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<title>Active Damping applied on the Simscape Model</title> <title>Active Damping applied on the Simscape Model</title>
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<h1 class="title">Active Damping applied on the Simscape Model</h1> <h1 class="title">Active Damping applied on the Simscape Model</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -274,17 +273,17 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#orga668d6d">1.1. Identification of the dynamics for Active Damping</a> <li><a href="#orga668d6d">1.1. Identification of the dynamics for Active Damping</a>
<ul> <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> <li><a href="#orge632d78">1.1.2. Obtained Plants for Active Damping</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgacbac97">1.2. Identification of the dynamics for High Authority Control</a> <li><a href="#orgacbac97">1.2. Identification of the dynamics for High Authority Control</a>
<ul> <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> <li><a href="#org245ebc9">1.2.2. Obtained Plants</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org072b32a">1.3. Tomography Experiment</a> <li><a href="#orgc633a52">1.3. Tomography Experiment</a>
<ul> <ul>
<li><a href="#orgd2384a9">1.3.1. Simulation</a></li> <li><a href="#orgd2384a9">1.3.1. Simulation</a></li>
<li><a href="#orgd00d359">1.3.2. Results</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>
<li><a href="#org89179a2">2.4. Variation of the Tilt Angle</a></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="#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> </ul>
</li> </li>
<li><a href="#org28bb8b8">3. Integral Force Feedback</a> <li><a href="#org28bb8b8">3. Integral Force Feedback</a>
<ul> <ul>
<li><a href="#orga2142db">3.1. Control Design</a> <li><a href="#org8147539">3.1. Control Design</a>
<ul> <ul>
<li><a href="#orgcf1bf17">3.1.1. Plant</a></li> <li><a href="#org7579fa1">3.1.1. Plant</a></li>
<li><a href="#orgaca3b16">3.1.2. Control Design</a></li> <li><a href="#org1069779">3.1.2. Control Design</a></li>
<li><a href="#org39a3259">3.1.3. Diagonal Controller</a></li> <li><a href="#org0929a5f">3.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orge945074">3.2. Tomography Experiment</a> <li><a href="#org92b7e4a">3.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#orge827289">3.2.1. Simulation with IFF Controller</a></li> <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> </ul>
</li> </li>
<li><a href="#orge036b39">3.3. Conclusion</a></li> <li><a href="#orge208898">3.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orge2515a1">4. Direct Velocity Feedback</a> <li><a href="#orge2515a1">4. Direct Velocity Feedback</a>
<ul> <ul>
<li><a href="#org7a0849a">4.1. Control Design</a> <li><a href="#org2454b5d">4.1. Control Design</a>
<ul> <ul>
<li><a href="#org9a95e47">4.1.1. Plant</a></li> <li><a href="#orgd36a459">4.1.1. Plant</a></li>
<li><a href="#orgb9858c3">4.1.2. Control Design</a></li> <li><a href="#orgf771969">4.1.2. Control Design</a></li>
<li><a href="#orgb9638f1">4.1.3. Diagonal Controller</a></li> <li><a href="#org1fa78ea">4.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgc633a52">4.2. Tomography Experiment</a> <li><a href="#orgdc2cc7d">4.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#org4d239c9">4.2.1. Initialize the Simulation</a></li> <li><a href="#org315e901">4.2.1. Initialize the Simulation</a></li>
<li><a href="#org34c04f2">4.2.2. Compare with Undamped system</a></li> <li><a href="#orgbe122b9">4.2.2. Compare with Undamped system</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org24a50bf">4.3. Conclusion</a></li> <li><a href="#org2edf5bd">4.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org5047e99">5. Inertial Control</a> <li><a href="#org5047e99">5. Inertial Control</a>
<ul> <ul>
<li><a href="#org1069779">5.1. Control Design</a> <li><a href="#org5bec512">5.1. Control Design</a>
<ul> <ul>
<li><a href="#org7579fa1">5.1.1. Plant</a></li> <li><a href="#org16795b0">5.1.1. Plant</a></li>
<li><a href="#orgc4c6a5a">5.1.2. Control Design</a></li> <li><a href="#org9ce4e10">5.1.2. Control Design</a></li>
<li><a href="#org0929a5f">5.1.3. Diagonal Controller</a></li> <li><a href="#org132c666">5.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org1b61fb2">5.2. Conclusion</a></li> <li><a href="#org408de58">5.2. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd2a9c18">6. Comparison</a> <li><a href="#orgd2a9c18">6. Comparison</a>
@ -367,16 +366,16 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#orgcf56890">7.1. prepareLinearizeIdentification</a> <li><a href="#orgcf56890">7.1. prepareLinearizeIdentification</a>
<ul> <ul>
<li><a href="#org56ccd79">Function Description</a></li> <li><a href="#org2b7c7da">Function Description</a></li>
<li><a href="#orgdbd3a09">Optional Parameters</a></li> <li><a href="#org6e16103">Optional Parameters</a></li>
<li><a href="#orgdd3adc1">Initialize the Simulation</a></li> <li><a href="#org552f1ca">Initialize the Simulation</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgc2b4408">7.2. prepareTomographyExperiment</a> <li><a href="#orgc2b4408">7.2. prepareTomographyExperiment</a>
<ul> <ul>
<li><a href="#org2b7c7da">Function Description</a></li> <li><a href="#org6dacc19">Function Description</a></li>
<li><a href="#org6e16103">Optional Parameters</a></li> <li><a href="#org65022a7">Optional Parameters</a></li>
<li><a href="#org315e901">Initialize the Simulation</a></li> <li><a href="#orga0e6a80">Initialize the Simulation</a></li>
</ul> </ul>
</li> </li>
</ul> </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> <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 class="outline-text-3" id="text-1-1">
</div> </div>
<div id="outline-container-orgbaab9df" class="outline-4"> <div id="outline-container-orgd1a656e" class="outline-4">
<h4 id="orgbaab9df"><span class="section-number-4">1.1.1</span> Identification</h4> <h4 id="orgd1a656e"><span class="section-number-4">1.1.1</span> Identification</h4>
<div class="outline-text-4" id="text-1-1-1"> <div class="outline-text-4" id="text-1-1-1">
<p> <p>
We initialize all the stages with the default parameters. 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> <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 class="outline-text-3" id="text-1-2">
</div> </div>
<div id="outline-container-orgd1a656e" class="outline-4"> <div id="outline-container-org9dde5ce" class="outline-4">
<h4 id="orgd1a656e"><span class="section-number-4">1.2.1</span> Identification</h4> <h4 id="org9dde5ce"><span class="section-number-4">1.2.1</span> Identification</h4>
<div class="outline-text-4" id="text-1-2-1"> <div class="outline-text-4" id="text-1-2-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -612,8 +611,8 @@ And we save them for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org072b32a" class="outline-3"> <div id="outline-container-orgc633a52" class="outline-3">
<h3 id="org072b32a"><span class="section-number-3">1.3</span> Tomography Experiment</h3> <h3 id="orgc633a52"><span class="section-number-3">1.3</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
</div> </div>
<div id="outline-container-orgd2384a9" class="outline-4"> <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> </div>
<div id="outline-container-orga697040" class="outline-3"> <div id="outline-container-org1b61fb2" class="outline-3">
<h3 id="orga697040"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org1b61fb2"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<table id="org664ed44" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <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> <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> </div>
<div id="outline-container-orga2142db" class="outline-3"> <div id="outline-container-org8147539" class="outline-3">
<h3 id="orga2142db"><span class="section-number-3">3.1</span> Control Design</h3> <h3 id="org8147539"><span class="section-number-3">3.1</span> Control Design</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
</div> </div>
<div id="outline-container-orgcf1bf17" class="outline-4"> <div id="outline-container-org7579fa1" class="outline-4">
<h4 id="orgcf1bf17"><span class="section-number-4">3.1.1</span> Plant</h4> <h4 id="org7579fa1"><span class="section-number-4">3.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-3-1-1"> <div class="outline-text-4" id="text-3-1-1">
<p> <p>
Let&rsquo;s load the previously identified undamped plant: 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> </div>
<div id="outline-container-orgaca3b16" class="outline-4"> <div id="outline-container-org1069779" class="outline-4">
<h4 id="orgaca3b16"><span class="section-number-4">3.1.2</span> Control Design</h4> <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"> <div class="outline-text-4" id="text-3-1-2">
<p> <p>
The controller for each pair of actuator/sensor is: 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> </div>
<div id="outline-container-org39a3259" class="outline-4"> <div id="outline-container-org0929a5f" class="outline-4">
<h4 id="org39a3259"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4> <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"> <div class="outline-text-4" id="text-3-1-3">
<p> <p>
We create the diagonal controller and we add a minus sign as we have a positive 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> </div>
<div id="outline-container-orge945074" class="outline-3"> <div id="outline-container-org92b7e4a" class="outline-3">
<h3 id="orge945074"><span class="section-number-3">3.2</span> Tomography Experiment</h3> <h3 id="org92b7e4a"><span class="section-number-3">3.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
</div> </div>
<div id="outline-container-orge827289" class="outline-4"> <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> </div>
<div id="outline-container-org0ca3dfa" class="outline-4"> <div id="outline-container-org34c04f2" class="outline-4">
<h4 id="org0ca3dfa"><span class="section-number-4">3.2.2</span> Compare with Undamped system</h4> <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 class="outline-text-4" id="text-3-2-2">
<div id="orgc83ffab" class="figure"> <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> </div>
<div id="outline-container-orge036b39" class="outline-3"> <div id="outline-container-orge208898" class="outline-3">
<h3 id="orge036b39"><span class="section-number-3">3.3</span> Conclusion</h3> <h3 id="orge208898"><span class="section-number-3">3.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<div class="important"> <div class="important">
<p> <p>
@ -1286,12 +1285,12 @@ The actuator displacement can be measured with a capacitive sensor for instance.
</p> </p>
</div> </div>
<div id="outline-container-org7a0849a" class="outline-3"> <div id="outline-container-org2454b5d" class="outline-3">
<h3 id="org7a0849a"><span class="section-number-3">4.1</span> Control Design</h3> <h3 id="org2454b5d"><span class="section-number-3">4.1</span> Control Design</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
</div> </div>
<div id="outline-container-org9a95e47" class="outline-4"> <div id="outline-container-orgd36a459" class="outline-4">
<h4 id="org9a95e47"><span class="section-number-4">4.1.1</span> Plant</h4> <h4 id="orgd36a459"><span class="section-number-4">4.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-4-1-1"> <div class="outline-text-4" id="text-4-1-1">
<p> <p>
Let&rsquo;s load the undamped plant: 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> </div>
<div id="outline-container-orgb9858c3" class="outline-4"> <div id="outline-container-orgf771969" class="outline-4">
<h4 id="orgb9858c3"><span class="section-number-4">4.1.2</span> Control Design</h4> <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"> <div class="outline-text-4" id="text-4-1-2">
<p> <p>
The Direct Velocity Feedback is defined below. 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> </div>
<div id="outline-container-orgb9638f1" class="outline-4"> <div id="outline-container-org1fa78ea" class="outline-4">
<h4 id="orgb9638f1"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4> <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"> <div class="outline-text-4" id="text-4-1-3">
<p> <p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture. 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> </div>
<div id="outline-container-orgc633a52" class="outline-3"> <div id="outline-container-orgdc2cc7d" class="outline-3">
<h3 id="orgc633a52"><span class="section-number-3">4.2</span> Tomography Experiment</h3> <h3 id="orgdc2cc7d"><span class="section-number-3">4.2</span> Tomography Experiment</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
</div> </div>
<div id="outline-container-org4d239c9" class="outline-4"> <div id="outline-container-org315e901" class="outline-4">
<h4 id="org4d239c9"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4> <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"> <div class="outline-text-4" id="text-4-2-1">
<p> <p>
We initialize elements for the tomography experiment. 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> </div>
<div id="outline-container-org34c04f2" class="outline-4"> <div id="outline-container-orgbe122b9" class="outline-4">
<h4 id="org34c04f2"><span class="section-number-4">4.2.2</span> Compare with Undamped system</h4> <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 class="outline-text-4" id="text-4-2-2">
<div id="orge2d1a4a" class="figure"> <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> </div>
<div id="outline-container-org24a50bf" class="outline-3"> <div id="outline-container-org2edf5bd" class="outline-3">
<h3 id="org24a50bf"><span class="section-number-3">4.3</span> Conclusion</h3> <h3 id="org2edf5bd"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<div class="important"> <div class="important">
<p> <p>
@ -1475,12 +1474,12 @@ In Inertial Control, a feedback is applied between the measured <b>absolute</b>
</p> </p>
</div> </div>
<div id="outline-container-org1069779" class="outline-3"> <div id="outline-container-org5bec512" class="outline-3">
<h3 id="org1069779"><span class="section-number-3">5.1</span> Control Design</h3> <h3 id="org5bec512"><span class="section-number-3">5.1</span> Control Design</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
</div> </div>
<div id="outline-container-org7579fa1" class="outline-4"> <div id="outline-container-org16795b0" class="outline-4">
<h4 id="org7579fa1"><span class="section-number-4">5.1.1</span> Plant</h4> <h4 id="org16795b0"><span class="section-number-4">5.1.1</span> Plant</h4>
<div class="outline-text-4" id="text-5-1-1"> <div class="outline-text-4" id="text-5-1-1">
<p> <p>
Let&rsquo;s load the undamped plant: 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> </div>
<div id="outline-container-orgc4c6a5a" class="outline-4"> <div id="outline-container-org9ce4e10" class="outline-4">
<h4 id="orgc4c6a5a"><span class="section-number-4">5.1.2</span> Control Design</h4> <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"> <div class="outline-text-4" id="text-5-1-2">
<p> <p>
The controller is defined below and the obtained loop gain is shown in figure <a href="#org76d929a">41</a>. 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> </div>
<div id="outline-container-org0929a5f" class="outline-4"> <div id="outline-container-org132c666" class="outline-4">
<h4 id="org0929a5f"><span class="section-number-4">5.1.3</span> Diagonal Controller</h4> <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"> <div class="outline-text-4" id="text-5-1-3">
<p> <p>
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture. 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> </div>
<div id="outline-container-org1b61fb2" class="outline-3"> <div id="outline-container-org408de58" class="outline-3">
<h3 id="org1b61fb2"><span class="section-number-3">5.2</span> Conclusion</h3> <h3 id="org408de58"><span class="section-number-3">5.2</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-5-2">
<div class="important"> <div class="important">
<p> <p>
@ -1724,9 +1723,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
</p> </p>
</div> </div>
<div id="outline-container-org56ccd79" class="outline-4"> <div id="outline-container-org2b7c7da" class="outline-4">
<h4 id="org56ccd79">Function Description</h4> <h4 id="org2b7c7da">Function Description</h4>
<div class="outline-text-4" id="text-org56ccd79"> <div class="outline-text-4" id="text-org2b7c7da">
<div class="org-src-container"> <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 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> </pre>
@ -1734,9 +1733,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
</div> </div>
</div> </div>
<div id="outline-container-orgdbd3a09" class="outline-4"> <div id="outline-container-org6e16103" class="outline-4">
<h4 id="orgdbd3a09">Optional Parameters</h4> <h4 id="org6e16103">Optional Parameters</h4>
<div class="outline-text-4" id="text-orgdbd3a09"> <div class="outline-text-4" id="text-org6e16103">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <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> 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> </div>
<div id="outline-container-orgdd3adc1" class="outline-4"> <div id="outline-container-org552f1ca" class="outline-4">
<h4 id="orgdd3adc1">Initialize the Simulation</h4> <h4 id="org552f1ca">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-orgdd3adc1"> <div class="outline-text-4" id="text-org552f1ca">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
</p> </p>
@ -1822,9 +1821,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</p> </p>
</div> </div>
<div id="outline-container-org2b7c7da" class="outline-4"> <div id="outline-container-org6dacc19" class="outline-4">
<h4 id="org2b7c7da">Function Description</h4> <h4 id="org6dacc19">Function Description</h4>
<div class="outline-text-4" id="text-org2b7c7da"> <div class="outline-text-4" id="text-org6dacc19">
<div class="org-src-container"> <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 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> </pre>
@ -1832,9 +1831,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</div> </div>
</div> </div>
<div id="outline-container-org6e16103" class="outline-4"> <div id="outline-container-org65022a7" class="outline-4">
<h4 id="org6e16103">Optional Parameters</h4> <h4 id="org65022a7">Optional Parameters</h4>
<div class="outline-text-4" id="text-org6e16103"> <div class="outline-text-4" id="text-org65022a7">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <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> 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> </div>
<div id="outline-container-org315e901" class="outline-4"> <div id="outline-container-orga0e6a80" class="outline-4">
<h4 id="org315e901">Initialize the Simulation</h4> <h4 id="orga0e6a80">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-org315e901"> <div class="outline-text-4" id="text-orga0e6a80">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
</p> </p>
@ -1916,7 +1915,7 @@ We log the signals.
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:07</p> <p class="date">Created: 2020-02-25 mar. 18:20</p>
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@ -1,11 +1,10 @@
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<title>Active Damping with an uni-axial model</title> <title>Active Damping with an uni-axial model</title>
@ -195,13 +194,13 @@
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</div><div id="content"> </div><div id="content">
<h1 class="title">Active Damping with an uni-axial model</h1> <h1 class="title">Active Damping with an uni-axial model</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -274,63 +273,63 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#org7409841">1.1. Init</a></li> <li><a href="#org7409841">1.1. Init</a></li>
<li><a href="#org7514f31">1.2. Identification</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> <li><a href="#orgdda82c0">1.4. Undamped Plant</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org5a3389e">2. Integral Force Feedback</a> <li><a href="#org5a3389e">2. Integral Force Feedback</a>
<ul> <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> <ul>
<li><a href="#orgfba4e95">2.1.1. Equations</a></li> <li><a href="#orge4d9f41">2.1.1. Equations</a></li>
<li><a href="#org8487491">2.1.2. Matlab Example</a></li> <li><a href="#org3305ce8">2.1.2. Matlab Example</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf884e9a">2.2. Control Design</a></li> <li><a href="#orgc2ae0be">2.2. Control Design</a></li>
<li><a href="#org55e3bff">2.3. Identification of the damped plant</a></li> <li><a href="#org6eda033">2.3. Identification of the damped plant</a></li>
<li><a href="#org340a3d7">2.4. Sensitivity to disturbances</a></li> <li><a href="#orgae8bf4a">2.4. Sensitivity to disturbances</a></li>
<li><a href="#orgba948f4">2.5. Damped Plant</a></li> <li><a href="#orgf8558bc">2.5. Damped Plant</a></li>
<li><a href="#org8b5a4f4">2.6. Conclusion</a></li> <li><a href="#org7146202">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgc4ca1b5">3. Relative Motion Control</a> <li><a href="#orgc4ca1b5">3. Relative Motion Control</a>
<ul> <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> <ul>
<li><a href="#orgc75e93d">3.1.1. Equations</a></li> <li><a href="#orgd5a2de5">3.1.1. Equations</a></li>
<li><a href="#org6772235">3.1.2. Matlab Example</a></li> <li><a href="#orgfebe737">3.1.2. Matlab Example</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf74b07b">3.2. Control Design</a></li> <li><a href="#orgf3a1477">3.2. Control Design</a></li>
<li><a href="#org2b50744">3.3. Identification of the damped plant</a></li> <li><a href="#org0c94d61">3.3. Identification of the damped plant</a></li>
<li><a href="#orgfe16b4e">3.4. Sensitivity to disturbances</a></li> <li><a href="#orgae7a685">3.4. Sensitivity to disturbances</a></li>
<li><a href="#org1d28b24">3.5. Damped Plant</a></li> <li><a href="#orgb0045d5">3.5. Damped Plant</a></li>
<li><a href="#org69267d0">3.6. Conclusion</a></li> <li><a href="#orgeacd46f">3.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3cc03b0">4. Direct Velocity Feedback</a> <li><a href="#org3cc03b0">4. Direct Velocity Feedback</a>
<ul> <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> <ul>
<li><a href="#orge4d9f41">4.1.1. Equations</a></li> <li><a href="#org0d13907">4.1.1. Equations</a></li>
<li><a href="#org3305ce8">4.1.2. Matlab Example</a></li> <li><a href="#org5d7b09d">4.1.2. Matlab Example</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgc2ae0be">4.2. Control Design</a></li> <li><a href="#org1fe076f">4.2. Control Design</a></li>
<li><a href="#org6eda033">4.3. Identification of the damped plant</a></li> <li><a href="#orgee6ab5a">4.3. Identification of the damped plant</a></li>
<li><a href="#orgbc3b2d2">4.4. Sensitivity to disturbances</a></li> <li><a href="#org455bb51">4.4. Sensitivity to disturbances</a></li>
<li><a href="#org69d8b1b">4.5. Damped Plant</a></li> <li><a href="#org6d852f5">4.5. Damped Plant</a></li>
<li><a href="#org0fffc79">4.6. Conclusion</a></li> <li><a href="#org5d33a43">4.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org21441bc">5. Comparison</a> <li><a href="#org21441bc">5. Comparison</a>
<ul> <ul>
<li><a href="#orgbe907b4">5.1. Load the plants</a></li> <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="#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> </ul>
</li> </li>
<li><a href="#org7146202">6. Conclusion</a></li> <li><a href="#org333697a">6. Conclusion</a></li>
</ul> </ul>
</div> </div>
</div> </div>
@ -444,8 +443,8 @@ And we save it for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org30a5b37" class="outline-3"> <div id="outline-container-orgbc3b2d2" class="outline-3">
<h3 id="org30a5b37"><span class="section-number-3">1.3</span> Sensitivity to disturbances</h3> <h3 id="orgbc3b2d2"><span class="section-number-3">1.3</span> Sensitivity to disturbances</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
The sensitivity to disturbances are shown on figure <a href="#orgcf7fa15">1</a>. 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> </p>
</div> </div>
<div id="outline-container-orgf3a80f4" class="outline-3"> <div id="outline-container-org8fee25f" class="outline-3">
<h3 id="orgf3a80f4"><span class="section-number-3">2.1</span> One degree-of-freedom example</h3> <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"> <div class="outline-text-3" id="text-2-1">
<p> <p>
<a id="org7f37ded"></a> <a id="org7f37ded"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgfba4e95" class="outline-4"> <div id="outline-container-orge4d9f41" class="outline-4">
<h4 id="orgfba4e95"><span class="section-number-4">2.1.1</span> Equations</h4> <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 class="outline-text-4" id="text-2-1-1">
<div id="org1acdc30" class="figure"> <div id="org1acdc30" class="figure">
@ -577,8 +576,8 @@ This is attainable if we have:
</div> </div>
</div> </div>
<div id="outline-container-org8487491" class="outline-4"> <div id="outline-container-org3305ce8" class="outline-4">
<h4 id="org8487491"><span class="section-number-4">2.1.2</span> Matlab Example</h4> <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"> <div class="outline-text-4" id="text-2-1-2">
<p> <p>
Let define the system parameters. Let define the system parameters.
@ -641,8 +640,8 @@ And the closed loop system is computed below.
</div> </div>
</div> </div>
<div id="outline-container-orgf884e9a" class="outline-3"> <div id="outline-container-orgc2ae0be" class="outline-3">
<h3 id="orgf884e9a"><span class="section-number-3">2.2</span> Control Design</h3> <h3 id="orgc2ae0be"><span class="section-number-3">2.2</span> Control Design</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
Let&rsquo;s load the undamped plant: 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> </div>
<div id="outline-container-org55e3bff" class="outline-3"> <div id="outline-container-org6eda033" class="outline-3">
<h3 id="org55e3bff"><span class="section-number-3">2.3</span> Identification of the damped plant</h3> <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"> <div class="outline-text-3" id="text-2-3">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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> </div>
<div id="outline-container-org340a3d7" class="outline-3"> <div id="outline-container-orgae8bf4a" class="outline-3">
<h3 id="org340a3d7"><span class="section-number-3">2.4</span> Sensitivity to disturbances</h3> <h3 id="orgae8bf4a"><span class="section-number-3">2.4</span> Sensitivity to disturbances</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
As shown on figure <a href="#org38217ee">8</a>: 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> </div>
<div id="outline-container-orgba948f4" class="outline-3"> <div id="outline-container-orgf8558bc" class="outline-3">
<h3 id="orgba948f4"><span class="section-number-3">2.5</span> Damped Plant</h3> <h3 id="orgf8558bc"><span class="section-number-3">2.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
Now, look at the new damped plant to control. 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> </div>
<div id="outline-container-org8b5a4f4" class="outline-3"> <div id="outline-container-org7146202" class="outline-3">
<h3 id="org8b5a4f4"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org7146202"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<div class="important"> <div class="important">
<p> <p>
@ -840,15 +839,15 @@ In the Relative Motion Control (RMC), a derivative feedback is applied between t
</p> </p>
</div> </div>
<div id="outline-container-org3a4a38f" class="outline-3"> <div id="outline-container-orgff968f4" class="outline-3">
<h3 id="org3a4a38f"><span class="section-number-3">3.1</span> One degree-of-freedom example</h3> <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"> <div class="outline-text-3" id="text-3-1">
<p> <p>
<a id="org6f16e09"></a> <a id="org6f16e09"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgc75e93d" class="outline-4"> <div id="outline-container-orgd5a2de5" class="outline-4">
<h4 id="orgc75e93d"><span class="section-number-4">3.1.1</span> Equations</h4> <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 class="outline-text-4" id="text-3-1-1">
<div id="org64900ec" class="figure"> <div id="org64900ec" class="figure">
@ -907,8 +906,8 @@ This corresponds to a gain:
</div> </div>
</div> </div>
<div id="outline-container-org6772235" class="outline-4"> <div id="outline-container-orgfebe737" class="outline-4">
<h4 id="org6772235"><span class="section-number-4">3.1.2</span> Matlab Example</h4> <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"> <div class="outline-text-4" id="text-3-1-2">
<p> <p>
Let define the system parameters. Let define the system parameters.
@ -971,8 +970,8 @@ And the closed loop system is computed below.
</div> </div>
</div> </div>
<div id="outline-container-orgf74b07b" class="outline-3"> <div id="outline-container-orgf3a1477" class="outline-3">
<h3 id="orgf74b07b"><span class="section-number-3">3.2</span> Control Design</h3> <h3 id="orgf3a1477"><span class="section-number-3">3.2</span> Control Design</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
Let&rsquo;s load the undamped plant: 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> </div>
<div id="outline-container-org2b50744" class="outline-3"> <div id="outline-container-org0c94d61" class="outline-3">
<h3 id="org2b50744"><span class="section-number-3">3.3</span> Identification of the damped plant</h3> <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"> <div class="outline-text-3" id="text-3-3">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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> </div>
<div id="outline-container-orgfe16b4e" class="outline-3"> <div id="outline-container-orgae7a685" class="outline-3">
<h3 id="orgfe16b4e"><span class="section-number-3">3.4</span> Sensitivity to disturbances</h3> <h3 id="orgae7a685"><span class="section-number-3">3.4</span> Sensitivity to disturbances</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<p> <p>
As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering the sensitivity to disturbances near resonance of the system. 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> </div>
<div id="outline-container-org1d28b24" class="outline-3"> <div id="outline-container-orgb0045d5" class="outline-3">
<h3 id="org1d28b24"><span class="section-number-3">3.5</span> Damped Plant</h3> <h3 id="orgb0045d5"><span class="section-number-3">3.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<div id="org2267bd4" class="figure"> <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> </div>
<div id="outline-container-org69267d0" class="outline-3"> <div id="outline-container-orgeacd46f" class="outline-3">
<h3 id="org69267d0"><span class="section-number-3">3.6</span> Conclusion</h3> <h3 id="orgeacd46f"><span class="section-number-3">3.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-6"> <div class="outline-text-3" id="text-3-6">
<div class="important"> <div class="important">
<p> <p>
@ -1137,15 +1136,15 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</p> </p>
</div> </div>
<div id="outline-container-org8fee25f" class="outline-3"> <div id="outline-container-orgb2d2757" class="outline-3">
<h3 id="org8fee25f"><span class="section-number-3">4.1</span> One degree-of-freedom example</h3> <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"> <div class="outline-text-3" id="text-4-1">
<p> <p>
<a id="org3a699cb"></a> <a id="org3a699cb"></a>
</p> </p>
</div> </div>
<div id="outline-container-orge4d9f41" class="outline-4"> <div id="outline-container-org0d13907" class="outline-4">
<h4 id="orge4d9f41"><span class="section-number-4">4.1.1</span> Equations</h4> <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 class="outline-text-4" id="text-4-1-1">
<div id="org93ae6e4" class="figure"> <div id="org93ae6e4" class="figure">
@ -1204,8 +1203,8 @@ This corresponds to a gain:
</div> </div>
</div> </div>
<div id="outline-container-org3305ce8" class="outline-4"> <div id="outline-container-org5d7b09d" class="outline-4">
<h4 id="org3305ce8"><span class="section-number-4">4.1.2</span> Matlab Example</h4> <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"> <div class="outline-text-4" id="text-4-1-2">
<p> <p>
Let define the system parameters. Let define the system parameters.
@ -1292,8 +1291,8 @@ The obtained sensitivity to disturbances is shown in figure <a href="#org1c3277a
</div> </div>
</div> </div>
<div id="outline-container-orgc2ae0be" class="outline-3"> <div id="outline-container-org1fe076f" class="outline-3">
<h3 id="orgc2ae0be"><span class="section-number-3">4.2</span> Control Design</h3> <h3 id="org1fe076f"><span class="section-number-3">4.2</span> Control Design</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<p> <p>
Let&rsquo;s load the undamped plant: 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> </div>
<div id="outline-container-org6eda033" class="outline-3"> <div id="outline-container-orgee6ab5a" class="outline-3">
<h3 id="org6eda033"><span class="section-number-3">4.3</span> Identification of the damped plant</h3> <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"> <div class="outline-text-3" id="text-4-3">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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> </div>
<div id="outline-container-orgbc3b2d2" class="outline-3"> <div id="outline-container-org455bb51" class="outline-3">
<h3 id="orgbc3b2d2"><span class="section-number-3">4.4</span> Sensitivity to disturbances</h3> <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 class="outline-text-3" id="text-4-4">
<div id="org2558226" class="figure"> <div id="org2558226" class="figure">
@ -1406,8 +1405,8 @@ And we save the damped plant for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org69d8b1b" class="outline-3"> <div id="outline-container-org6d852f5" class="outline-3">
<h3 id="org69d8b1b"><span class="section-number-3">4.5</span> Damped Plant</h3> <h3 id="org6d852f5"><span class="section-number-3">4.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-5"> <div class="outline-text-3" id="text-4-5">
<div id="org2fa3671" class="figure"> <div id="org2fa3671" class="figure">
@ -1418,8 +1417,8 @@ And we save the damped plant for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org0fffc79" class="outline-3"> <div id="outline-container-org5d33a43" class="outline-3">
<h3 id="org0fffc79"><span class="section-number-3">4.6</span> Conclusion</h3> <h3 id="org5d33a43"><span class="section-number-3">4.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-6"> <div class="outline-text-3" id="text-4-6">
<div class="important"> <div class="important">
<p> <p>
@ -1490,8 +1489,8 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
<div id="outline-container-orgf8558bc" class="outline-3"> <div id="outline-container-orgb849304" class="outline-3">
<h3 id="orgf8558bc"><span class="section-number-3">5.3</span> Damped Plant</h3> <h3 id="orgb849304"><span class="section-number-3">5.3</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-5-3">
<div id="org043ecf3" class="figure"> <div id="org043ecf3" class="figure">
@ -1517,8 +1516,8 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
<div id="outline-container-org7146202" class="outline-2"> <div id="outline-container-org333697a" class="outline-2">
<h2 id="org7146202"><span class="section-number-2">6</span> Conclusion</h2> <h2 id="org333697a"><span class="section-number-2">6</span> Conclusion</h2>
<div class="outline-text-2" id="text-6"> <div class="outline-text-2" id="text-6">
<p> <p>
<a id="org58549a4"></a> <a id="org58549a4"></a>
@ -1528,7 +1527,7 @@ Direct Velocity Feedback:
</div> </div>
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<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
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@ -592,7 +591,7 @@ save(<span class="org-string">'./disturbances/mat/dist_psd.mat'</span>, <span cl
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
<a accesskey="h" href="../index.html"> UP </a> <a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a> <a accesskey="H" href="./index.html"> HOME </a>
</div><div id="content"> </div><div id="content">
<h1 class="title">Tomography Experiment</h1> <h1 class="title">Tomography Experiment</h1>
<div id="table-of-contents"> <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="#org03b2a76">1. Simscape Model</a></li>
<li><a href="#org6ed78a0">2. Tomography Experiment with no disturbances</a> <li><a href="#org6ed78a0">2. Tomography Experiment with no disturbances</a>
<ul> <ul>
<li><a href="#orgc1321b7">2.1. Simulation Setup</a></li> <li><a href="#org5778305">2.1. Simulation Setup</a></li>
<li><a href="#orgebeb6c3">2.2. Analysis</a></li> <li><a href="#org3f73a44">2.2. Analysis</a></li>
<li><a href="#orge9a06c9">2.3. Conclusion</a></li> <li><a href="#org67ff024">2.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org16d8e58">3. Tomography Experiment with included perturbations</a> <li><a href="#org16d8e58">3. Tomography Experiment with included perturbations</a>
<ul> <ul>
<li><a href="#orgc6ab502">3.1. Simulation Setup</a></li> <li><a href="#orgc064b4d">3.1. Simulation Setup</a></li>
<li><a href="#orga551571">3.2. Analysis</a></li> <li><a href="#org35d72fe">3.2. Analysis</a></li>
<li><a href="#org3eee8bd">3.3. Conclusion</a></li> <li><a href="#org1f14bc2">3.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org72f01ab">4. Tomography when the micro-hexapod is not centered</a> <li><a href="#org72f01ab">4. Tomography when the micro-hexapod is not centered</a>
<ul> <ul>
<li><a href="#orga42880e">4.1. Simulation Setup</a></li> <li><a href="#org0fe7352">4.1. Simulation Setup</a></li>
<li><a href="#org58e1909">4.2. Analysis</a></li> <li><a href="#org3fda1a5">4.2. Analysis</a></li>
<li><a href="#org4670aba">4.3. Conclusion</a></li> <li><a href="#org5042570">4.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org8fa1632">5. Raster Scans with the translation stage</a> <li><a href="#org8fa1632">5. Raster Scans with the translation stage</a>
<ul> <ul>
<li><a href="#org5778305">5.1. Simulation Setup</a></li> <li><a href="#org8a2f4a2">5.1. Simulation Setup</a></li>
<li><a href="#org3f73a44">5.2. Analysis</a></li> <li><a href="#org55d191f">5.2. Analysis</a></li>
<li><a href="#org67ff024">5.3. Conclusion</a></li> <li><a href="#orgae2c5b3">5.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </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> <a id="org3effbb8"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgc1321b7" class="outline-3"> <div id="outline-container-org5778305" class="outline-3">
<h3 id="orgc1321b7"><span class="section-number-3">2.1</span> Simulation Setup</h3> <h3 id="org5778305"><span class="section-number-3">2.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
And we initialize the disturbances to be equal to zero. 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> </div>
<div id="outline-container-orgebeb6c3" class="outline-3"> <div id="outline-container-org3f73a44" class="outline-3">
<h3 id="orgebeb6c3"><span class="section-number-3">2.2</span> Analysis</h3> <h3 id="org3f73a44"><span class="section-number-3">2.2</span> Analysis</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <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>); <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> </div>
<div id="outline-container-orge9a06c9" class="outline-3"> <div id="outline-container-org67ff024" class="outline-3">
<h3 id="orge9a06c9"><span class="section-number-3">2.3</span> Conclusion</h3> <h3 id="org67ff024"><span class="section-number-3">2.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="important"> <div class="important">
<p> <p>
@ -468,8 +467,8 @@ This residual error motion probably comes from a small misalignment somewhere.
<a id="org4e7f626"></a> <a id="org4e7f626"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgc6ab502" class="outline-3"> <div id="outline-container-orgc064b4d" class="outline-3">
<h3 id="orgc6ab502"><span class="section-number-3">3.1</span> Simulation Setup</h3> <h3 id="orgc064b4d"><span class="section-number-3">3.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
We now activate the disturbances. We now activate the disturbances.
@ -505,8 +504,8 @@ save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>,
</div> </div>
</div> </div>
<div id="outline-container-orga551571" class="outline-3"> <div id="outline-container-org35d72fe" class="outline-3">
<h3 id="orga551571"><span class="section-number-3">3.2</span> Analysis</h3> <h3 id="org35d72fe"><span class="section-number-3">3.2</span> Analysis</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<div class="org-src-container"> <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>); <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> </div>
<div id="outline-container-org3eee8bd" class="outline-3"> <div id="outline-container-org1f14bc2" class="outline-3">
<h3 id="org3eee8bd"><span class="section-number-3">3.3</span> Conclusion</h3> <h3 id="org1f14bc2"><span class="section-number-3">3.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<div class="important"> <div class="important">
<p> <p>
@ -562,8 +561,8 @@ Error motion is what expected from the disturbance measurements.
<a id="orgb31e3fb"></a> <a id="orgb31e3fb"></a>
</p> </p>
</div> </div>
<div id="outline-container-orga42880e" class="outline-3"> <div id="outline-container-org0fe7352" class="outline-3">
<h3 id="orga42880e"><span class="section-number-3">4.1</span> Simulation Setup</h3> <h3 id="org0fe7352"><span class="section-number-3">4.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<p> <p>
We first set the wanted translation of the Micro Hexapod. 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> </div>
<div id="outline-container-org58e1909" class="outline-3"> <div id="outline-container-org3fda1a5" class="outline-3">
<h3 id="org58e1909"><span class="section-number-3">4.2</span> Analysis</h3> <h3 id="org3fda1a5"><span class="section-number-3">4.2</span> Analysis</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<div class="org-src-container"> <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>); <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> </div>
<div id="outline-container-org4670aba" class="outline-3"> <div id="outline-container-org5042570" class="outline-3">
<h3 id="org4670aba"><span class="section-number-3">4.3</span> Conclusion</h3> <h3 id="org5042570"><span class="section-number-3">4.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<div class="important"> <div class="important">
<p> <p>
@ -680,8 +679,8 @@ The main motions are translations in the X direction of the mobile platform (cor
<a id="org6aaeb53"></a> <a id="org6aaeb53"></a>
</p> </p>
</div> </div>
<div id="outline-container-org5778305" class="outline-3"> <div id="outline-container-org8a2f4a2" class="outline-3">
<h3 id="org5778305"><span class="section-number-3">5.1</span> Simulation Setup</h3> <h3 id="org8a2f4a2"><span class="section-number-3">5.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
<p> <p>
We set the reference path. We set the reference path.
@ -742,8 +741,8 @@ save(<span class="org-string">'experiment_tomography/mat/experiment.mat'</span>,
</div> </div>
</div> </div>
<div id="outline-container-org3f73a44" class="outline-3"> <div id="outline-container-org55d191f" class="outline-3">
<h3 id="org3f73a44"><span class="section-number-3">5.2</span> Analysis</h3> <h3 id="org55d191f"><span class="section-number-3">5.2</span> Analysis</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-5-2">
<div class="org-src-container"> <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>); <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> </div>
<div id="outline-container-org67ff024" class="outline-3"> <div id="outline-container-orgae2c5b3" class="outline-3">
<h3 id="org67ff024"><span class="section-number-3">5.3</span> Conclusion</h3> <h3 id="orgae2c5b3"><span class="section-number-3">5.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-5-3">
<div class="important"> <div class="important">
<p> <p>
@ -795,7 +794,7 @@ In order to reduce the errors, we can make a smoother reference path for the tra
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p> <p class="date">Created: 2020-02-25 mar. 18:21</p>
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<title>Matlab Functions used for the NASS Project</title> <title>Matlab Functions used for the NASS Project</title>
@ -195,13 +194,13 @@
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<a accesskey="H" href="../index.html"> HOME </a> <a accesskey="H" href="./index.html"> HOME </a>
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<h1 class="title">Matlab Functions used for the NASS Project</h1> <h1 class="title">Matlab Functions used for the NASS Project</h1>
<div id="table-of-contents"> <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>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
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<h1 class="title">HAC-LAC applied on the Simscape Model</h1> <h1 class="title">HAC-LAC applied on the Simscape Model</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -264,10 +263,10 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#org05b902d">1.1. Identification of the plant</a> <li><a href="#org05b902d">1.1. Identification of the plant</a>
<ul> <ul>
<li><a href="#orgfd2208d">1.1.1. Initialize the Simulation</a></li> <li><a href="#orga716982">1.1.1. Initialize the Simulation</a></li>
<li><a href="#orgd132773">1.1.2. Identification</a></li> <li><a href="#org2a3d76d">1.1.2. Identification</a></li>
<li><a href="#org9d87e76">1.1.3. Display TF</a></li> <li><a href="#org86a6b3a">1.1.3. Display TF</a></li>
<li><a href="#org5c51ae8">1.1.4. Obtained Plants for Active Damping</a></li> <li><a href="#org51e23f6">1.1.4. Obtained Plants for Active Damping</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgaf40de5">1.2. Tomography Experiment</a> <li><a href="#orgaf40de5">1.2. Tomography Experiment</a>
@ -278,10 +277,10 @@ for the JavaScript code in this tag.
</li> </li>
<li><a href="#orgdcbab01">1.3. Verification of the transfer function from nano hexapod to metrology</a> <li><a href="#orgdcbab01">1.3. Verification of the transfer function from nano hexapod to metrology</a>
<ul> <ul>
<li><a href="#orga716982">1.3.1. Initialize the Simulation</a></li> <li><a href="#org9edf24c">1.3.1. Initialize the Simulation</a></li>
<li><a href="#org2a3d76d">1.3.2. Identification</a></li> <li><a href="#org9ff767e">1.3.2. Identification</a></li>
<li><a href="#org86a6b3a">1.3.3. Display TF</a></li> <li><a href="#org5c0b9bf">1.3.3. Display TF</a></li>
<li><a href="#org51e23f6">1.3.4. Obtained Plants for Active Damping</a></li> <li><a href="#org6288fb1">1.3.4. Obtained Plants for Active Damping</a></li>
</ul> </ul>
</li> </li>
</ul> </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> <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 class="outline-text-3" id="text-1-1">
</div> </div>
<div id="outline-container-orgfd2208d" class="outline-4"> <div id="outline-container-orga716982" class="outline-4">
<h4 id="orgfd2208d"><span class="section-number-4">1.1.1</span> Initialize the Simulation</h4> <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"> <div class="outline-text-4" id="text-1-1-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -355,8 +354,8 @@ And all the controllers are set to 0.
</div> </div>
</div> </div>
<div id="outline-container-orgd132773" class="outline-4"> <div id="outline-container-org2a3d76d" class="outline-4">
<h4 id="orgd132773"><span class="section-number-4">1.1.2</span> Identification</h4> <h4 id="org2a3d76d"><span class="section-number-4">1.1.2</span> Identification</h4>
<div class="outline-text-4" id="text-1-1-2"> <div class="outline-text-4" id="text-1-1-2">
<p> <p>
First, we identify the dynamics of the system using the <code>linearize</code> function. 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> </div>
<div id="outline-container-org9d87e76" class="outline-4"> <div id="outline-container-org86a6b3a" class="outline-4">
<h4 id="org9d87e76"><span class="section-number-4">1.1.3</span> Display TF</h4> <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 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><img src="figs/plant_G_cart.png" alt="plant_G_cart.png" />
</p> </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> <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> </div>
<div id="outline-container-org5c51ae8" class="outline-4"> <div id="outline-container-org51e23f6" class="outline-4">
<h4 id="org5c51ae8"><span class="section-number-4">1.1.4</span> Obtained Plants for Active Damping</h4> <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 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><img src="figs/nass_active_damping_iff_plant.png" alt="nass_active_damping_iff_plant.png" />
</p> </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> <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>
<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><img src="figs/nass_active_damping_ine_plant.png" alt="nass_active_damping_ine_plant.png" />
</p> </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> <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>
<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><img src="figs/nass_active_damping_inertial_plant.png" alt="nass_active_damping_inertial_plant.png" />
</p> </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> <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> <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 class="outline-text-3" id="text-1-3">
</div> </div>
<div id="outline-container-orga716982" class="outline-4"> <div id="outline-container-org9edf24c" class="outline-4">
<h4 id="orga716982"><span class="section-number-4">1.3.1</span> Initialize the Simulation</h4> <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"> <div class="outline-text-4" id="text-1-3-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -563,8 +562,8 @@ And all the controllers are set to 0.
</div> </div>
</div> </div>
<div id="outline-container-org2a3d76d" class="outline-4"> <div id="outline-container-org9ff767e" class="outline-4">
<h4 id="org2a3d76d"><span class="section-number-4">1.3.2</span> Identification</h4> <h4 id="org9ff767e"><span class="section-number-4">1.3.2</span> Identification</h4>
<div class="outline-text-4" id="text-1-3-2"> <div class="outline-text-4" id="text-1-3-2">
<p> <p>
First, we identify the dynamics of the system using the <code>linearize</code> function. 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> </div>
<div id="outline-container-org86a6b3a" class="outline-4"> <div id="outline-container-org5c0b9bf" class="outline-4">
<h4 id="org86a6b3a"><span class="section-number-4">1.3.3</span> Display TF</h4> <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 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><img src="figs/plant_G_cart.png" alt="plant_G_cart.png" />
</p> </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> <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> </div>
<div id="outline-container-org51e23f6" class="outline-4"> <div id="outline-container-org6288fb1" class="outline-4">
<h4 id="org51e23f6"><span class="section-number-4">1.3.4</span> Obtained Plants for Active Damping</h4> <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 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><img src="figs/nass_active_damping_iff_plant.png" alt="nass_active_damping_iff_plant.png" />
</p> </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> <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>
<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><img src="figs/nass_active_damping_ine_plant.png" alt="nass_active_damping_ine_plant.png" />
</p> </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> <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>
<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><img src="figs/nass_active_damping_inertial_plant.png" alt="nass_active_damping_inertial_plant.png" />
</p> </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> <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>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p> <p class="date">Created: 2020-02-25 mar. 18:20</p>
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<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<title>Identification</title> <title>Identification</title>
@ -195,13 +194,13 @@
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@ -261,9 +260,9 @@ for the JavaScript code in this tag.
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
<a accesskey="h" href="../index.html"> UP </a> <a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a> <a accesskey="H" href="./index.html"> HOME </a>
</div><div id="content"> </div><div id="content">
<h1 class="title">Identification</h1> <h1 class="title">Identification</h1>
<div id="table-of-contents"> <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>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
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<?xml version="1.0" encoding="utf-8"?> <?xml version="1.0" encoding="utf-8"?>
<?xml version="1.0" encoding="utf-8"?> <?xml version="1.0" encoding="utf-8"?>
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<title>Kinematics of the station</title> <title>Kinematics of the station</title>
@ -195,13 +194,13 @@
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<h1 class="title">Kinematics of the station</h1> <h1 class="title">Kinematics of the station</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -595,7 +594,7 @@ And we verify that we indeed succeed to go to the wanted position.
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
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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> <h1 class="title">Computation of the Positioning Error with respect to the nano-hexapod</h1>
<div id="table-of-contents"> <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="#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> <li><a href="#orgb3d760a">2. Verify that the function to compute the reference pose is correct</a>
<ul> <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="#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> </ul>
</li> </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> <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> <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="#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="#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> </ul>
</li> </li>
</ul> </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. 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> </p>
</div> </div>
<div id="outline-container-orgffeb030" class="outline-3"> <div id="outline-container-org5c3ae81" class="outline-3">
<h3 id="orgffeb030"><span class="section-number-3">2.1</span> Prepare the Simulation</h3> <h3 id="org5c3ae81"><span class="section-number-3">2.1</span> Prepare the Simulation</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We set a small <code>StopTime</code>. We set a small <code>StopTime</code>.
@ -542,8 +541,8 @@ ans =
</div> </div>
</div> </div>
<div id="outline-container-orgc56cbe3" class="outline-3"> <div id="outline-container-org00066db" class="outline-3">
<h3 id="orgc56cbe3"><span class="section-number-3">2.3</span> Conclusion</h3> <h3 id="org00066db"><span class="section-number-3">2.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="important"> <div class="important">
<p> <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. 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> </p>
</div> </div>
<div id="outline-container-org5c3ae81" class="outline-3"> <div id="outline-container-org4efa9f2" class="outline-3">
<h3 id="org5c3ae81"><span class="section-number-3">3.1</span> Prepare the Simulation</h3> <h3 id="org4efa9f2"><span class="section-number-3">3.1</span> Prepare the Simulation</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
We set a small <code>StopTime</code>. We set a small <code>StopTime</code>.
@ -896,8 +895,8 @@ Verify that the pose error is small.
</div> </div>
</div> </div>
<div id="outline-container-org00066db" class="outline-3"> <div id="outline-container-orga90edfe" class="outline-3">
<h3 id="org00066db"><span class="section-number-3">3.4</span> Conclusion</h3> <h3 id="orga90edfe"><span class="section-number-3">3.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<div class="important"> <div class="important">
<p> <p>
@ -911,7 +910,7 @@ Indeed, we are able to convert the position error in the frame of the NASS and t
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p> <p class="date">Created: 2020-02-25 mar. 18:20</p>
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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@ -195,13 +194,13 @@
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<a accesskey="h" href="../index.html"> UP </a> <a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a> <a accesskey="H" href="./index.html"> HOME </a>
</div><div id="content"> </div><div id="content">
<h1 class="title">Simscape Model</h1> <h1 class="title">Simscape Model</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -776,7 +775,7 @@ Internal force, acting reciprocally between base and following origins is implem
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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@ -195,13 +194,13 @@
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<a accesskey="h" href="../index.html"> UP </a> <a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a> <a accesskey="H" href="./index.html"> HOME </a>
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<h1 class="title">Simulink Project for the NASS</h1> <h1 class="title">Simulink Project for the NASS</h1>
@ -323,7 +322,7 @@ The project also permits to automatically add defined folder to the path when th
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p> <p class="date">Created: 2020-02-25 mar. 18:21</p>
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</div><div id="content"> </div><div id="content">
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<div id="table-of-contents"> <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="#org227ba84">1. Simscape Model</a></li>
<li><a href="#org6bfb35d">2. Undamped System</a> <li><a href="#org6bfb35d">2. Undamped System</a>
<ul> <ul>
<li><a href="#org61775db">2.1. Init</a></li> <li><a href="#org5265d72">2.1. Init</a></li>
<li><a href="#org3019170">2.2. Identification</a></li> <li><a href="#org3b15675">2.2. Identification</a></li>
<li><a href="#org6a3e875">2.3. Sensitivity to Disturbances</a></li> <li><a href="#org3492011">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#orgaf6bea7">2.4. Noise Budget</a></li> <li><a href="#orgd860077">2.4. Noise Budget</a></li>
<li><a href="#orgdb3535a">2.5. Plant</a></li> <li><a href="#orgdb3535a">2.5. Plant</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org90e581d">3. Integral Force Feedback</a> <li><a href="#org66a1e03">3. Integral Force Feedback</a>
<ul> <ul>
<li><a href="#orgd591c6e">3.1. Control Design</a></li> <li><a href="#org5d899b2">3.1. Control Design</a></li>
<li><a href="#org33f4bcf">3.2. Identification</a></li> <li><a href="#orge386fb1">3.2. Identification</a></li>
<li><a href="#org9f881a5">3.3. Sensitivity to Disturbance</a></li> <li><a href="#orgbd405f9">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#org1c61625">3.4. Damped Plant</a></li> <li><a href="#orgbe8aa64">3.4. Damped Plant</a></li>
<li><a href="#org4fa7707">3.5. Conclusion</a></li> <li><a href="#orgfa342b9">3.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org07ff58f">4. Relative Motion Control</a> <li><a href="#org07ff58f">4. Relative Motion Control</a>
<ul> <ul>
<li><a href="#org185ae89">4.1. Control Design</a></li> <li><a href="#org971bdb9">4.1. Control Design</a></li>
<li><a href="#org743899e">4.2. Identification</a></li> <li><a href="#orgfce3b27">4.2. Identification</a></li>
<li><a href="#org2fa5702">4.3. Sensitivity to Disturbance</a></li> <li><a href="#org2123e6c">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#org19e990c">4.4. Damped Plant</a></li> <li><a href="#org7e3e638">4.4. Damped Plant</a></li>
<li><a href="#org47c65d5">4.5. Conclusion</a></li> <li><a href="#org0ec985e">4.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgc9b3622">5. Direct Velocity Feedback</a> <li><a href="#orgc9b3622">5. Direct Velocity Feedback</a>
<ul> <ul>
<li><a href="#orgd11a858">5.1. Control Design</a></li> <li><a href="#orgd5df5f2">5.1. Control Design</a></li>
<li><a href="#orgd06082d">5.2. Identification</a></li> <li><a href="#orgca551cb">5.2. Identification</a></li>
<li><a href="#org3111d50">5.3. Sensitivity to Disturbance</a></li> <li><a href="#orga45e582">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#org8451460">5.4. Damped Plant</a></li> <li><a href="#orgdbf551f">5.4. Damped Plant</a></li>
<li><a href="#org4792e6e">5.5. Conclusion</a></li> <li><a href="#orge883751">5.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org5ac7dda">6. With Cedrat Piezo-electric Actuators</a> <li><a href="#org5ac7dda">6. With Cedrat Piezo-electric Actuators</a>
<ul> <ul>
<li><a href="#orga4db73c">6.1. Identification</a></li> <li><a href="#orgddd7da8">6.1. Identification</a></li>
<li><a href="#org5d899b2">6.2. Control Design</a></li> <li><a href="#orgb6ef594">6.2. Control Design</a></li>
<li><a href="#orgc9ca496">6.3. Identification</a></li> <li><a href="#org5314588">6.3. Identification</a></li>
<li><a href="#org82723ce">6.4. Sensitivity to Disturbance</a></li> <li><a href="#orgd226771">6.4. Sensitivity to Disturbance</a></li>
<li><a href="#orgf696e7c">6.5. Damped Plant</a></li> <li><a href="#org294b781">6.5. Damped Plant</a></li>
<li><a href="#orgfc63bb2">6.6. Conclusion</a></li> <li><a href="#orga768e31">6.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org77a79e6">7. Comparison of Active Damping Techniques</a> <li><a href="#org77a79e6">7. Comparison of Active Damping Techniques</a>
<ul> <ul>
<li><a href="#orgb0afe4f">7.1. Load the plants</a></li> <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="#org948b91d">7.2. Sensitivity to Disturbance</a></li>
<li><a href="#org76ed406">7.3. Noise Budget</a></li> <li><a href="#org234479d">7.3. Noise Budget</a></li>
<li><a href="#orgbe8aa64">7.4. Damped Plant</a></li> <li><a href="#orgf591690">7.4. Damped Plant</a></li>
<li><a href="#org74fe486">7.5. Conclusion</a></li> <li><a href="#orgf332379">7.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org15965e0">8. Voice Coil</a> <li><a href="#org15965e0">8. Voice Coil</a>
<ul> <ul>
<li><a href="#org5265d72">8.1. Init</a></li> <li><a href="#orgefc326e">8.1. Init</a></li>
<li><a href="#org3b15675">8.2. Identification</a></li> <li><a href="#orgae49d6e">8.2. Identification</a></li>
<li><a href="#org3492011">8.3. Sensitivity to Disturbances</a></li> <li><a href="#org72047d5">8.3. Sensitivity to Disturbances</a></li>
<li><a href="#org45c8e35">8.4. Noise Budget</a></li> <li><a href="#orgbcac95d">8.4. Noise Budget</a></li>
<li><a href="#org66a1e03">8.5. Integral Force Feedback</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="#org2a655f7">8.6. Identification of the Damped Plant</a></li>
<li><a href="#orgd860077">8.7. Noise Budget</a></li> <li><a href="#orgc8d2daf">8.7. Noise Budget</a></li>
<li><a href="#orgfa342b9">8.8. Conclusion</a></li> <li><a href="#orgb885664">8.8. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </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. Let&rsquo;s start by study the undamped system.
</p> </p>
</div> </div>
<div id="outline-container-org61775db" class="outline-3"> <div id="outline-container-org5265d72" class="outline-3">
<h3 id="org61775db"><span class="section-number-3">2.1</span> Init</h3> <h3 id="org5265d72"><span class="section-number-3">2.1</span> Init</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -446,8 +445,8 @@ All the controllers are set to 0 (Open Loop).
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org3019170" class="outline-3"> <div id="outline-container-org3b15675" class="outline-3">
<h3 id="org3019170"><span class="section-number-3">2.2</span> Identification</h3> <h3 id="org3b15675"><span class="section-number-3">2.2</span> Identification</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We identify the dynamics of the system. We identify the dynamics of the system.
@ -510,8 +509,8 @@ Finally, we save the identified system dynamics for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org6a3e875" class="outline-3"> <div id="outline-container-org3492011" class="outline-3">
<h3 id="org6a3e875"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3> <h3 id="org3492011"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We show several plots representing the sensitivity to disturbances: 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> </div>
<div id="outline-container-orgaf6bea7" class="outline-3"> <div id="outline-container-orgd860077" class="outline-3">
<h3 id="orgaf6bea7"><span class="section-number-3">2.4</span> Noise Budget</h3> <h3 id="orgd860077"><span class="section-number-3">2.4</span> Noise Budget</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We first load the measured PSD of the disturbance. We first load the measured PSD of the disturbance.
@ -598,8 +597,8 @@ It corresponds to the plant to control.
</div> </div>
</div> </div>
<div id="outline-container-org90e581d" class="outline-2"> <div id="outline-container-org66a1e03" class="outline-2">
<h2 id="org90e581d"><span class="section-number-2">3</span> Integral Force Feedback</h2> <h2 id="org66a1e03"><span class="section-number-2">3</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="org37f1b7d"></a> <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> <p><span class="figure-number">Figure 8: </span>Uniaxial IFF Control Schematic</p>
</div> </div>
</div> </div>
<div id="outline-container-orgd591c6e" class="outline-3"> <div id="outline-container-org5d899b2" class="outline-3">
<h3 id="orgd591c6e"><span class="section-number-3">3.1</span> Control Design</h3> <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="outline-text-3" id="text-3-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>); <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> </div>
<div id="outline-container-org33f4bcf" class="outline-3"> <div id="outline-container-orge386fb1" class="outline-3">
<h3 id="org33f4bcf"><span class="section-number-3">3.2</span> Identification</h3> <h3 id="orge386fb1"><span class="section-number-3">3.2</span> Identification</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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> </div>
<div id="outline-container-org9f881a5" class="outline-3"> <div id="outline-container-orgbd405f9" class="outline-3">
<h3 id="org9f881a5"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3> <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 class="outline-text-3" id="text-3-3">
<div id="orge528565" class="figure"> <div id="orge528565" class="figure">
@ -750,8 +749,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org1c61625" class="outline-3"> <div id="outline-container-orgbe8aa64" class="outline-3">
<h3 id="org1c61625"><span class="section-number-3">3.4</span> Damped Plant</h3> <h3 id="orgbe8aa64"><span class="section-number-3">3.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<div id="org57280cb" class="figure"> <div id="org57280cb" class="figure">
@ -762,8 +761,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org4fa7707" class="outline-3"> <div id="outline-container-orgfa342b9" class="outline-3">
<h3 id="org4fa7707"><span class="section-number-3">3.5</span> Conclusion</h3> <h3 id="orgfa342b9"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<div class="important"> <div class="important">
<p> <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> <p><span class="figure-number">Figure 14: </span>Uniaxial RMC Control Schematic</p>
</div> </div>
</div> </div>
<div id="outline-container-org185ae89" class="outline-3"> <div id="outline-container-org971bdb9" class="outline-3">
<h3 id="org185ae89"><span class="section-number-3">4.1</span> Control Design</h3> <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="outline-text-3" id="text-4-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>); <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> </div>
<div id="outline-container-org743899e" class="outline-3"> <div id="outline-container-orgfce3b27" class="outline-3">
<h3 id="org743899e"><span class="section-number-3">4.2</span> Identification</h3> <h3 id="orgfce3b27"><span class="section-number-3">4.2</span> Identification</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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>
<div id="outline-container-org2fa5702" class="outline-3"> <div id="outline-container-org2123e6c" class="outline-3">
<h3 id="org2fa5702"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3> <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 class="outline-text-3" id="text-4-3">
<div id="org9e0dde4" class="figure"> <div id="org9e0dde4" class="figure">
@ -933,8 +932,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org19e990c" class="outline-3"> <div id="outline-container-org7e3e638" class="outline-3">
<h3 id="org19e990c"><span class="section-number-3">4.4</span> Damped Plant</h3> <h3 id="org7e3e638"><span class="section-number-3">4.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-4-4"> <div class="outline-text-3" id="text-4-4">
<div id="org18786e8" class="figure"> <div id="org18786e8" class="figure">
@ -945,8 +944,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org47c65d5" class="outline-3"> <div id="outline-container-org0ec985e" class="outline-3">
<h3 id="org47c65d5"><span class="section-number-3">4.5</span> Conclusion</h3> <h3 id="org0ec985e"><span class="section-number-3">4.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-5"> <div class="outline-text-3" id="text-4-5">
<div class="important"> <div class="important">
<p> <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> <p><span class="figure-number">Figure 20: </span>Uniaxial DVF Control Schematic</p>
</div> </div>
</div> </div>
<div id="outline-container-orgd11a858" class="outline-3"> <div id="outline-container-orgd5df5f2" class="outline-3">
<h3 id="orgd11a858"><span class="section-number-3">5.1</span> Control Design</h3> <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="outline-text-3" id="text-5-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>); <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> </div>
<div id="outline-container-orgd06082d" class="outline-3"> <div id="outline-container-orgca551cb" class="outline-3">
<h3 id="orgd06082d"><span class="section-number-3">5.2</span> Identification</h3> <h3 id="orgca551cb"><span class="section-number-3">5.2</span> Identification</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-5-2">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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> </div>
<div id="outline-container-org3111d50" class="outline-3"> <div id="outline-container-orga45e582" class="outline-3">
<h3 id="org3111d50"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3> <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 class="outline-text-3" id="text-5-3">
<div id="orgf9d4052" class="figure"> <div id="orgf9d4052" class="figure">
@ -1107,8 +1106,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org8451460" class="outline-3"> <div id="outline-container-orgdbf551f" class="outline-3">
<h3 id="org8451460"><span class="section-number-3">5.4</span> Damped Plant</h3> <h3 id="orgdbf551f"><span class="section-number-3">5.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-5-4"> <div class="outline-text-3" id="text-5-4">
<div id="orgbc9c953" class="figure"> <div id="orgbc9c953" class="figure">
@ -1119,8 +1118,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org4792e6e" class="outline-3"> <div id="outline-container-orge883751" class="outline-3">
<h3 id="org4792e6e"><span class="section-number-3">5.5</span> Conclusion</h3> <h3 id="orge883751"><span class="section-number-3">5.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-5"> <div class="outline-text-3" id="text-5-5">
<div class="important"> <div class="important">
<p> <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> <p><span class="figure-number">Figure 26: </span>Schematic of the model used for the Cedrat Actuator</p>
</div> </div>
</div> </div>
<div id="outline-container-orga4db73c" class="outline-3"> <div id="outline-container-orgddd7da8" class="outline-3">
<h3 id="orga4db73c"><span class="section-number-3">6.1</span> Identification</h3> <h3 id="orgddd7da8"><span class="section-number-3">6.1</span> Identification</h3>
<div class="outline-text-3" id="text-6-1"> <div class="outline-text-3" id="text-6-1">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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> </div>
<div id="outline-container-org5d899b2" class="outline-3"> <div id="outline-container-orgb6ef594" class="outline-3">
<h3 id="org5d899b2"><span class="section-number-3">6.2</span> Control Design</h3> <h3 id="orgb6ef594"><span class="section-number-3">6.2</span> Control Design</h3>
<div class="outline-text-3" id="text-6-2"> <div class="outline-text-3" id="text-6-2">
<p> <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. 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> </div>
<div id="outline-container-orgc9ca496" class="outline-3"> <div id="outline-container-org5314588" class="outline-3">
<h3 id="orgc9ca496"><span class="section-number-3">6.3</span> Identification</h3> <h3 id="org5314588"><span class="section-number-3">6.3</span> Identification</h3>
<div class="outline-text-3" id="text-6-3"> <div class="outline-text-3" id="text-6-3">
<p> <p>
Let&rsquo;s initialize the system prior to identification. 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> </div>
<div id="outline-container-org82723ce" class="outline-3"> <div id="outline-container-orgd226771" class="outline-3">
<h3 id="org82723ce"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3> <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 class="outline-text-3" id="text-6-4">
<div id="org90f5c2b" class="figure"> <div id="org90f5c2b" class="figure">
@ -1372,8 +1371,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div> </div>
</div> </div>
<div id="outline-container-orgf696e7c" class="outline-3"> <div id="outline-container-org294b781" class="outline-3">
<h3 id="orgf696e7c"><span class="section-number-3">6.5</span> Damped Plant</h3> <h3 id="org294b781"><span class="section-number-3">6.5</span> Damped Plant</h3>
<div class="outline-text-3" id="text-6-5"> <div class="outline-text-3" id="text-6-5">
<div id="org0c4e61a" class="figure"> <div id="org0c4e61a" class="figure">
@ -1384,8 +1383,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div> </div>
</div> </div>
<div id="outline-container-orgfc63bb2" class="outline-3"> <div id="outline-container-orga768e31" class="outline-3">
<h3 id="orgfc63bb2"><span class="section-number-3">6.6</span> Conclusion</h3> <h3 id="orga768e31"><span class="section-number-3">6.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-6-6"> <div class="outline-text-3" id="text-6-6">
<div class="important"> <div class="important">
<p> <p>
@ -1414,8 +1413,8 @@ This gives similar results than with a classical force sensor.
</div> </div>
</div> </div>
<div id="outline-container-orgbd405f9" class="outline-3"> <div id="outline-container-org948b91d" class="outline-3">
<h3 id="orgbd405f9"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3> <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 class="outline-text-3" id="text-7-2">
<div id="org8c59440" class="figure"> <div id="org8c59440" class="figure">
@ -1448,8 +1447,8 @@ This gives similar results than with a classical force sensor.
</div> </div>
</div> </div>
<div id="outline-container-org76ed406" class="outline-3"> <div id="outline-container-org234479d" class="outline-3">
<h3 id="org76ed406"><span class="section-number-3">7.3</span> Noise Budget</h3> <h3 id="org234479d"><span class="section-number-3">7.3</span> Noise Budget</h3>
<div class="outline-text-3" id="text-7-3"> <div class="outline-text-3" id="text-7-3">
<p> <p>
We first load the measured PSD of the disturbance. 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> </div>
<div id="outline-container-orgbe8aa64" class="outline-3"> <div id="outline-container-orgf591690" class="outline-3">
<h3 id="orgbe8aa64"><span class="section-number-3">7.4</span> Damped Plant</h3> <h3 id="orgf591690"><span class="section-number-3">7.4</span> Damped Plant</h3>
<div class="outline-text-3" id="text-7-4"> <div class="outline-text-3" id="text-7-4">
<div id="orga0c1298" class="figure"> <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> </div>
<div id="outline-container-org74fe486" class="outline-3"> <div id="outline-container-orgf332379" class="outline-3">
<h3 id="org74fe486"><span class="section-number-3">7.5</span> Conclusion</h3> <h3 id="orgf332379"><span class="section-number-3">7.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-7-5"> <div class="outline-text-3" id="text-7-5">
<table id="org46e95c2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <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> <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> <a id="orgf9e9d51"></a>
</p> </p>
</div> </div>
<div id="outline-container-org5265d72" class="outline-3"> <div id="outline-container-orgefc326e" class="outline-3">
<h3 id="org5265d72"><span class="section-number-3">8.1</span> Init</h3> <h3 id="orgefc326e"><span class="section-number-3">8.1</span> Init</h3>
<div class="outline-text-3" id="text-8-1"> <div class="outline-text-3" id="text-8-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -1618,8 +1617,8 @@ All the controllers are set to 0 (Open Loop).
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org3b15675" class="outline-3"> <div id="outline-container-orgae49d6e" class="outline-3">
<h3 id="org3b15675"><span class="section-number-3">8.2</span> Identification</h3> <h3 id="orgae49d6e"><span class="section-number-3">8.2</span> Identification</h3>
<div class="outline-text-3" id="text-8-2"> <div class="outline-text-3" id="text-8-2">
<p> <p>
We identify the dynamics of the system. We identify the dynamics of the system.
@ -1682,8 +1681,8 @@ Finally, we save the identified system dynamics for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org3492011" class="outline-3"> <div id="outline-container-org72047d5" class="outline-3">
<h3 id="org3492011"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3> <h3 id="org72047d5"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3>
<div class="outline-text-3" id="text-8-3"> <div class="outline-text-3" id="text-8-3">
<p> <p>
We load the dynamics when using a piezo-electric nano hexapod to compare the results. 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> </div>
<div id="outline-container-org45c8e35" class="outline-3"> <div id="outline-container-orgbcac95d" class="outline-3">
<h3 id="org45c8e35"><span class="section-number-3">8.4</span> Noise Budget</h3> <h3 id="orgbcac95d"><span class="section-number-3">8.4</span> Noise Budget</h3>
<div class="outline-text-3" id="text-8-4"> <div class="outline-text-3" id="text-8-4">
<p> <p>
We first load the measured PSD of the disturbance. 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>
</div> </div>
<div id="outline-container-org66a1e03" class="outline-3"> <div id="outline-container-org95b95ac" class="outline-3">
<h3 id="org66a1e03"><span class="section-number-3">8.5</span> Integral Force Feedback</h3> <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="outline-text-3" id="text-8-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">K_iff = <span class="org-type">-</span>20<span class="org-type">/</span>s; <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> </div>
<div id="outline-container-orgd860077" class="outline-3"> <div id="outline-container-orgc8d2daf" class="outline-3">
<h3 id="orgd860077"><span class="section-number-3">8.7</span> Noise Budget</h3> <h3 id="orgc8d2daf"><span class="section-number-3">8.7</span> Noise Budget</h3>
<div class="outline-text-3" id="text-8-7"> <div class="outline-text-3" id="text-8-7">
<p> <p>
We compute the obtain PSD of the displacement \(D\) when using IFF. 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> </div>
<div id="outline-container-orgfa342b9" class="outline-3"> <div id="outline-container-orgb885664" class="outline-3">
<h3 id="orgfa342b9"><span class="section-number-3">8.8</span> Conclusion</h3> <h3 id="orgb885664"><span class="section-number-3">8.8</span> Conclusion</h3>
<div class="outline-text-3" id="text-8-8"> <div class="outline-text-3" id="text-8-8">
<div class="important"> <div class="important">
<p> <p>
@ -1897,7 +1896,7 @@ Similarly, it would require much lower bandwidth to attain the same level of dis
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-02-25 mar. 18:08</p> <p class="date">Created: 2020-02-25 mar. 18:20</p>
</div> </div>
</body> </body>
</html> </html>

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@ -6,16 +6,16 @@
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#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
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@ -6,16 +6,16 @@
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#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
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@ -6,16 +6,16 @@
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#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
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#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
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#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

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#+EMAIL: dehaeze.thomas@gmail.com #+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

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#+EMAIL: dehaeze.thomas@gmail.com #+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
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#+EMAIL: dehaeze.thomas@gmail.com #+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

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#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+EMAIL: dehaeze.thomas@gmail.com #+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

View File

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#+EMAIL: dehaeze.thomas@gmail.com #+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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View File

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#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

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@ -6,16 +6,16 @@
#+EMAIL: dehaeze.thomas@gmail.com #+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas #+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX