parameters</h4>
<div class="outline-text-4" id="text-org6e16103">
<div class="org-src-container">
<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
</div>
</div>
<div id="outline-container-orgdd3adc1" class="outline-4">
<h4 id="orgdd3adc1">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-orgdd3adc1">
<div id="outline-container-org552f1ca" class="outline-4">
<h4 id="org552f1ca">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-org552f1ca">
<p>
We initialize all the stages with the default parameters.
</p>
@ -1822,9 +1821,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</p>
</div>
<div id="outline-container-org2b7c7da" class="outline-4">
<h4 id="org2b7c7da">Function Description</h4>
<div class="outline-text-4" id="text-org2b7c7da">
<div id="outline-container-org6dacc19" class="outline-4">
<h4 id="org6dacc19">Function Description</h4>
<div class="outline-text-4" id="text-org6dacc19">
<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">prepareTomographyExperiment</span>(<span class="org-variable-name">args</span>)
</pre>
@ -1832,9 +1831,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</div>
</div>
<div id="outline-container-org6e16103" class="outline-4">
<h4 id="org6e16103">Optional Parameters</h4>
<div class="outline-text-4" id="text-org6e16103">
<div id="outline-container-org65022a7" class="outline-4">
<h4 id="org65022a7">Optional Parameters</h4>
<div class="outline-text-4" id="text-org65022a7">
<div class="org-src-container">
<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
</div>
</div>
<div id="outline-container-org315e901" class="outline-4">
<h4 id="org315e901">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-org315e901">
<div id="outline-container-orga0e6a80" class="outline-4">
<h4 id="orga0e6a80">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-orga0e6a80">
<p>
We initialize all the stages with the default parameters.
</p>
@ -1916,7 +1915,7 @@ We log the signals.
</div>
<div id="postamble" class="status">
<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>
</div>
</body>
</html>

185
docs/active_damping_uniaxial.html
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@ -1,11 +1,10 @@
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@ -261,9 +260,9 @@ for the JavaScript code in this tag.
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</div><div id="content">
<h1 class="title">Active Damping with an uni-axial model</h1>
<div id="table-of-contents">
@ -274,63 +273,63 @@ for the JavaScript code in this tag.
<ul>
<li><a href="#org7409841">1.1. Init</a></li>
<li><a href="#org7514f31">1.2. Identification</a></li>
<li><a href="#org30a5b37">1.3. Sensitivity to disturbances</a></li>
<li><a href="#orgbc3b2d2">1.3. Sensitivity to disturbances</a></li>
<li><a href="#orgdda82c0">1.4. Undamped Plant</a></li>
</ul>
</li>
<li><a href="#org5a3389e">2. Integral Force Feedback</a>
<ul>
<li><a href="#orgf3a80f4">2.1. One degree-of-freedom example</a>
<li><a href="#org8fee25f">2.1. One degree-of-freedom example</a>
<ul>
<li><a href="#orgfba4e95">2.1.1. Equations</a></li>
<li><a href="#org8487491">2.1.2. Matlab Example</a></li>
<li><a href="#orge4d9f41">2.1.1. Equations</a></li>
<li><a href="#org3305ce8">2.1.2. Matlab Example</a></li>
</ul>
</li>
<li><a href="#orgf884e9a">2.2. Control Design</a></li>
<li><a href="#org55e3bff">2.3. Identification of the damped plant</a></li>
<li><a href="#org340a3d7">2.4. Sensitivity to disturbances</a></li>
<li><a href="#orgba948f4">2.5. Damped Plant</a></li>
<li><a href="#org8b5a4f4">2.6. Conclusion</a></li>
<li><a href="#orgc2ae0be">2.2. Control Design</a></li>
<li><a href="#org6eda033">2.3. Identification of the damped plant</a></li>
<li><a href="#orgae8bf4a">2.4. Sensitivity to disturbances</a></li>
<li><a href="#orgf8558bc">2.5. Damped Plant</a></li>
<li><a href="#org7146202">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgc4ca1b5">3. Relative Motion Control</a>
<ul>
<li><a href="#org3a4a38f">3.1. One degree-of-freedom example</a>
<li><a href="#orgff968f4">3.1. One degree-of-freedom example</a>
<ul>
<li><a href="#orgc75e93d">3.1.1. Equations</a></li>
<li><a href="#org6772235">3.1.2. Matlab Example</a></li>
<li><a href="#orgd5a2de5">3.1.1. Equations</a></li>
<li><a href="#orgfebe737">3.1.2. Matlab Example</a></li>
</ul>
</li>
<li><a href="#orgf74b07b">3.2. Control Design</a></li>
<li><a href="#org2b50744">3.3. Identification of the damped plant</a></li>
<li><a href="#orgfe16b4e">3.4. Sensitivity to disturbances</a></li>
<li><a href="#org1d28b24">3.5. Damped Plant</a></li>
<li><a href="#org69267d0">3.6. Conclusion</a></li>
<li><a href="#orgf3a1477">3.2. Control Design</a></li>
<li><a href="#org0c94d61">3.3. Identification of the damped plant</a></li>
<li><a href="#orgae7a685">3.4. Sensitivity to disturbances</a></li>
<li><a href="#orgb0045d5">3.5. Damped Plant</a></li>
<li><a href="#orgeacd46f">3.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org3cc03b0">4. Direct Velocity Feedback</a>
<ul>
<li><a href="#org8fee25f">4.1. One degree-of-freedom example</a>
<li><a href="#orgb2d2757">4.1. One degree-of-freedom example</a>
<ul>
<li><a href="#orge4d9f41">4.1.1. Equations</a></li>
<li><a href="#org3305ce8">4.1.2. Matlab Example</a></li>
<li><a href="#org0d13907">4.1.1. Equations</a></li>
<li><a href="#org5d7b09d">4.1.2. Matlab Example</a></li>
</ul>
</li>
<li><a href="#orgc2ae0be">4.2. Control Design</a></li>
<li><a href="#org6eda033">4.3. Identification of the damped plant</a></li>
<li><a href="#orgbc3b2d2">4.4. Sensitivity to disturbances</a></li>
<li><a href="#org69d8b1b">4.5. Damped Plant</a></li>
<li><a href="#org0fffc79">4.6. Conclusion</a></li>
<li><a href="#org1fe076f">4.2. Control Design</a></li>
<li><a href="#orgee6ab5a">4.3. Identification of the damped plant</a></li>
<li><a href="#org455bb51">4.4. Sensitivity to disturbances</a></li>
<li><a href="#org6d852f5">4.5. Damped Plant</a></li>
<li><a href="#org5d33a43">4.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org21441bc">5. Comparison</a>
<ul>
<li><a href="#orgbe907b4">5.1. Load the plants</a></li>
<li><a href="#orgde6308d">5.2. Sensitivity to Disturbance</a></li>
<li><a href="#orgf8558bc">5.3. Damped Plant</a></li>
<li><a href="#orgb849304">5.3. Damped Plant</a></li>
</ul>
</li>
<li><a href="#org7146202">6. Conclusion</a></li>
<li><a href="#org333697a">6. Conclusion</a></li>
</ul>
</div>
</div>
@ -444,8 +443,8 @@ And we save it for further analysis.
</div>
</div>
<div id="outline-container-org30a5b37" class="outline-3">
<h3 id="org30a5b37"><span class="section-number-3">1.3</span> Sensitivity to disturbances</h3>
<div id="outline-container-orgbc3b2d2" class="outline-3">
<h3 id="orgbc3b2d2"><span class="section-number-3">1.3</span> Sensitivity to disturbances</h3>
<div class="outline-text-3" id="text-1-3">
<p>
The sensitivity to disturbances are shown on figure <a href="#orgcf7fa15">1</a>.
@ -503,15 +502,15 @@ Then, it is applied on the simscape model.
</p>
</div>
<div id="outline-container-orgf3a80f4" class="outline-3">
<h3 id="orgf3a80f4"><span class="section-number-3">2.1</span> One degree-of-freedom example</h3>
<div id="outline-container-org8fee25f" class="outline-3">
<h3 id="org8fee25f"><span class="section-number-3">2.1</span> One degree-of-freedom example</h3>
<div class="outline-text-3" id="text-2-1">
<p>
<a id="org7f37ded"></a>
</p>
</div>
<div id="outline-container-orgfba4e95" class="outline-4">
<h4 id="orgfba4e95"><span class="section-number-4">2.1.1</span> Equations</h4>
<div id="outline-container-orge4d9f41" class="outline-4">
<h4 id="orge4d9f41"><span class="section-number-4">2.1.1</span> Equations</h4>
<div class="outline-text-4" id="text-2-1-1">
<div id="org1acdc30" class="figure">
@ -577,8 +576,8 @@ This is attainable if we have:
</div>
</div>
<div id="outline-container-org8487491" class="outline-4">
<h4 id="org8487491"><span class="section-number-4">2.1.2</span> Matlab Example</h4>
<div id="outline-container-org3305ce8" class="outline-4">
<h4 id="org3305ce8"><span class="section-number-4">2.1.2</span> Matlab Example</h4>
<div class="outline-text-4" id="text-2-1-2">
<p>
Let define the system parameters.
@ -641,8 +640,8 @@ And the closed loop system is computed below.
</div>
</div>
<div id="outline-container-orgf884e9a" class="outline-3">
<h3 id="orgf884e9a"><span class="section-number-3">2.2</span> Control Design</h3>
<div id="outline-container-orgc2ae0be" class="outline-3">
<h3 id="orgc2ae0be"><span class="section-number-3">2.2</span> Control Design</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Let&rsquo;s load the undamped plant:
@ -684,8 +683,8 @@ The corresponding loop gains are shown in figure <a href="#org36e3a94">7</a>.
</div>
</div>
<div id="outline-container-org55e3bff" class="outline-3">
<h3 id="org55e3bff"><span class="section-number-3">2.3</span> Identification of the damped plant</h3>
<div id="outline-container-org6eda033" class="outline-3">
<h3 id="org6eda033"><span class="section-number-3">2.3</span> Identification of the damped plant</h3>
<div class="outline-text-3" id="text-2-3">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -738,8 +737,8 @@ And we save the damped plant for further analysis
</div>
</div>
<div id="outline-container-org340a3d7" class="outline-3">
<h3 id="org340a3d7"><span class="section-number-3">2.4</span> Sensitivity to disturbances</h3>
<div id="outline-container-orgae8bf4a" class="outline-3">
<h3 id="orgae8bf4a"><span class="section-number-3">2.4</span> Sensitivity to disturbances</h3>
<div class="outline-text-3" id="text-2-4">
<p>
As shown on figure <a href="#org38217ee">8</a>:
@ -775,8 +774,8 @@ For instance, the plots are not the same when using <code>minreal</code>.
</div>
</div>
<div id="outline-container-orgba948f4" class="outline-3">
<h3 id="orgba948f4"><span class="section-number-3">2.5</span> Damped Plant</h3>
<div id="outline-container-orgf8558bc" class="outline-3">
<h3 id="orgf8558bc"><span class="section-number-3">2.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-2-5">
<p>
Now, look at the new damped plant to control.
@ -805,8 +804,8 @@ However, it increases coupling at low frequency (figure <a href="#org8017b2f">11
</div>
</div>
<div id="outline-container-org8b5a4f4" class="outline-3">
<h3 id="org8b5a4f4"><span class="section-number-3">2.6</span> Conclusion</h3>
<div id="outline-container-org7146202" class="outline-3">
<h3 id="org7146202"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<p>
@ -840,15 +839,15 @@ In the Relative Motion Control (RMC), a derivative feedback is applied between t
</p>
</div>
<div id="outline-container-org3a4a38f" class="outline-3">
<h3 id="org3a4a38f"><span class="section-number-3">3.1</span> One degree-of-freedom example</h3>
<div id="outline-container-orgff968f4" class="outline-3">
<h3 id="orgff968f4"><span class="section-number-3">3.1</span> One degree-of-freedom example</h3>
<div class="outline-text-3" id="text-3-1">
<p>
<a id="org6f16e09"></a>
</p>
</div>
<div id="outline-container-orgc75e93d" class="outline-4">
<h4 id="orgc75e93d"><span class="section-number-4">3.1.1</span> Equations</h4>
<div id="outline-container-orgd5a2de5" class="outline-4">
<h4 id="orgd5a2de5"><span class="section-number-4">3.1.1</span> Equations</h4>
<div class="outline-text-4" id="text-3-1-1">
<div id="org64900ec" class="figure">
@ -907,8 +906,8 @@ This corresponds to a gain:
</div>
</div>
<div id="outline-container-org6772235" class="outline-4">
<h4 id="org6772235"><span class="section-number-4">3.1.2</span> Matlab Example</h4>
<div id="outline-container-orgfebe737" class="outline-4">
<h4 id="orgfebe737"><span class="section-number-4">3.1.2</span> Matlab Example</h4>
<div class="outline-text-4" id="text-3-1-2">
<p>
Let define the system parameters.
@ -971,8 +970,8 @@ And the closed loop system is computed below.
</div>
</div>
<div id="outline-container-orgf74b07b" class="outline-3">
<h3 id="orgf74b07b"><span class="section-number-3">3.2</span> Control Design</h3>
<div id="outline-container-orgf3a1477" class="outline-3">
<h3 id="orgf3a1477"><span class="section-number-3">3.2</span> Control Design</h3>
<div class="outline-text-3" id="text-3-2">
<p>
Let&rsquo;s load the undamped plant:
@ -1015,8 +1014,8 @@ The obtained loop gains are shown in figure <a href="#orga5b8f12">15</a>.
</div>
</div>
<div id="outline-container-org2b50744" class="outline-3">
<h3 id="org2b50744"><span class="section-number-3">3.3</span> Identification of the damped plant</h3>
<div id="outline-container-org0c94d61" class="outline-3">
<h3 id="org0c94d61"><span class="section-number-3">3.3</span> Identification of the damped plant</h3>
<div class="outline-text-3" id="text-3-3">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -1069,8 +1068,8 @@ And we save the damped plant for further analysis.
</div>
</div>
<div id="outline-container-orgfe16b4e" class="outline-3">
<h3 id="orgfe16b4e"><span class="section-number-3">3.4</span> Sensitivity to disturbances</h3>
<div id="outline-container-orgae7a685" class="outline-3">
<h3 id="orgae7a685"><span class="section-number-3">3.4</span> Sensitivity to disturbances</h3>
<div class="outline-text-3" id="text-3-4">
<p>
As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering the sensitivity to disturbances near resonance of the system.
@ -1092,8 +1091,8 @@ As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering
</div>
</div>
<div id="outline-container-org1d28b24" class="outline-3">
<h3 id="org1d28b24"><span class="section-number-3">3.5</span> Damped Plant</h3>
<div id="outline-container-orgb0045d5" class="outline-3">
<h3 id="orgb0045d5"><span class="section-number-3">3.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-5">
<div id="org2267bd4" class="figure">
@ -1104,8 +1103,8 @@ As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering
</div>
</div>
<div id="outline-container-org69267d0" class="outline-3">
<h3 id="org69267d0"><span class="section-number-3">3.6</span> Conclusion</h3>
<div id="outline-container-orgeacd46f" class="outline-3">
<h3 id="orgeacd46f"><span class="section-number-3">3.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-6">
<div class="important">
<p>
@ -1137,15 +1136,15 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</p>
</div>
<div id="outline-container-org8fee25f" class="outline-3">
<h3 id="org8fee25f"><span class="section-number-3">4.1</span> One degree-of-freedom example</h3>
<div id="outline-container-orgb2d2757" class="outline-3">
<h3 id="orgb2d2757"><span class="section-number-3">4.1</span> One degree-of-freedom example</h3>
<div class="outline-text-3" id="text-4-1">
<p>
<a id="org3a699cb"></a>
</p>
</div>
<div id="outline-container-orge4d9f41" class="outline-4">
<h4 id="orge4d9f41"><span class="section-number-4">4.1.1</span> Equations</h4>
<div id="outline-container-org0d13907" class="outline-4">
<h4 id="org0d13907"><span class="section-number-4">4.1.1</span> Equations</h4>
<div class="outline-text-4" id="text-4-1-1">
<div id="org93ae6e4" class="figure">
@ -1204,8 +1203,8 @@ This corresponds to a gain:
</div>
</div>
<div id="outline-container-org3305ce8" class="outline-4">
<h4 id="org3305ce8"><span class="section-number-4">4.1.2</span> Matlab Example</h4>
<div id="outline-container-org5d7b09d" class="outline-4">
<h4 id="org5d7b09d"><span class="section-number-4">4.1.2</span> Matlab Example</h4>
<div class="outline-text-4" id="text-4-1-2">
<p>
Let define the system parameters.
@ -1292,8 +1291,8 @@ The obtained sensitivity to disturbances is shown in figure <a href="#org1c3277a
</div>
</div>
<div id="outline-container-orgc2ae0be" class="outline-3">
<h3 id="orgc2ae0be"><span class="section-number-3">4.2</span> Control Design</h3>
<div id="outline-container-org1fe076f" class="outline-3">
<h3 id="org1fe076f"><span class="section-number-3">4.2</span> Control Design</h3>
<div class="outline-text-3" id="text-4-2">
<p>
Let&rsquo;s load the undamped plant:
@ -1332,8 +1331,8 @@ The controller is defined below and the obtained loop gain is shown in figure <a
</div>
</div>
<div id="outline-container-org6eda033" class="outline-3">
<h3 id="org6eda033"><span class="section-number-3">4.3</span> Identification of the damped plant</h3>
<div id="outline-container-orgee6ab5a" class="outline-3">
<h3 id="orgee6ab5a"><span class="section-number-3">4.3</span> Identification of the damped plant</h3>
<div class="outline-text-3" id="text-4-3">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -1386,8 +1385,8 @@ And we save the damped plant for further analysis.
</div>
</div>
<div id="outline-container-orgbc3b2d2" class="outline-3">
<h3 id="orgbc3b2d2"><span class="section-number-3">4.4</span> Sensitivity to disturbances</h3>
<div id="outline-container-org455bb51" class="outline-3">
<h3 id="org455bb51"><span class="section-number-3">4.4</span> Sensitivity to disturbances</h3>
<div class="outline-text-3" id="text-4-4">
<div id="org2558226" class="figure">
@ -1406,8 +1405,8 @@ And we save the damped plant for further analysis.
</div>
</div>
<div id="outline-container-org69d8b1b" class="outline-3">
<h3 id="org69d8b1b"><span class="section-number-3">4.5</span> Damped Plant</h3>
<div id="outline-container-org6d852f5" class="outline-3">
<h3 id="org6d852f5"><span class="section-number-3">4.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-5">
<div id="org2fa3671" class="figure">
@ -1418,8 +1417,8 @@ And we save the damped plant for further analysis.
</div>
</div>
<div id="outline-container-org0fffc79" class="outline-3">
<h3 id="org0fffc79"><span class="section-number-3">4.6</span> Conclusion</h3>
<div id="outline-container-org5d33a43" class="outline-3">
<h3 id="org5d33a43"><span class="section-number-3">4.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-6">
<div class="important">
<p>
@ -1490,8 +1489,8 @@ Direct Velocity Feedback:
</div>
</div>
<div id="outline-container-orgf8558bc" class="outline-3">
<h3 id="orgf8558bc"><span class="section-number-3">5.3</span> Damped Plant</h3>
<div id="outline-container-orgb849304" class="outline-3">
<h3 id="orgb849304"><span class="section-number-3">5.3</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-3">
<div id="org043ecf3" class="figure">
@ -1517,8 +1516,8 @@ Direct Velocity Feedback:
</div>
</div>
<div id="outline-container-org7146202" class="outline-2">
<h2 id="org7146202"><span class="section-number-2">6</span> Conclusion</h2>
<div id="outline-container-org333697a" class="outline-2">
<h2 id="org333697a"><span class="section-number-2">6</span> Conclusion</h2>
<div class="outline-text-2" id="text-6">
<p>
<a id="org58549a4"></a>
@ -1528,7 +1527,7 @@ Direct Velocity Feedback:
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
<p class="date">Created: 2020-02-25 mar. 18:21</p>
</div>
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@ -1,11 +1,10 @@
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<p class="author">Author: Dehaeze Thomas</p>
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@ -1,11 +1,10 @@
<?xml version="1.0" encoding="utf-8"?>
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</div><div id="content">
<h1 class="title">Identification of the disturbances</h1>
<div id="table-of-contents">
@ -592,7 +591,7 @@ save(<span class="org-string">'./disturbances/mat/dist_psd.mat'</span>, <span cl
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
<p class="date">Created: 2020-02-25 mar. 18:21</p>
</div>
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95
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@ -1,11 +1,10 @@
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<h1 class="title">Tomography Experiment</h1>
<div id="table-of-contents">
@ -263,30 +262,30 @@ for the JavaScript code in this tag.
<li><a href="#org03b2a76">1. Simscape Model</a></li>
<li><a href="#org6ed78a0">2. Tomography Experiment with no disturbances</a>
<ul>
<li><a href="#orgc1321b7">2.1. Simulation Setup</a></li>
<li><a href="#orgebeb6c3">2.2. Analysis</a></li>
<li><a href="#orge9a06c9">2.3. Conclusion</a></li>
<li><a href="#org5778305">2.1. Simulation Setup</a></li>
<li><a href="#org3f73a44">2.2. Analysis</a></li>
<li><a href="#org67ff024">2.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org16d8e58">3. Tomography Experiment with included perturbations</a>
<ul>
<li><a href="#orgc6ab502">3.1. Simulation Setup</a></li>
<li><a href="#orga551571">3.2. Analysis</a></li>
<li><a href="#org3eee8bd">3.3. Conclusion</a></li>
<li><a href="#orgc064b4d">3.1. Simulation Setup</a></li>
<li><a href="#org35d72fe">3.2. Analysis</a></li>
<li><a href="#org1f14bc2">3.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org72f01ab">4. Tomography when the micro-hexapod is not centered</a>
<ul>
<li><a href="#orga42880e">4.1. Simulation Setup</a></li>
<li><a href="#org58e1909">4.2. Analysis</a></li>
<li><a href="#org4670aba">4.3. Conclusion</a></li>
<li><a href="#org0fe7352">4.1. Simulation Setup</a></li>
<li><a href="#org3fda1a5">4.2. Analysis</a></li>
<li><a href="#org5042570">4.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org8fa1632">5. Raster Scans with the translation stage</a>
<ul>
<li><a href="#org5778305">5.1. Simulation Setup</a></li>
<li><a href="#org3f73a44">5.2. Analysis</a></li>
<li><a href="#org67ff024">5.3. Conclusion</a></li>
<li><a href="#org8a2f4a2">5.1. Simulation Setup</a></li>
<li><a href="#org55d191f">5.2. Analysis</a></li>
<li><a href="#orgae2c5b3">5.3. Conclusion</a></li>
</ul>
</li>
</ul>
@ -373,8 +372,8 @@ All stage is set to its zero position except the Spindle which is rotating at 60
<a id="org3effbb8"></a>
</p>
</div>
<div id="outline-container-orgc1321b7" class="outline-3">
<h3 id="orgc1321b7"><span class="section-number-3">2.1</span> Simulation Setup</h3>
<div id="outline-container-org5778305" class="outline-3">
<h3 id="org5778305"><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.
@ -410,8 +409,8 @@ save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>,
</div>
</div>
<div id="outline-container-orgebeb6c3" class="outline-3">
<h3 id="orgebeb6c3"><span class="section-number-3">2.2</span> Analysis</h3>
<div id="outline-container-org3f73a44" class="outline-3">
<h3 id="org3f73a44"><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(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
@ -447,8 +446,8 @@ Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-ty
</div>
</div>
<div id="outline-container-orge9a06c9" class="outline-3">
<h3 id="orge9a06c9"><span class="section-number-3">2.3</span> Conclusion</h3>
<div id="outline-container-org67ff024" class="outline-3">
<h3 id="org67ff024"><span class="section-number-3">2.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-3">
<div class="important">
<p>
@ -468,8 +467,8 @@ This residual error motion probably comes from a small misalignment somewhere.
<a id="org4e7f626"></a>
</p>
</div>
<div id="outline-container-orgc6ab502" class="outline-3">
<h3 id="orgc6ab502"><span class="section-number-3">3.1</span> Simulation Setup</h3>
<div id="outline-container-orgc064b4d" class="outline-3">
<h3 id="orgc064b4d"><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.
@ -505,8 +504,8 @@ save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>,
</div>
</div>
<div id="outline-container-orga551571" class="outline-3">
<h3 id="orga551571"><span class="section-number-3">3.2</span> Analysis</h3>
<div id="outline-container-org35d72fe" class="outline-3">
<h3 id="org35d72fe"><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(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
@ -542,8 +541,8 @@ Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-ty
</div>
</div>
<div id="outline-container-org3eee8bd" class="outline-3">
<h3 id="org3eee8bd"><span class="section-number-3">3.3</span> Conclusion</h3>
<div id="outline-container-org1f14bc2" class="outline-3">
<h3 id="org1f14bc2"><span class="section-number-3">3.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-3">
<div class="important">
<p>
@ -562,8 +561,8 @@ Error motion is what expected from the disturbance measurements.
<a id="orgb31e3fb"></a>
</p>
</div>
<div id="outline-container-orga42880e" class="outline-3">
<h3 id="orga42880e"><span class="section-number-3">4.1</span> Simulation Setup</h3>
<div id="outline-container-org0fe7352" class="outline-3">
<h3 id="org0fe7352"><span class="section-number-3">4.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-4-1">
<p>
We first set the wanted translation of the Micro Hexapod.
@ -623,8 +622,8 @@ save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>,
</div>
</div>
<div id="outline-container-org58e1909" class="outline-3">
<h3 id="org58e1909"><span class="section-number-3">4.2</span> Analysis</h3>
<div id="outline-container-org3fda1a5" class="outline-3">
<h3 id="org3fda1a5"><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(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'tomo_not_align'</span>);
@ -660,8 +659,8 @@ Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-ty
</div>
</div>
<div id="outline-container-org4670aba" class="outline-3">
<h3 id="org4670aba"><span class="section-number-3">4.3</span> Conclusion</h3>
<div id="outline-container-org5042570" class="outline-3">
<h3 id="org5042570"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3">
<div class="important">
<p>
@ -680,8 +679,8 @@ The main motions are translations in the X direction of the mobile platform (cor
<a id="org6aaeb53"></a>
</p>
</div>
<div id="outline-container-org5778305" class="outline-3">
<h3 id="org5778305"><span class="section-number-3">5.1</span> Simulation Setup</h3>
<div id="outline-container-org8a2f4a2" class="outline-3">
<h3 id="org8a2f4a2"><span class="section-number-3">5.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-5-1">
<p>
We set the reference path.
@ -742,8 +741,8 @@ save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>,
</div>
</div>
<div id="outline-container-org3f73a44" class="outline-3">
<h3 id="org3f73a44"><span class="section-number-3">5.2</span> Analysis</h3>
<div id="outline-container-org55d191f" class="outline-3">
<h3 id="org55d191f"><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(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>, <span class="org-string">'ty_scan'</span>);
@ -779,8 +778,8 @@ Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-ty
</div>
</div>
<div id="outline-container-org67ff024" class="outline-3">
<h3 id="org67ff024"><span class="section-number-3">5.3</span> Conclusion</h3>
<div id="outline-container-orgae2c5b3" class="outline-3">
<h3 id="orgae2c5b3"><span class="section-number-3">5.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-3">
<div class="important">
<p>
@ -795,7 +794,7 @@ In order to reduce the errors, we can make a smoother reference path for the tra
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
<p class="date">Created: 2020-02-25 mar. 18:21</p>
</div>
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@ -1,11 +1,10 @@
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@ -195,13 +194,13 @@
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<h1 class="title">Matlab Functions used for the NASS Project</h1>
<div id="table-of-contents">
@ -659,7 +658,7 @@ MTr = [WTm(1<span class="org-type">:</span>3,1<span class="org-type">:</span>3)<
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
<p class="date">Created: 2020-02-25 mar. 18:20</p>
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<h1 class="title">HAC-LAC applied on the Simscape Model</h1>
<div id="table-of-contents">
@ -264,10 +263,10 @@ for the JavaScript code in this tag.
<ul>
<li><a href="#org05b902d">1.1. Identification of the plant</a>
<ul>
<li><a href="#orgfd2208d">1.1.1. Initialize the Simulation</a></li>
<li><a href="#orgd132773">1.1.2. Identification</a></li>
<li><a href="#org9d87e76">1.1.3. Display TF</a></li>
<li><a href="#org5c51ae8">1.1.4. Obtained Plants for Active Damping</a></li>
<li><a href="#orga716982">1.1.1. Initialize the Simulation</a></li>
<li><a href="#org2a3d76d">1.1.2. Identification</a></li>
<li><a href="#org86a6b3a">1.1.3. Display TF</a></li>
<li><a href="#org51e23f6">1.1.4. Obtained Plants for Active Damping</a></li>
</ul>
</li>
<li><a href="#orgaf40de5">1.2. Tomography Experiment</a>
@ -278,10 +277,10 @@ for the JavaScript code in this tag.
</li>
<li><a href="#orgdcbab01">1.3. Verification of the transfer function from nano hexapod to metrology</a>
<ul>
<li><a href="#orga716982">1.3.1. Initialize the Simulation</a></li>
<li><a href="#org2a3d76d">1.3.2. Identification</a></li>
<li><a href="#org86a6b3a">1.3.3. Display TF</a></li>
<li><a href="#org51e23f6">1.3.4. Obtained Plants for Active Damping</a></li>
<li><a href="#org9edf24c">1.3.1. Initialize the Simulation</a></li>
<li><a href="#org9ff767e">1.3.2. Identification</a></li>
<li><a href="#org5c0b9bf">1.3.3. Display TF</a></li>
<li><a href="#org6288fb1">1.3.4. Obtained Plants for Active Damping</a></li>
</ul>
</li>
</ul>
@ -302,8 +301,8 @@ for the JavaScript code in this tag.
<h3 id="org05b902d"><span class="section-number-3">1.1</span> Identification of the plant</h3>
<div class="outline-text-3" id="text-1-1">
</div>
<div id="outline-container-orgfd2208d" class="outline-4">
<h4 id="orgfd2208d"><span class="section-number-4">1.1.1</span> Initialize the Simulation</h4>
<div id="outline-container-orga716982" class="outline-4">
<h4 id="orga716982"><span class="section-number-4">1.1.1</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-1-1-1">
<p>
We initialize all the stages with the default parameters.
@ -355,8 +354,8 @@ And all the controllers are set to 0.
</div>
</div>
<div id="outline-container-orgd132773" class="outline-4">
<h4 id="orgd132773"><span class="section-number-4">1.1.2</span> Identification</h4>
<div id="outline-container-org2a3d76d" class="outline-4">
<h4 id="org2a3d76d"><span class="section-number-4">1.1.2</span> Identification</h4>
<div class="outline-text-4" id="text-1-1-2">
<p>
First, we identify the dynamics of the system using the <code>linearize</code> function.
@ -396,11 +395,11 @@ G_legs.OutputName = {<span class="org-string">'e1'</span>, <span class="org-stri
</div>
</div>
<div id="outline-container-org9d87e76" class="outline-4">
<h4 id="org9d87e76"><span class="section-number-4">1.1.3</span> Display TF</h4>
<div id="outline-container-org86a6b3a" class="outline-4">
<h4 id="org86a6b3a"><span class="section-number-4">1.1.3</span> Display TF</h4>
<div class="outline-text-4" id="text-1-1-3">
<div id="org0cc732b" class="figure">
<div id="org37e58f3" class="figure">
<p><img src="figs/plant_G_cart.png" alt="plant_G_cart.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Transfer Function from forces applied by the nano-hexapod to position error (<a href="./figs/plant_G_cart.png">png</a>, <a href="./figs/plant_G_cart.pdf">pdf</a>)</p>
@ -408,25 +407,25 @@ G_legs.OutputName = {<span class="org-string">'e1'</span>, <span class="org-stri
</div>
</div>
<div id="outline-container-org5c51ae8" class="outline-4">
<h4 id="org5c51ae8"><span class="section-number-4">1.1.4</span> Obtained Plants for Active Damping</h4>
<div id="outline-container-org51e23f6" class="outline-4">
<h4 id="org51e23f6"><span class="section-number-4">1.1.4</span> Obtained Plants for Active Damping</h4>
<div class="outline-text-4" id="text-1-1-4">
<div id="org76f625d" class="figure">
<div id="orga98bcf7" class="figure">
<p><img src="figs/nass_active_damping_iff_plant.png" alt="nass_active_damping_iff_plant.png" />
</p>
<p><span class="figure-number">Figure 2: </span><code>G_iff</code>: IFF Plant (<a href="./figs/nass_active_damping_iff_plant.png">png</a>, <a href="./figs/nass_active_damping_iff_plant.pdf">pdf</a>)</p>
</div>
<div id="org8206b3b" class="figure">
<div id="orgf5e6d6e" class="figure">
<p><img src="figs/nass_active_damping_ine_plant.png" alt="nass_active_damping_ine_plant.png" />
</p>
<p><span class="figure-number">Figure 3: </span><code>G_dvf</code>: Plant for Direct Velocity Feedback (<a href="./figs/nass_active_damping_dvf_plant.png">png</a>, <a href="./figs/nass_active_damping_dvf_plant.pdf">pdf</a>)</p>
</div>
<div id="org145c602" class="figure">
<div id="orgfe31dcc" class="figure">
<p><img src="figs/nass_active_damping_inertial_plant.png" alt="nass_active_damping_inertial_plant.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Inertial Feedback Plant (<a href="./figs/nass_active_damping_inertial_plant.png">png</a>, <a href="./figs/nass_active_damping_inertial_plant.pdf">pdf</a>)</p>
@ -510,8 +509,8 @@ t = linspace(0, 3, length(En(<span class="org-type">:</span>,1)));
<h3 id="orgdcbab01"><span class="section-number-3">1.3</span> Verification of the transfer function from nano hexapod to metrology</h3>
<div class="outline-text-3" id="text-1-3">
</div>
<div id="outline-container-orga716982" class="outline-4">
<h4 id="orga716982"><span class="section-number-4">1.3.1</span> Initialize the Simulation</h4>
<div id="outline-container-org9edf24c" class="outline-4">
<h4 id="org9edf24c"><span class="section-number-4">1.3.1</span> Initialize the Simulation</h4>
<div class="outline-text-4" id="text-1-3-1">
<p>
We initialize all the stages with the default parameters.
@ -563,8 +562,8 @@ And all the controllers are set to 0.
</div>
</div>
<div id="outline-container-org2a3d76d" class="outline-4">
<h4 id="org2a3d76d"><span class="section-number-4">1.3.2</span> Identification</h4>
<div id="outline-container-org9ff767e" class="outline-4">
<h4 id="org9ff767e"><span class="section-number-4">1.3.2</span> Identification</h4>
<div class="outline-text-4" id="text-1-3-2">
<p>
First, we identify the dynamics of the system using the <code>linearize</code> function.
@ -604,11 +603,11 @@ G_legs.OutputName = {<span class="org-string">'e1'</span>, <span class="org-stri
</div>
</div>
<div id="outline-container-org86a6b3a" class="outline-4">
<h4 id="org86a6b3a"><span class="section-number-4">1.3.3</span> Display TF</h4>
<div id="outline-container-org5c0b9bf" class="outline-4">
<h4 id="org5c0b9bf"><span class="section-number-4">1.3.3</span> Display TF</h4>
<div class="outline-text-4" id="text-1-3-3">
<div id="org37e58f3" class="figure">
<div id="org85c36b6" class="figure">
<p><img src="figs/plant_G_cart.png" alt="plant_G_cart.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Transfer Function from forces applied by the nano-hexapod to position error (<a href="./figs/plant_G_cart.png">png</a>, <a href="./figs/plant_G_cart.pdf">pdf</a>)</p>
@ -616,25 +615,25 @@ G_legs.OutputName = {<span class="org-string">'e1'</span>, <span class="org-stri
</div>
</div>
<div id="outline-container-org51e23f6" class="outline-4">
<h4 id="org51e23f6"><span class="section-number-4">1.3.4</span> Obtained Plants for Active Damping</h4>
<div id="outline-container-org6288fb1" class="outline-4">
<h4 id="org6288fb1"><span class="section-number-4">1.3.4</span> Obtained Plants for Active Damping</h4>
<div class="outline-text-4" id="text-1-3-4">
<div id="orga98bcf7" class="figure">
<div id="org29fb6b2" class="figure">
<p><img src="figs/nass_active_damping_iff_plant.png" alt="nass_active_damping_iff_plant.png" />
</p>
<p><span class="figure-number">Figure 8: </span><code>G_iff</code>: IFF Plant (<a href="./figs/nass_active_damping_iff_plant.png">png</a>, <a href="./figs/nass_active_damping_iff_plant.pdf">pdf</a>)</p>
</div>
<div id="orgf5e6d6e" class="figure">
<div id="org9412773" class="figure">
<p><img src="figs/nass_active_damping_ine_plant.png" alt="nass_active_damping_ine_plant.png" />
</p>
<p><span class="figure-number">Figure 9: </span><code>G_dvf</code>: Plant for Direct Velocity Feedback (<a href="./figs/nass_active_damping_dvf_plant.png">png</a>, <a href="./figs/nass_active_damping_dvf_plant.pdf">pdf</a>)</p>
</div>
<div id="orgfe31dcc" class="figure">
<div id="orgea280f2" class="figure">
<p><img src="figs/nass_active_damping_inertial_plant.png" alt="nass_active_damping_inertial_plant.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Inertial Feedback Plant (<a href="./figs/nass_active_damping_inertial_plant.png">png</a>, <a href="./figs/nass_active_damping_inertial_plant.pdf">pdf</a>)</p>
@ -646,7 +645,7 @@ G_legs.OutputName = {<span class="org-string">'e1'</span>, <span class="org-stri
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
<p class="date">Created: 2020-02-25 mar. 18:20</p>
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<h1 class="title">Identification</h1>
<div id="table-of-contents">
@ -770,7 +769,7 @@ For such a complex system, we believe that the Simscape Model represents the dyn
</div>
<div id="postamble" class="status">
<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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<h1 class="title">Kinematics of the station</h1>
<div id="table-of-contents">
@ -595,7 +594,7 @@ And we verify that we indeed succeed to go to the wanted position.
</div>
<div id="postamble" class="status">
<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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docs/positioning_error.html
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@ -1,11 +1,10 @@
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@ -195,13 +194,13 @@
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<h1 class="title">Computation of the Positioning Error with respect to the nano-hexapod</h1>
<div id="table-of-contents">
@ -273,17 +272,17 @@ for the JavaScript code in this tag.
<li><a href="#orgf8376ef">1. How do we measure the position of the sample with respect to the granite</a></li>
<li><a href="#orgb3d760a">2. Verify that the function to compute the reference pose is correct</a>
<ul>
<li><a href="#orgffeb030">2.1. Prepare the Simulation</a></li>
<li><a href="#org5c3ae81">2.1. Prepare the Simulation</a></li>
<li><a href="#orgd2fa379">2.2. Verify that the pose of the sample is the same as the computed one</a></li>
<li><a href="#orgc56cbe3">2.3. Conclusion</a></li>
<li><a href="#org00066db">2.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgf6fa84d">3. Verify that the function to convert the position error in the frame fixed to the nano-hexapod is working</a>
<ul>
<li><a href="#org5c3ae81">3.1. Prepare the Simulation</a></li>
<li><a href="#org4efa9f2">3.1. Prepare the Simulation</a></li>
<li><a href="#org4e6a2dc">3.2. Compute the wanted pose of the sample in the NASS Base from the metrology and the reference</a></li>
<li><a href="#orga048dbb">3.3. Verify that be imposing the error motion on the nano-hexapod, we indeed have zero error at the end</a></li>
<li><a href="#org00066db">3.4. Conclusion</a></li>
<li><a href="#orga90edfe">3.4. Conclusion</a></li>
</ul>
</li>
</ul>
@ -371,8 +370,8 @@ We can then determine extract other orientation conventions such that Euler angl
The goal here is to perfectly move the station and verify that there is no mismatch between the metrology measurement and the computation of the reference pose.
</p>
</div>
<div id="outline-container-orgffeb030" class="outline-3">
<h3 id="orgffeb030"><span class="section-number-3">2.1</span> Prepare the Simulation</h3>
<div id="outline-container-org5c3ae81" class="outline-3">
<h3 id="org5c3ae81"><span class="section-number-3">2.1</span> Prepare the Simulation</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We set a small <code>StopTime</code>.
@ -542,8 +541,8 @@ ans =
</div>
</div>
<div id="outline-container-orgc56cbe3" class="outline-3">
<h3 id="orgc56cbe3"><span class="section-number-3">2.3</span> Conclusion</h3>
<div id="outline-container-org00066db" class="outline-3">
<h3 id="org00066db"><span class="section-number-3">2.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-3">
<div class="important">
<p>
@ -571,8 +570,8 @@ This will induce a global positioning error of the sample with respect to the de
We want to verify that we are able to measure this positioning error and convert it in the frame attached to the Nano-hexapod.
</p>
</div>
<div id="outline-container-org5c3ae81" class="outline-3">
<h3 id="org5c3ae81"><span class="section-number-3">3.1</span> Prepare the Simulation</h3>
<div id="outline-container-org4efa9f2" class="outline-3">
<h3 id="org4efa9f2"><span class="section-number-3">3.1</span> Prepare the Simulation</h3>
<div class="outline-text-3" id="text-3-1">
<p>
We set a small <code>StopTime</code>.
@ -896,8 +895,8 @@ Verify that the pose error is small.
</div>
</div>
<div id="outline-container-org00066db" class="outline-3">
<h3 id="org00066db"><span class="section-number-3">3.4</span> Conclusion</h3>
<div id="outline-container-orga90edfe" class="outline-3">
<h3 id="orga90edfe"><span class="section-number-3">3.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-4">
<div class="important">
<p>
@ -911,7 +910,7 @@ Indeed, we are able to convert the position error in the frame of the NASS and t
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
<p class="date">Created: 2020-02-25 mar. 18:20</p>
</div>
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@ -776,7 +775,7 @@ Internal force, acting reciprocally between base and following origins is implem
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
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@ -323,7 +322,7 @@ The project also permits to automatically add defined folder to the path when th
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
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</div><div id="content">
<h1 class="title">Simscape Uniaxial Model</h1>
<div id="table-of-contents">
@ -273,69 +272,69 @@ for the JavaScript code in this tag.
<li><a href="#org227ba84">1. Simscape Model</a></li>
<li><a href="#org6bfb35d">2. Undamped System</a>
<ul>
<li><a href="#org61775db">2.1. Init</a></li>
<li><a href="#org3019170">2.2. Identification</a></li>
<li><a href="#org6a3e875">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#orgaf6bea7">2.4. Noise Budget</a></li>
<li><a href="#org5265d72">2.1. Init</a></li>
<li><a href="#org3b15675">2.2. Identification</a></li>
<li><a href="#org3492011">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#orgd860077">2.4. Noise Budget</a></li>
<li><a href="#orgdb3535a">2.5. Plant</a></li>
</ul>
</li>
<li><a href="#org90e581d">3. Integral Force Feedback</a>
<li><a href="#org66a1e03">3. Integral Force Feedback</a>
<ul>
<li><a href="#orgd591c6e">3.1. Control Design</a></li>
<li><a href="#org33f4bcf">3.2. Identification</a></li>
<li><a href="#org9f881a5">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#org1c61625">3.4. Damped Plant</a></li>
<li><a href="#org4fa7707">3.5. Conclusion</a></li>
<li><a href="#org5d899b2">3.1. Control Design</a></li>
<li><a href="#orge386fb1">3.2. Identification</a></li>
<li><a href="#orgbd405f9">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#orgbe8aa64">3.4. Damped Plant</a></li>
<li><a href="#orgfa342b9">3.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org07ff58f">4. Relative Motion Control</a>
<ul>
<li><a href="#org185ae89">4.1. Control Design</a></li>
<li><a href="#org743899e">4.2. Identification</a></li>
<li><a href="#org2fa5702">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#org19e990c">4.4. Damped Plant</a></li>
<li><a href="#org47c65d5">4.5. Conclusion</a></li>
<li><a href="#org971bdb9">4.1. Control Design</a></li>
<li><a href="#orgfce3b27">4.2. Identification</a></li>
<li><a href="#org2123e6c">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#org7e3e638">4.4. Damped Plant</a></li>
<li><a href="#org0ec985e">4.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgc9b3622">5. Direct Velocity Feedback</a>
<ul>
<li><a href="#orgd11a858">5.1. Control Design</a></li>
<li><a href="#orgd06082d">5.2. Identification</a></li>
<li><a href="#org3111d50">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#org8451460">5.4. Damped Plant</a></li>
<li><a href="#org4792e6e">5.5. Conclusion</a></li>
<li><a href="#orgd5df5f2">5.1. Control Design</a></li>
<li><a href="#orgca551cb">5.2. Identification</a></li>
<li><a href="#orga45e582">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#orgdbf551f">5.4. Damped Plant</a></li>
<li><a href="#orge883751">5.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org5ac7dda">6. With Cedrat Piezo-electric Actuators</a>
<ul>
<li><a href="#orga4db73c">6.1. Identification</a></li>
<li><a href="#org5d899b2">6.2. Control Design</a></li>
<li><a href="#orgc9ca496">6.3. Identification</a></li>
<li><a href="#org82723ce">6.4. Sensitivity to Disturbance</a></li>
<li><a href="#orgf696e7c">6.5. Damped Plant</a></li>
<li><a href="#orgfc63bb2">6.6. Conclusion</a></li>
<li><a href="#orgddd7da8">6.1. Identification</a></li>
<li><a href="#orgb6ef594">6.2. Control Design</a></li>
<li><a href="#org5314588">6.3. Identification</a></li>
<li><a href="#orgd226771">6.4. Sensitivity to Disturbance</a></li>
<li><a href="#org294b781">6.5. Damped Plant</a></li>
<li><a href="#orga768e31">6.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org77a79e6">7. Comparison of Active Damping Techniques</a>
<ul>
<li><a href="#orgb0afe4f">7.1. Load the plants</a></li>
<li><a href="#orgbd405f9">7.2. Sensitivity to Disturbance</a></li>
<li><a href="#org76ed406">7.3. Noise Budget</a></li>
<li><a href="#orgbe8aa64">7.4. Damped Plant</a></li>
<li><a href="#org74fe486">7.5. Conclusion</a></li>
<li><a href="#org948b91d">7.2. Sensitivity to Disturbance</a></li>
<li><a href="#org234479d">7.3. Noise Budget</a></li>
<li><a href="#orgf591690">7.4. Damped Plant</a></li>
<li><a href="#orgf332379">7.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org15965e0">8. Voice Coil</a>
<ul>
<li><a href="#org5265d72">8.1. Init</a></li>
<li><a href="#org3b15675">8.2. Identification</a></li>
<li><a href="#org3492011">8.3. Sensitivity to Disturbances</a></li>
<li><a href="#org45c8e35">8.4. Noise Budget</a></li>
<li><a href="#org66a1e03">8.5. Integral Force Feedback</a></li>
<li><a href="#orgefc326e">8.1. Init</a></li>
<li><a href="#orgae49d6e">8.2. Identification</a></li>
<li><a href="#org72047d5">8.3. Sensitivity to Disturbances</a></li>
<li><a href="#orgbcac95d">8.4. Noise Budget</a></li>
<li><a href="#org95b95ac">8.5. Integral Force Feedback</a></li>
<li><a href="#org2a655f7">8.6. Identification of the Damped Plant</a></li>
<li><a href="#orgd860077">8.7. Noise Budget</a></li>
<li><a href="#orgfa342b9">8.8. Conclusion</a></li>
<li><a href="#orgc8d2daf">8.7. Noise Budget</a></li>
<li><a href="#orgb885664">8.8. Conclusion</a></li>
</ul>
</li>
</ul>
@ -433,8 +432,8 @@ Schematics of the active damping techniques are displayed in figure <a href="#or
Let&rsquo;s start by study the undamped system.
</p>
</div>
<div id="outline-container-org61775db" class="outline-3">
<h3 id="org61775db"><span class="section-number-3">2.1</span> Init</h3>
<div id="outline-container-org5265d72" class="outline-3">
<h3 id="org5265d72"><span class="section-number-3">2.1</span> Init</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We initialize all the stages with the default parameters.
@ -446,8 +445,8 @@ All the controllers are set to 0 (Open Loop).
</p>
</div>
</div>
<div id="outline-container-org3019170" class="outline-3">
<h3 id="org3019170"><span class="section-number-3">2.2</span> Identification</h3>
<div id="outline-container-org3b15675" class="outline-3">
<h3 id="org3b15675"><span class="section-number-3">2.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We identify the dynamics of the system.
@ -510,8 +509,8 @@ Finally, we save the identified system dynamics for further analysis.
</div>
</div>
<div id="outline-container-org6a3e875" class="outline-3">
<h3 id="org6a3e875"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
<div id="outline-container-org3492011" class="outline-3">
<h3 id="org3492011"><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:
@ -538,8 +537,8 @@ We show several plots representing the sensitivity to disturbances:
</div>
</div>
<div id="outline-container-orgaf6bea7" class="outline-3">
<h3 id="orgaf6bea7"><span class="section-number-3">2.4</span> Noise Budget</h3>
<div id="outline-container-orgd860077" class="outline-3">
<h3 id="orgd860077"><span class="section-number-3">2.4</span> Noise Budget</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We first load the measured PSD of the disturbance.
@ -598,8 +597,8 @@ It corresponds to the plant to control.
</div>
</div>
<div id="outline-container-org90e581d" class="outline-2">
<h2 id="org90e581d"><span class="section-number-2">3</span> Integral Force Feedback</h2>
<div id="outline-container-org66a1e03" class="outline-2">
<h2 id="org66a1e03"><span class="section-number-2">3</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org37f1b7d"></a>
@ -611,8 +610,8 @@ It corresponds to the plant to control.
<p><span class="figure-number">Figure 8: </span>Uniaxial IFF Control Schematic</p>
</div>
</div>
<div id="outline-container-orgd591c6e" class="outline-3">
<h3 id="orgd591c6e"><span class="section-number-3">3.1</span> Control Design</h3>
<div id="outline-container-org5d899b2" class="outline-3">
<h3 id="org5d899b2"><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">
<pre class="src src-matlab">load(<span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>);
@ -647,8 +646,8 @@ The controller for each pair of actuator/sensor is:
</div>
</div>
<div id="outline-container-org33f4bcf" class="outline-3">
<h3 id="org33f4bcf"><span class="section-number-3">3.2</span> Identification</h3>
<div id="outline-container-orge386fb1" class="outline-3">
<h3 id="orge386fb1"><span class="section-number-3">3.2</span> Identification</h3>
<div class="outline-text-3" id="text-3-2">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -731,8 +730,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org9f881a5" class="outline-3">
<h3 id="org9f881a5"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
<div id="outline-container-orgbd405f9" class="outline-3">
<h3 id="orgbd405f9"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-3-3">
<div id="orge528565" class="figure">
@ -750,8 +749,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org1c61625" class="outline-3">
<h3 id="org1c61625"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div id="outline-container-orgbe8aa64" class="outline-3">
<h3 id="orgbe8aa64"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-4">
<div id="org57280cb" class="figure">
@ -762,8 +761,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org4fa7707" class="outline-3">
<h3 id="org4fa7707"><span class="section-number-3">3.5</span> Conclusion</h3>
<div id="outline-container-orgfa342b9" class="outline-3">
<h3 id="orgfa342b9"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5">
<div class="important">
<p>
@ -792,8 +791,8 @@ In the Relative Motion Control (RMC), a derivative feedback is applied between t
<p><span class="figure-number">Figure 14: </span>Uniaxial RMC Control Schematic</p>
</div>
</div>
<div id="outline-container-org185ae89" class="outline-3">
<h3 id="org185ae89"><span class="section-number-3">4.1</span> Control Design</h3>
<div id="outline-container-org971bdb9" class="outline-3">
<h3 id="org971bdb9"><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">
<pre class="src src-matlab">load(<span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>);
@ -829,8 +828,8 @@ A Low pass Filter is added to make the controller transfer function proper.
</div>
</div>
<div id="outline-container-org743899e" class="outline-3">
<h3 id="org743899e"><span class="section-number-3">4.2</span> Identification</h3>
<div id="outline-container-orgfce3b27" class="outline-3">
<h3 id="orgfce3b27"><span class="section-number-3">4.2</span> Identification</h3>
<div class="outline-text-3" id="text-4-2">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -914,8 +913,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
<div id="outline-container-org2fa5702" class="outline-3">
<h3 id="org2fa5702"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
<div id="outline-container-org2123e6c" class="outline-3">
<h3 id="org2123e6c"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-4-3">
<div id="org9e0dde4" class="figure">
@ -933,8 +932,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org19e990c" class="outline-3">
<h3 id="org19e990c"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div id="outline-container-org7e3e638" class="outline-3">
<h3 id="org7e3e638"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-4">
<div id="org18786e8" class="figure">
@ -945,8 +944,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org47c65d5" class="outline-3">
<h3 id="org47c65d5"><span class="section-number-3">4.5</span> Conclusion</h3>
<div id="outline-container-org0ec985e" class="outline-3">
<h3 id="org0ec985e"><span class="section-number-3">4.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-5">
<div class="important">
<p>
@ -975,8 +974,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
<p><span class="figure-number">Figure 20: </span>Uniaxial DVF Control Schematic</p>
</div>
</div>
<div id="outline-container-orgd11a858" class="outline-3">
<h3 id="orgd11a858"><span class="section-number-3">5.1</span> Control Design</h3>
<div id="outline-container-orgd5df5f2" class="outline-3">
<h3 id="orgd5df5f2"><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">
<pre class="src src-matlab">load(<span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>);
@ -1004,8 +1003,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div>
</div>
<div id="outline-container-orgd06082d" class="outline-3">
<h3 id="orgd06082d"><span class="section-number-3">5.2</span> Identification</h3>
<div id="outline-container-orgca551cb" class="outline-3">
<h3 id="orgca551cb"><span class="section-number-3">5.2</span> Identification</h3>
<div class="outline-text-3" id="text-5-2">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -1088,8 +1087,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org3111d50" class="outline-3">
<h3 id="org3111d50"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
<div id="outline-container-orga45e582" class="outline-3">
<h3 id="orga45e582"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-5-3">
<div id="orgf9d4052" class="figure">
@ -1107,8 +1106,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org8451460" class="outline-3">
<h3 id="org8451460"><span class="section-number-3">5.4</span> Damped Plant</h3>
<div id="outline-container-orgdbf551f" class="outline-3">
<h3 id="orgdbf551f"><span class="section-number-3">5.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-4">
<div id="orgbc9c953" class="figure">
@ -1119,8 +1118,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div>
</div>
<div id="outline-container-org4792e6e" class="outline-3">
<h3 id="org4792e6e"><span class="section-number-3">5.5</span> Conclusion</h3>
<div id="outline-container-orge883751" class="outline-3">
<h3 id="orge883751"><span class="section-number-3">5.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-5">
<div class="important">
<p>
@ -1148,8 +1147,8 @@ The model used for the Cedrat actuator is shown in figure <a href="#org83591fa">
<p><span class="figure-number">Figure 26: </span>Schematic of the model used for the Cedrat Actuator</p>
</div>
</div>
<div id="outline-container-orga4db73c" class="outline-3">
<h3 id="orga4db73c"><span class="section-number-3">6.1</span> Identification</h3>
<div id="outline-container-orgddd7da8" class="outline-3">
<h3 id="orgddd7da8"><span class="section-number-3">6.1</span> Identification</h3>
<div class="outline-text-3" id="text-6-1">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -1237,8 +1236,8 @@ G.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comm
</div>
</div>
<div id="outline-container-org5d899b2" class="outline-3">
<h3 id="org5d899b2"><span class="section-number-3">6.2</span> Control Design</h3>
<div id="outline-container-orgb6ef594" class="outline-3">
<h3 id="orgb6ef594"><span class="section-number-3">6.2</span> Control Design</h3>
<div class="outline-text-3" id="text-6-2">
<p>
Let&rsquo;s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor.
@ -1268,8 +1267,8 @@ The controller for each pair of actuator/sensor is:
</div>
</div>
<div id="outline-container-orgc9ca496" class="outline-3">
<h3 id="orgc9ca496"><span class="section-number-3">6.3</span> Identification</h3>
<div id="outline-container-org5314588" class="outline-3">
<h3 id="org5314588"><span class="section-number-3">6.3</span> Identification</h3>
<div class="outline-text-3" id="text-6-3">
<p>
Let&rsquo;s initialize the system prior to identification.
@ -1353,8 +1352,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div>
</div>
<div id="outline-container-org82723ce" class="outline-3">
<h3 id="org82723ce"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
<div id="outline-container-orgd226771" class="outline-3">
<h3 id="orgd226771"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-6-4">
<div id="org90f5c2b" class="figure">
@ -1372,8 +1371,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div>
</div>
<div id="outline-container-orgf696e7c" class="outline-3">
<h3 id="orgf696e7c"><span class="section-number-3">6.5</span> Damped Plant</h3>
<div id="outline-container-org294b781" class="outline-3">
<h3 id="org294b781"><span class="section-number-3">6.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-6-5">
<div id="org0c4e61a" class="figure">
@ -1384,8 +1383,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div>
</div>
<div id="outline-container-orgfc63bb2" class="outline-3">
<h3 id="orgfc63bb2"><span class="section-number-3">6.6</span> Conclusion</h3>
<div id="outline-container-orga768e31" class="outline-3">
<h3 id="orga768e31"><span class="section-number-3">6.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-6-6">
<div class="important">
<p>
@ -1414,8 +1413,8 @@ This gives similar results than with a classical force sensor.
</div>
</div>
<div id="outline-container-orgbd405f9" class="outline-3">
<h3 id="orgbd405f9"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
<div id="outline-container-org948b91d" class="outline-3">
<h3 id="org948b91d"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
<div class="outline-text-3" id="text-7-2">
<div id="org8c59440" class="figure">
@ -1448,8 +1447,8 @@ This gives similar results than with a classical force sensor.
</div>
</div>
<div id="outline-container-org76ed406" class="outline-3">
<h3 id="org76ed406"><span class="section-number-3">7.3</span> Noise Budget</h3>
<div id="outline-container-org234479d" class="outline-3">
<h3 id="org234479d"><span class="section-number-3">7.3</span> Noise Budget</h3>
<div class="outline-text-3" id="text-7-3">
<p>
We first load the measured PSD of the disturbance.
@ -1516,8 +1515,8 @@ It is important to note that the effect of direct forces applied to the sample a
</div>
</div>
<div id="outline-container-orgbe8aa64" class="outline-3">
<h3 id="orgbe8aa64"><span class="section-number-3">7.4</span> Damped Plant</h3>
<div id="outline-container-orgf591690" class="outline-3">
<h3 id="orgf591690"><span class="section-number-3">7.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-7-4">
<div id="orga0c1298" class="figure">
@ -1528,8 +1527,8 @@ It is important to note that the effect of direct forces applied to the sample a
</div>
</div>
<div id="outline-container-org74fe486" class="outline-3">
<h3 id="org74fe486"><span class="section-number-3">7.5</span> Conclusion</h3>
<div id="outline-container-orgf332379" class="outline-3">
<h3 id="orgf332379"><span class="section-number-3">7.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-7-5">
<table id="org46e95c2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Comparison of proposed active damping techniques</caption>
@ -1605,8 +1604,8 @@ It is important to note that the effect of direct forces applied to the sample a
<a id="orgf9e9d51"></a>
</p>
</div>
<div id="outline-container-org5265d72" class="outline-3">
<h3 id="org5265d72"><span class="section-number-3">8.1</span> Init</h3>
<div id="outline-container-orgefc326e" class="outline-3">
<h3 id="orgefc326e"><span class="section-number-3">8.1</span> Init</h3>
<div class="outline-text-3" id="text-8-1">
<p>
We initialize all the stages with the default parameters.
@ -1618,8 +1617,8 @@ All the controllers are set to 0 (Open Loop).
</p>
</div>
</div>
<div id="outline-container-org3b15675" class="outline-3">
<h3 id="org3b15675"><span class="section-number-3">8.2</span> Identification</h3>
<div id="outline-container-orgae49d6e" class="outline-3">
<h3 id="orgae49d6e"><span class="section-number-3">8.2</span> Identification</h3>
<div class="outline-text-3" id="text-8-2">
<p>
We identify the dynamics of the system.
@ -1682,8 +1681,8 @@ Finally, we save the identified system dynamics for further analysis.
</div>
</div>
<div id="outline-container-org3492011" class="outline-3">
<h3 id="org3492011"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3>
<div id="outline-container-org72047d5" class="outline-3">
<h3 id="org72047d5"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3>
<div class="outline-text-3" id="text-8-3">
<p>
We load the dynamics when using a piezo-electric nano hexapod to compare the results.
@ -1717,8 +1716,8 @@ We show several plots representing the sensitivity to disturbances:
</div>
</div>
<div id="outline-container-org45c8e35" class="outline-3">
<h3 id="org45c8e35"><span class="section-number-3">8.4</span> Noise Budget</h3>
<div id="outline-container-orgbcac95d" class="outline-3">
<h3 id="orgbcac95d"><span class="section-number-3">8.4</span> Noise Budget</h3>
<div class="outline-text-3" id="text-8-4">
<p>
We first load the measured PSD of the disturbance.
@ -1767,8 +1766,8 @@ Thus, it may be desirable to use voice coil actuators.
</div>
</div>
</div>
<div id="outline-container-org66a1e03" class="outline-3">
<h3 id="org66a1e03"><span class="section-number-3">8.5</span> Integral Force Feedback</h3>
<div id="outline-container-org95b95ac" class="outline-3">
<h3 id="org95b95ac"><span class="section-number-3">8.5</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-8-5">
<div class="org-src-container">
<pre class="src src-matlab">K_iff = <span class="org-type">-</span>20<span class="org-type">/</span>s;
@ -1863,8 +1862,8 @@ G_vc_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div>
</div>
<div id="outline-container-orgd860077" class="outline-3">
<h3 id="orgd860077"><span class="section-number-3">8.7</span> Noise Budget</h3>
<div id="outline-container-orgc8d2daf" class="outline-3">
<h3 id="orgc8d2daf"><span class="section-number-3">8.7</span> Noise Budget</h3>
<div class="outline-text-3" id="text-8-7">
<p>
We compute the obtain PSD of the displacement \(D\) when using IFF.
@ -1878,8 +1877,8 @@ We compute the obtain PSD of the displacement \(D\) when using IFF.
</div>
</div>
<div id="outline-container-orgfa342b9" class="outline-3">
<h3 id="orgfa342b9"><span class="section-number-3">8.8</span> Conclusion</h3>
<div id="outline-container-orgb885664" class="outline-3">
<h3 id="orgb885664"><span class="section-number-3">8.8</span> Conclusion</h3>
<div class="outline-text-3" id="text-8-8">
<div class="important">
<p>
@ -1897,7 +1896,7 @@ Similarly, it would require much lower bandwidth to attain the same level of dis
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p>
<p class="date">Created: 2020-02-25 mar. 18:20</p>
</div>
</body>
</html>

18
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@ -6,16 +6,16 @@
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18
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org/functions.org
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org/identification.org
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18
org/kinematics.org
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18
org/positioning_error.org
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18
org/simscape.org
View File

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18
org/simscape_subsystems.org
View File

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18
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18
org/uniaxial.org
View File

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