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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -251,63 +39,63 @@
<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="#org380e20f">1.3. Sensitivity to disturbances</a></li> <li><a href="#org5ffc5f1">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="#orgbaae6a1">2.1. One degree-of-freedom example</a> <li><a href="#orgbe39d04">2.1. One degree-of-freedom example</a>
<ul> <ul>
<li><a href="#orgc436f05">2.1.1. Equations</a></li> <li><a href="#orgdb4e3a8">2.1.1. Equations</a></li>
<li><a href="#org238893b">2.1.2. Matlab Example</a></li> <li><a href="#orgeec7ed9">2.1.2. Matlab Example</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org824be47">2.2. Control Design</a></li> <li><a href="#org767264d">2.2. Control Design</a></li>
<li><a href="#orgfdd4556">2.3. Identification of the damped plant</a></li> <li><a href="#org945fe08">2.3. Identification of the damped plant</a></li>
<li><a href="#org4802ab9">2.4. Sensitivity to disturbances</a></li> <li><a href="#orgfd53164">2.4. Sensitivity to disturbances</a></li>
<li><a href="#org2cbe422">2.5. Damped Plant</a></li> <li><a href="#org685bc2a">2.5. Damped Plant</a></li>
<li><a href="#orgdade398">2.6. Conclusion</a></li> <li><a href="#org6b26d75">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="#org39a3687">3.1. One degree-of-freedom example</a> <li><a href="#org54d13d6">3.1. One degree-of-freedom example</a>
<ul> <ul>
<li><a href="#org994b142">3.1.1. Equations</a></li> <li><a href="#org54758f7">3.1.1. Equations</a></li>
<li><a href="#org6a1f411">3.1.2. Matlab Example</a></li> <li><a href="#org31ae910">3.1.2. Matlab Example</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org13a97a7">3.2. Control Design</a></li> <li><a href="#orga66a259">3.2. Control Design</a></li>
<li><a href="#orge00b37b">3.3. Identification of the damped plant</a></li> <li><a href="#org6a2522d">3.3. Identification of the damped plant</a></li>
<li><a href="#orgcd3874b">3.4. Sensitivity to disturbances</a></li> <li><a href="#org164a6e3">3.4. Sensitivity to disturbances</a></li>
<li><a href="#orgfcc3787">3.5. Damped Plant</a></li> <li><a href="#org5f7ca3b">3.5. Damped Plant</a></li>
<li><a href="#org37ceb38">3.6. Conclusion</a></li> <li><a href="#org7e0c0fc">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="#org20ee26e">4.1. One degree-of-freedom example</a> <li><a href="#org77792c1">4.1. One degree-of-freedom example</a>
<ul> <ul>
<li><a href="#org0d2ea8d">4.1.1. Equations</a></li> <li><a href="#org82cc039">4.1.1. Equations</a></li>
<li><a href="#orgaddbb82">4.1.2. Matlab Example</a></li> <li><a href="#org935ed32">4.1.2. Matlab Example</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf1bd80b">4.2. Control Design</a></li> <li><a href="#org6a45963">4.2. Control Design</a></li>
<li><a href="#org54ebde8">4.3. Identification of the damped plant</a></li> <li><a href="#org9b2a9e2">4.3. Identification of the damped plant</a></li>
<li><a href="#org454c0c8">4.4. Sensitivity to disturbances</a></li> <li><a href="#org7d01fa7">4.4. Sensitivity to disturbances</a></li>
<li><a href="#org5f21dd1">4.5. Damped Plant</a></li> <li><a href="#org91db5e4">4.5. Damped Plant</a></li>
<li><a href="#org53572a3">4.6. Conclusion</a></li> <li><a href="#org228bb9f">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="#orga1cf9f2">5.3. Damped Plant</a></li> <li><a href="#org1de78b5">5.3. Damped Plant</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org4d89cbd">6. Conclusion</a></li> <li><a href="#org1ff0703">6. Conclusion</a></li>
</ul> </ul>
</div> </div>
</div> </div>
@ -421,8 +209,8 @@ And we save it for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org380e20f" class="outline-3"> <div id="outline-container-org5ffc5f1" class="outline-3">
<h3 id="org380e20f"><span class="section-number-3">1.3</span> Sensitivity to disturbances</h3> <h3 id="org5ffc5f1"><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>.
@ -480,15 +268,15 @@ Then, it is applied on the simscape model.
</p> </p>
</div> </div>
<div id="outline-container-orgbaae6a1" class="outline-3"> <div id="outline-container-orgbe39d04" class="outline-3">
<h3 id="orgbaae6a1"><span class="section-number-3">2.1</span> One degree-of-freedom example</h3> <h3 id="orgbe39d04"><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-orgc436f05" class="outline-4"> <div id="outline-container-orgdb4e3a8" class="outline-4">
<h4 id="orgc436f05"><span class="section-number-4">2.1.1</span> Equations</h4> <h4 id="orgdb4e3a8"><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">
@ -554,8 +342,8 @@ This is attainable if we have:
</div> </div>
</div> </div>
<div id="outline-container-org238893b" class="outline-4"> <div id="outline-container-orgeec7ed9" class="outline-4">
<h4 id="org238893b"><span class="section-number-4">2.1.2</span> Matlab Example</h4> <h4 id="orgeec7ed9"><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.
@ -618,8 +406,8 @@ And the closed loop system is computed below.
</div> </div>
</div> </div>
<div id="outline-container-org824be47" class="outline-3"> <div id="outline-container-org767264d" class="outline-3">
<h3 id="org824be47"><span class="section-number-3">2.2</span> Control Design</h3> <h3 id="org767264d"><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:
@ -661,8 +449,8 @@ The corresponding loop gains are shown in figure <a href="#org36e3a94">7</a>.
</div> </div>
</div> </div>
<div id="outline-container-orgfdd4556" class="outline-3"> <div id="outline-container-org945fe08" class="outline-3">
<h3 id="orgfdd4556"><span class="section-number-3">2.3</span> Identification of the damped plant</h3> <h3 id="org945fe08"><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.
@ -715,8 +503,8 @@ And we save the damped plant for further analysis
</div> </div>
</div> </div>
<div id="outline-container-org4802ab9" class="outline-3"> <div id="outline-container-orgfd53164" class="outline-3">
<h3 id="org4802ab9"><span class="section-number-3">2.4</span> Sensitivity to disturbances</h3> <h3 id="orgfd53164"><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>:
@ -752,8 +540,8 @@ For instance, the plots are not the same when using <code>minreal</code>.
</div> </div>
</div> </div>
<div id="outline-container-org2cbe422" class="outline-3"> <div id="outline-container-org685bc2a" class="outline-3">
<h3 id="org2cbe422"><span class="section-number-3">2.5</span> Damped Plant</h3> <h3 id="org685bc2a"><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.
@ -782,8 +570,8 @@ However, it increases coupling at low frequency (figure <a href="#org8017b2f">11
</div> </div>
</div> </div>
<div id="outline-container-orgdade398" class="outline-3"> <div id="outline-container-org6b26d75" class="outline-3">
<h3 id="orgdade398"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org6b26d75"><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>
@ -817,15 +605,15 @@ In the Relative Motion Control (RMC), a derivative feedback is applied between t
</p> </p>
</div> </div>
<div id="outline-container-org39a3687" class="outline-3"> <div id="outline-container-org54d13d6" class="outline-3">
<h3 id="org39a3687"><span class="section-number-3">3.1</span> One degree-of-freedom example</h3> <h3 id="org54d13d6"><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-org994b142" class="outline-4"> <div id="outline-container-org54758f7" class="outline-4">
<h4 id="org994b142"><span class="section-number-4">3.1.1</span> Equations</h4> <h4 id="org54758f7"><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">
@ -884,8 +672,8 @@ This corresponds to a gain:
</div> </div>
</div> </div>
<div id="outline-container-org6a1f411" class="outline-4"> <div id="outline-container-org31ae910" class="outline-4">
<h4 id="org6a1f411"><span class="section-number-4">3.1.2</span> Matlab Example</h4> <h4 id="org31ae910"><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.
@ -948,8 +736,8 @@ And the closed loop system is computed below.
</div> </div>
</div> </div>
<div id="outline-container-org13a97a7" class="outline-3"> <div id="outline-container-orga66a259" class="outline-3">
<h3 id="org13a97a7"><span class="section-number-3">3.2</span> Control Design</h3> <h3 id="orga66a259"><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:
@ -992,8 +780,8 @@ The obtained loop gains are shown in figure <a href="#orga5b8f12">15</a>.
</div> </div>
</div> </div>
<div id="outline-container-orge00b37b" class="outline-3"> <div id="outline-container-org6a2522d" class="outline-3">
<h3 id="orge00b37b"><span class="section-number-3">3.3</span> Identification of the damped plant</h3> <h3 id="org6a2522d"><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.
@ -1046,8 +834,8 @@ And we save the damped plant for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgcd3874b" class="outline-3"> <div id="outline-container-org164a6e3" class="outline-3">
<h3 id="orgcd3874b"><span class="section-number-3">3.4</span> Sensitivity to disturbances</h3> <h3 id="org164a6e3"><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.
@ -1069,8 +857,8 @@ As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering
</div> </div>
</div> </div>
<div id="outline-container-orgfcc3787" class="outline-3"> <div id="outline-container-org5f7ca3b" class="outline-3">
<h3 id="orgfcc3787"><span class="section-number-3">3.5</span> Damped Plant</h3> <h3 id="org5f7ca3b"><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">
@ -1081,8 +869,8 @@ As shown in figure <a href="#org58aec78">16</a>, RMC control succeed in lowering
</div> </div>
</div> </div>
<div id="outline-container-org37ceb38" class="outline-3"> <div id="outline-container-org7e0c0fc" class="outline-3">
<h3 id="org37ceb38"><span class="section-number-3">3.6</span> Conclusion</h3> <h3 id="org7e0c0fc"><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>
@ -1114,15 +902,15 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</p> </p>
</div> </div>
<div id="outline-container-org20ee26e" class="outline-3"> <div id="outline-container-org77792c1" class="outline-3">
<h3 id="org20ee26e"><span class="section-number-3">4.1</span> One degree-of-freedom example</h3> <h3 id="org77792c1"><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-org0d2ea8d" class="outline-4"> <div id="outline-container-org82cc039" class="outline-4">
<h4 id="org0d2ea8d"><span class="section-number-4">4.1.1</span> Equations</h4> <h4 id="org82cc039"><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">
@ -1181,8 +969,8 @@ This corresponds to a gain:
</div> </div>
</div> </div>
<div id="outline-container-orgaddbb82" class="outline-4"> <div id="outline-container-org935ed32" class="outline-4">
<h4 id="orgaddbb82"><span class="section-number-4">4.1.2</span> Matlab Example</h4> <h4 id="org935ed32"><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.
@ -1269,8 +1057,8 @@ The obtained sensitivity to disturbances is shown in figure <a href="#org1c3277a
</div> </div>
</div> </div>
<div id="outline-container-orgf1bd80b" class="outline-3"> <div id="outline-container-org6a45963" class="outline-3">
<h3 id="orgf1bd80b"><span class="section-number-3">4.2</span> Control Design</h3> <h3 id="org6a45963"><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:
@ -1309,8 +1097,8 @@ The controller is defined below and the obtained loop gain is shown in figure <a
</div> </div>
</div> </div>
<div id="outline-container-org54ebde8" class="outline-3"> <div id="outline-container-org9b2a9e2" class="outline-3">
<h3 id="org54ebde8"><span class="section-number-3">4.3</span> Identification of the damped plant</h3> <h3 id="org9b2a9e2"><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.
@ -1363,8 +1151,8 @@ And we save the damped plant for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org454c0c8" class="outline-3"> <div id="outline-container-org7d01fa7" class="outline-3">
<h3 id="org454c0c8"><span class="section-number-3">4.4</span> Sensitivity to disturbances</h3> <h3 id="org7d01fa7"><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">
@ -1383,8 +1171,8 @@ And we save the damped plant for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org5f21dd1" class="outline-3"> <div id="outline-container-org91db5e4" class="outline-3">
<h3 id="org5f21dd1"><span class="section-number-3">4.5</span> Damped Plant</h3> <h3 id="org91db5e4"><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">
@ -1395,8 +1183,8 @@ And we save the damped plant for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org53572a3" class="outline-3"> <div id="outline-container-org228bb9f" class="outline-3">
<h3 id="org53572a3"><span class="section-number-3">4.6</span> Conclusion</h3> <h3 id="org228bb9f"><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>
@ -1467,8 +1255,8 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
<div id="outline-container-orga1cf9f2" class="outline-3"> <div id="outline-container-org1de78b5" class="outline-3">
<h3 id="orga1cf9f2"><span class="section-number-3">5.3</span> Damped Plant</h3> <h3 id="org1de78b5"><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">
@ -1494,8 +1282,8 @@ Direct Velocity Feedback:
</div> </div>
</div> </div>
<div id="outline-container-org4d89cbd" class="outline-2"> <div id="outline-container-org1ff0703" class="outline-2">
<h2 id="org4d89cbd"><span class="section-number-2">6</span> Conclusion</h2> <h2 id="org1ff0703"><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>
@ -1505,7 +1293,7 @@ Direct Velocity Feedback:
</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: 2020-03-13 ven. 17:39</p> <p class="date">Created: 2020-04-17 ven. 09:36</p>
</div> </div>
</body> </body>
</html> </html>

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@ -269,9 +59,9 @@ In order to start the simulation at steady state in presence of gravity:
We don&rsquo;t inject any perturbations and no reference tracking. We don&rsquo;t inject any perturbations and no reference tracking.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> initializeReferences(); <pre class="src src-matlab">initializeReferences();
initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>); initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
initializeController(); initializeController();
</pre> </pre>
</div> </div>
@ -279,8 +69,8 @@ We don&rsquo;t inject any perturbations and no reference tracking.
We include the gravity and log all the signals to display. We include the gravity and log all the signals to display.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>); <pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">true</span>);
initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>); initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
</pre> </pre>
</div> </div>
</div> </div>
@ -295,28 +85,28 @@ Let&rsquo;s simulate the system without any compensation of gravity forces.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> initializeGround(); <pre class="src src-matlab">initializeGround();
initializeGranite(); initializeGranite();
initializeTy(); initializeTy();
initializeRy(); initializeRy();
initializeRz(); initializeRz();
initializeMicroHexapod(); initializeMicroHexapod();
initializeAxisc(); initializeAxisc();
initializeMirror(); initializeMirror();
initializeNanoHexapod(); initializeNanoHexapod();
initializeSample(); initializeSample();
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simulink.mat'</span>); <pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.5'</span>); <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.5'</span>);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>); <pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
sim_no_compensation = simout; sim_no_compensation = simout;
</pre> </pre>
</div> </div>
@ -341,16 +131,16 @@ We here wish to simulate the system in order to compute the required force in ea
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> initializeGround(); <pre class="src src-matlab">initializeGround();
initializeGranite(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>); initializeGranite(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
initializeTy(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>); initializeTy(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
initializeRy(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>); initializeRy(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
initializeRz(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>); initializeRz(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
initializeMicroHexapod(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>); initializeMicroHexapod(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
initializeAxisc(); initializeAxisc();
initializeMirror(); initializeMirror();
initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>); initializeNanoHexapod(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>); initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'init'</span>);
</pre> </pre>
</div> </div>
@ -358,13 +148,13 @@ We here wish to simulate the system in order to compute the required force in ea
We simulate for a short time period (all the bodies are solid, so nothing should move). We simulate for a short time period (all the bodies are solid, so nothing should move).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simulink.mat'</span>); <pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.1'</span>); <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.1'</span>);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>); <pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
</pre> </pre>
</div> </div>
@ -372,7 +162,7 @@ We simulate for a short time period (all the bodies are solid, so nothing should
Verification that nothing is moving by looking at the maximum displacement of the sample: Verification that nothing is moving by looking at the maximum displacement of the sample:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> max(max(simout.Em.En.Data)) <pre class="src src-matlab">max(max(simout.Em.En.Data))
</pre> </pre>
</div> </div>
@ -385,7 +175,7 @@ Verification that nothing is moving by looking at the maximum displacement of th
We here show the measured total force/torque applied at the location of each joint. We here show the measured total force/torque applied at the location of each joint.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> data2orgtable([Fgm 0 0 0; Ftym; Fym; Fsm], {<span class="org-string">'Granite'</span>, <span class="org-string">'Translation Stage'</span>, <span class="org-string">'Tilt Stage'</span>, <span class="org-string">'Sample'</span>}, {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>}, <span class="org-string">' %.1e '</span>); <pre class="src src-matlab">data2orgtable([Fgm 0 0 0; Ftym; Fym; Fsm], {<span class="org-string">'Granite'</span>, <span class="org-string">'Translation Stage'</span>, <span class="org-string">'Tilt Stage'</span>, <span class="org-string">'Sample'</span>}, {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>}, <span class="org-string">' %.1e '</span>);
</pre> </pre>
</div> </div>
@ -462,7 +252,7 @@ We here show the measured total force/torque applied at the location of each joi
</table> </table>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> data2orgtable([Fhm; Fnm], {<span class="org-string">'Micro-Hexapod'</span>, <span class="org-string">'Nano-Hexapod'</span>}, {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>}, <span class="org-string">' %.1e '</span>); <pre class="src src-matlab">data2orgtable([Fhm; Fnm], {<span class="org-string">'Micro-Hexapod'</span>, <span class="org-string">'Nano-Hexapod'</span>}, {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>}, <span class="org-string">' %.1e '</span>);
</pre> </pre>
</div> </div>
@ -522,7 +312,7 @@ We here show the measured total force/torque applied at the location of each joi
We save these forces in <code>Foffset.mat</code>. We save these forces in <code>Foffset.mat</code>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> save(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fgm'</span>, <span class="org-string">'Ftym'</span>, <span class="org-string">'Fym'</span>, <span class="org-string">'Fzm'</span>, <span class="org-string">'Fhm'</span>, <span class="org-string">'Fnm'</span>, <span class="org-string">'Fsm'</span>); <pre class="src src-matlab">save(<span class="org-string">'mat/Foffset.mat'</span>, <span class="org-string">'Fgm'</span>, <span class="org-string">'Ftym'</span>, <span class="org-string">'Fym'</span>, <span class="org-string">'Fzm'</span>, <span class="org-string">'Fhm'</span>, <span class="org-string">'Fnm'</span>, <span class="org-string">'Fsm'</span>);
</pre> </pre>
</div> </div>
</div> </div>
@ -536,16 +326,16 @@ We save these forces in <code>Foffset.mat</code>.
We now initialize the stages with the option <code>Foffset</code>. We now initialize the stages with the option <code>Foffset</code>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> initializeGround(); <pre class="src src-matlab">initializeGround();
initializeGranite(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>); initializeGranite(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>);
initializeTy(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>); initializeTy(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>);
initializeRy(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>); initializeRy(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>);
initializeRz(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>); initializeRz(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>);
initializeMicroHexapod(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>); initializeMicroHexapod(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>);
initializeAxisc(); initializeAxisc();
initializeMirror(); initializeMirror();
initializeNanoHexapod(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>); initializeNanoHexapod(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>);
initializeSample(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>); initializeSample(<span class="org-string">'Foffset'</span>, <span class="org-constant">true</span>);
</pre> </pre>
</div> </div>
@ -553,14 +343,14 @@ We now initialize the stages with the option <code>Foffset</code>.
And we simulate the system for 0.5 seconds. And we simulate the system for 0.5 seconds.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> load(<span class="org-string">'mat/conf_simulink.mat'</span>); <pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.5'</span>); <span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simulink</span>, <span class="org-string">'StopTime'</span>, <span class="org-string">'0.5'</span>);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"> <span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>); <pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
sim_compensation = simout; sim_compensation = simout;
</pre> </pre>
</div> </div>
@ -590,7 +380,7 @@ This initialization should be redone for each configuration (change of sample ma
</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: 2020-04-05 dim. 19:43</p> <p class="date">Created: 2020-04-17 ven. 09:34</p>
</div> </div>
</body> </body>
</html> </html>

310
docs/control.html
View File

@ -4,237 +4,25 @@
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</script> </script>
<script type="text/javascript" <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head> </head>
<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -266,6 +54,8 @@
<li><a href="#orgeb80da1">4.2. HAC-LAC using IFF and Tracking control in the Cartesian frame</a></li> <li><a href="#orgeb80da1">4.2. HAC-LAC using IFF and Tracking control in the Cartesian frame</a></li>
<li><a href="#org8b2b21e">4.3. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the task space</a></li> <li><a href="#org8b2b21e">4.3. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the task space</a></li>
<li><a href="#org1c04b26">4.4. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</a></li> <li><a href="#org1c04b26">4.4. HAC-LAC using IFF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</a></li>
<li><a href="#org83b9480">4.5. HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the task space</a></li>
<li><a href="#orgdbdd7d4">4.6. HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgab73896">5. Cascade Architectures (link)</a> <li><a href="#orgab73896">5. Cascade Architectures (link)</a>
@ -275,6 +65,11 @@
</ul> </ul>
</li> </li>
<li><a href="#org4ac6d11">6. Force Control (link)</a></li> <li><a href="#org4ac6d11">6. Force Control (link)</a></li>
<li><a href="#org5840a0b">7. Other Control Architectures</a>
<ul>
<li><a href="#org5be51f2">7.1. Control to force the nano-hexapod to not do any vertical rotation</a></li>
</ul>
</li>
</ul> </ul>
</div> </div>
</div> </div>
@ -620,6 +415,28 @@ Usually, the Low Authority Controller is first design, and then the High Authori
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org83b9480" class="outline-3">
<h3 id="org83b9480"><span class="section-number-3">4.5</span> HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the task space</h3>
<div class="outline-text-3" id="text-4-5">
<div class="figure">
<p><img src="figs/control_architecture_hac_dvf_pos_X.png" alt="control_architecture_hac_dvf_pos_X.png" />
</p>
</div>
</div>
</div>
<div id="outline-container-orgdbdd7d4" class="outline-3">
<h3 id="orgdbdd7d4"><span class="section-number-3">4.6</span> HAC-LAC using DVF - the HAC controller is positioning the sample w.r.t. the granite in the space of the legs</h3>
<div class="outline-text-3" id="text-4-6">
<div class="figure">
<p><img src="figs/control_architecture_hac_dvf_pos_L.png" alt="control_architecture_hac_dvf_pos_L.png" />
</p>
</div>
</div>
</div>
</div> </div>
<div id="outline-container-orgab73896" class="outline-2"> <div id="outline-container-orgab73896" class="outline-2">
@ -629,13 +446,13 @@ Usually, the Low Authority Controller is first design, and then the High Authori
<a id="orga038762"></a> <a id="orga038762"></a>
</p> </p>
<p> <p>
The principle of Cascade control is shown in Figure <a href="#org03ef231">13</a> and explained as follow: The principle of Cascade control is shown in Figure <a href="#org03ef231">15</a> and explained as follow:
</p> </p>
<blockquote> <blockquote>
<p> <p>
To follow <b>two objectives</b> with different properties in one control system, usually a <b>hierarchy</b> of two feedback loops is used in practice. To follow <b>two objectives</b> with different properties in one control system, usually a <b>hierarchy</b> of two feedback loops is used in practice.
This kind of control topology is called <b>cascade control</b>, which is used when there are <b>several measurements and one prime control variable</b>. This kind of control topology is called <b>cascade control</b>, which is used when there are <b>several measurements and one prime control variable</b>.
Cascade control is implemented by <b>nesting</b> the control loops, as shown in Figure <a href="#org03ef231">13</a>. Cascade control is implemented by <b>nesting</b> the control loops, as shown in Figure <a href="#org03ef231">15</a>.
The output control loop is called the <b>primary loop</b>, while the inner loop is called the secondary loop and is used to fulfill a secondary objective in the closed-loop system. &#x2013; <a class='org-ref-reference' href="#taghirad13_paral">taghirad13_paral</a> The output control loop is called the <b>primary loop</b>, while the inner loop is called the secondary loop and is used to fulfill a secondary objective in the closed-loop system. &#x2013; <a class='org-ref-reference' href="#taghirad13_paral">taghirad13_paral</a>
</p> </p>
</blockquote> </blockquote>
@ -644,7 +461,7 @@ The output control loop is called the <b>primary loop</b>, while the inner loop
<div id="org03ef231" class="figure"> <div id="org03ef231" class="figure">
<p><img src="figs/control_architecture_cascade_control.png" alt="control_architecture_cascade_control.png" /> <p><img src="figs/control_architecture_cascade_control.png" alt="control_architecture_cascade_control.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Cascade Control Architecture</p> <p><span class="figure-number">Figure 15: </span>Cascade Control Architecture</p>
</div> </div>
<p> <p>
@ -669,7 +486,7 @@ The inner loop can be composed of the system controlled with the HAC-LAC topolog
<div id="orgff7dfc6" class="figure"> <div id="orgff7dfc6" class="figure">
<p><img src="figs/control_architecture_cascade_L.png" alt="control_architecture_cascade_L.png" /> <p><img src="figs/control_architecture_cascade_L.png" alt="control_architecture_cascade_L.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Cascaded Control consisting of (from inner to outer loop): IFF, Linearization Loop, Tracking Control in the frame of the Legs</p> <p><span class="figure-number">Figure 16: </span>Cascaded Control consisting of (from inner to outer loop): IFF, Linearization Loop, Tracking Control in the frame of the Legs</p>
</div> </div>
</div> </div>
</div> </div>
@ -681,7 +498,7 @@ The inner loop can be composed of the system controlled with the HAC-LAC topolog
<div id="org4bc4c4c" class="figure"> <div id="org4bc4c4c" class="figure">
<p><img src="figs/control_architecture_cascade_X.png" alt="control_architecture_cascade_X.png" /> <p><img src="figs/control_architecture_cascade_X.png" alt="control_architecture_cascade_X.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Cascaded Control consisting of (from inner to outer loop): IFF, Linearization Loop, Tracking Control in the Cartesian Frame</p> <p><span class="figure-number">Figure 17: </span>Cascaded Control consisting of (from inner to outer loop): IFF, Linearization Loop, Tracking Control in the Cartesian Frame</p>
</div> </div>
</div> </div>
</div> </div>
@ -707,6 +524,43 @@ Signals:
</div> </div>
</div> </div>
<div id="outline-container-org5840a0b" class="outline-2">
<h2 id="org5840a0b"><span class="section-number-2">7</span> Other Control Architectures</h2>
<div class="outline-text-2" id="text-7">
</div>
<div id="outline-container-org5be51f2" class="outline-3">
<h3 id="org5be51f2"><span class="section-number-3">7.1</span> Control to force the nano-hexapod to not do any vertical rotation</h3>
<div class="outline-text-3" id="text-7-1">
<p>
As the sample rotation around the vertical axis is not measure, the best we can do with the nano-hexapod is to not rotate around this same axis.
</p>
<p>
One way to do it is shown in Figure <a href="#orga8781eb">19</a>.
</p>
<p>
The controller \(\bm{K}_{R_z}\) is decomposed as shown in Figure <a href="#org2f0522c">20</a>.
</p>
<div id="orga8781eb" class="figure">
<p><img src="figs/control_architecture_fixed_rz.png" alt="control_architecture_fixed_rz.png" />
</p>
<p><span class="figure-number">Figure 19: </span>Figure caption</p>
</div>
<div id="org2f0522c" class="figure">
<p><img src="figs/control_architecture_fixed_Krz.png" alt="control_architecture_fixed_Krz.png" />
</p>
<p><span class="figure-number">Figure 20: </span>Figure caption</p>
</div>
</div>
</div>
</div>
<p> <p>
<h1 class='org-ref-bib-h1'>Bibliography</h1> <h1 class='org-ref-bib-h1'>Bibliography</h1>
@ -718,7 +572,7 @@ 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: 2020-04-01 mer. 16:16</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
</body> </body>
</html> </html>

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@ -273,17 +39,17 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#orgb9bb91c">1.1. Identification of the dynamics for Active Damping</a> <li><a href="#orgb9bb91c">1.1. Identification of the dynamics for Active Damping</a>
<ul> <ul>
<li><a href="#org9be7a0a">1.1.1. Identification</a></li> <li><a href="#org0e0278d">1.1.1. Identification</a></li>
<li><a href="#org821239d">1.1.2. Obtained Plants for Active Damping</a></li> <li><a href="#org821239d">1.1.2. Obtained Plants for Active Damping</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org21a2e91">1.2. Identification of the dynamics for High Authority Control</a> <li><a href="#org21a2e91">1.2. Identification of the dynamics for High Authority Control</a>
<ul> <ul>
<li><a href="#orgae8b5f6">1.2.1. Identification</a></li> <li><a href="#org25cfa54">1.2.1. Identification</a></li>
<li><a href="#orgff85811">1.2.2. Obtained Plants</a></li> <li><a href="#orgff85811">1.2.2. Obtained Plants</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd249fa7">1.3. Tomography Experiment</a> <li><a href="#org2540d06">1.3. Tomography Experiment</a>
<ul> <ul>
<li><a href="#orgd5305ce">1.3.1. Simulation</a></li> <li><a href="#orgd5305ce">1.3.1. Simulation</a></li>
<li><a href="#orgd64a4bc">1.3.2. Results</a></li> <li><a href="#orgd64a4bc">1.3.2. Results</a></li>
@ -303,55 +69,55 @@ for the JavaScript code in this tag.
</li> </li>
<li><a href="#org47c5593">2.4. Variation of the Tilt Angle</a></li> <li><a href="#org47c5593">2.4. Variation of the Tilt Angle</a></li>
<li><a href="#org047e39c">2.5. Scans of the Translation Stage</a></li> <li><a href="#org047e39c">2.5. Scans of the Translation Stage</a></li>
<li><a href="#orga3a88c5">2.6. Conclusion</a></li> <li><a href="#org6e25821">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org11ab68f">3. Integral Force Feedback</a> <li><a href="#org11ab68f">3. Integral Force Feedback</a>
<ul> <ul>
<li><a href="#org7469e89">3.1. Control Design</a> <li><a href="#orga4d47de">3.1. Control Design</a>
<ul> <ul>
<li><a href="#org50113d6">3.1.1. Plant</a></li> <li><a href="#org506864d">3.1.1. Plant</a></li>
<li><a href="#org0279170">3.1.2. Control Design</a></li> <li><a href="#orgd147055">3.1.2. Control Design</a></li>
<li><a href="#orge6bfce6">3.1.3. Diagonal Controller</a></li> <li><a href="#orgeed5a23">3.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org93e3515">3.2. Tomography Experiment</a> <li><a href="#orge4bf8c1">3.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#org132e692">3.2.1. Simulation with IFF Controller</a></li> <li><a href="#org132e692">3.2.1. Simulation with IFF Controller</a></li>
<li><a href="#orge17626d">3.2.2. Compare with Undamped system</a></li> <li><a href="#org9c3f302">3.2.2. Compare with Undamped system</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org6bfc3c8">3.3. Conclusion</a></li> <li><a href="#orgd53cc4e">3.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org13393f4">4. Direct Velocity Feedback</a> <li><a href="#org13393f4">4. Direct Velocity Feedback</a>
<ul> <ul>
<li><a href="#org6ab2a22">4.1. Control Design</a> <li><a href="#org22d12df">4.1. Control Design</a>
<ul> <ul>
<li><a href="#orged52a69">4.1.1. Plant</a></li> <li><a href="#org0b48ca9">4.1.1. Plant</a></li>
<li><a href="#org44b5b14">4.1.2. Control Design</a></li> <li><a href="#org59030a3">4.1.2. Control Design</a></li>
<li><a href="#orgfb28f7d">4.1.3. Diagonal Controller</a></li> <li><a href="#org59cf352">4.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgdc93329">4.2. Tomography Experiment</a> <li><a href="#org76bbcf0">4.2. Tomography Experiment</a>
<ul> <ul>
<li><a href="#orgaf91898">4.2.1. Initialize the Simulation</a></li> <li><a href="#orge2c011b">4.2.1. Initialize the Simulation</a></li>
<li><a href="#orge68c2e6">4.2.2. Compare with Undamped system</a></li> <li><a href="#org8cb0050">4.2.2. Compare with Undamped system</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgdd6b994">4.3. Conclusion</a></li> <li><a href="#org5f85708">4.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org8f2508f">5. Inertial Control</a> <li><a href="#org8f2508f">5. Inertial Control</a>
<ul> <ul>
<li><a href="#org78934a1">5.1. Control Design</a> <li><a href="#org9f4c2b3">5.1. Control Design</a>
<ul> <ul>
<li><a href="#orga97b3aa">5.1.1. Plant</a></li> <li><a href="#org9ec605a">5.1.1. Plant</a></li>
<li><a href="#org92b0a5f">5.1.2. Control Design</a></li> <li><a href="#org94a1419">5.1.2. Control Design</a></li>
<li><a href="#org9e08e48">5.1.3. Diagonal Controller</a></li> <li><a href="#orgc596f9b">5.1.3. Diagonal Controller</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org054aff8">5.2. Conclusion</a></li> <li><a href="#orgdc8e915">5.2. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3557ae9">6. Comparison</a> <li><a href="#org3557ae9">6. Comparison</a>
@ -366,16 +132,16 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#org8642cf5">7.1. prepareLinearizeIdentification</a> <li><a href="#org8642cf5">7.1. prepareLinearizeIdentification</a>
<ul> <ul>
<li><a href="#org6a968ef">Function Description</a></li> <li><a href="#orga028903">Function Description</a></li>
<li><a href="#orgc14eed3">Optional Parameters</a></li> <li><a href="#orgbda1bf4">Optional Parameters</a></li>
<li><a href="#orgc7a07c5">Initialize the Simulation</a></li> <li><a href="#org2131c58">Initialize the Simulation</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgeb73896">7.2. prepareTomographyExperiment</a> <li><a href="#orgeb73896">7.2. prepareTomographyExperiment</a>
<ul> <ul>
<li><a href="#org34e8f09">Function Description</a></li> <li><a href="#org889b896">Function Description</a></li>
<li><a href="#org82d8c08">Optional Parameters</a></li> <li><a href="#orgf77fd6f">Optional Parameters</a></li>
<li><a href="#org2ece687">Initialize the Simulation</a></li> <li><a href="#org45b5800">Initialize the Simulation</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -447,8 +213,8 @@ After that, a tomography experiment is simulation without any active damping tec
<h3 id="orgb9bb91c"><span class="section-number-3">1.1</span> Identification of the dynamics for Active Damping</h3> <h3 id="orgb9bb91c"><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-org9be7a0a" class="outline-4"> <div id="outline-container-org0e0278d" class="outline-4">
<h4 id="org9be7a0a"><span class="section-number-4">1.1.1</span> Identification</h4> <h4 id="org0e0278d"><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.
@ -541,8 +307,8 @@ And we save them for further analysis.
<h3 id="org21a2e91"><span class="section-number-3">1.2</span> Identification of the dynamics for High Authority Control</h3> <h3 id="org21a2e91"><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-orgae8b5f6" class="outline-4"> <div id="outline-container-org25cfa54" class="outline-4">
<h4 id="orgae8b5f6"><span class="section-number-4">1.2.1</span> Identification</h4> <h4 id="org25cfa54"><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.
@ -611,8 +377,8 @@ And we save them for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgd249fa7" class="outline-3"> <div id="outline-container-org2540d06" class="outline-3">
<h3 id="orgd249fa7"><span class="section-number-3">1.3</span> Tomography Experiment</h3> <h3 id="org2540d06"><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-orgd5305ce" class="outline-4"> <div id="outline-container-orgd5305ce" class="outline-4">
@ -1000,8 +766,8 @@ We identify the dynamics at different positions (times) when scanning with the T
</div> </div>
</div> </div>
<div id="outline-container-orga3a88c5" class="outline-3"> <div id="outline-container-org6e25821" class="outline-3">
<h3 id="orga3a88c5"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org6e25821"><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="orgbd1a9f9" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgbd1a9f9" 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>
@ -1092,12 +858,12 @@ The control architecture is represented in figure <a href="#org3a1dbf1">29</a> w
</div> </div>
</div> </div>
<div id="outline-container-org7469e89" class="outline-3"> <div id="outline-container-orga4d47de" class="outline-3">
<h3 id="org7469e89"><span class="section-number-3">3.1</span> Control Design</h3> <h3 id="orga4d47de"><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-org50113d6" class="outline-4"> <div id="outline-container-org506864d" class="outline-4">
<h4 id="org50113d6"><span class="section-number-4">3.1.1</span> Plant</h4> <h4 id="org506864d"><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:
@ -1121,8 +887,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div> </div>
</div> </div>
<div id="outline-container-org0279170" class="outline-4"> <div id="outline-container-orgd147055" class="outline-4">
<h4 id="org0279170"><span class="section-number-4">3.1.2</span> Control Design</h4> <h4 id="orgd147055"><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:
@ -1146,8 +912,8 @@ The corresponding loop gains are shown in figure <a href="#org1f5c623">31</a>.
</div> </div>
</div> </div>
<div id="outline-container-orge6bfce6" class="outline-4"> <div id="outline-container-orgeed5a23" class="outline-4">
<h4 id="orge6bfce6"><span class="section-number-4">3.1.3</span> Diagonal Controller</h4> <h4 id="orgeed5a23"><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
@ -1169,8 +935,8 @@ We save the controller for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org93e3515" class="outline-3"> <div id="outline-container-orge4bf8c1" class="outline-3">
<h3 id="org93e3515"><span class="section-number-3">3.2</span> Tomography Experiment</h3> <h3 id="orge4bf8c1"><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-org132e692" class="outline-4"> <div id="outline-container-org132e692" class="outline-4">
@ -1222,8 +988,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-orge17626d" class="outline-4"> <div id="outline-container-org9c3f302" class="outline-4">
<h4 id="orge17626d"><span class="section-number-4">3.2.2</span> Compare with Undamped system</h4> <h4 id="org9c3f302"><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="org7547861" class="figure"> <div id="org7547861" class="figure">
@ -1249,8 +1015,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-org6bfc3c8" class="outline-3"> <div id="outline-container-orgd53cc4e" class="outline-3">
<h3 id="org6bfc3c8"><span class="section-number-3">3.3</span> Conclusion</h3> <h3 id="orgd53cc4e"><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>
@ -1285,12 +1051,12 @@ The actuator displacement can be measured with a capacitive sensor for instance.
</p> </p>
</div> </div>
<div id="outline-container-org6ab2a22" class="outline-3"> <div id="outline-container-org22d12df" class="outline-3">
<h3 id="org6ab2a22"><span class="section-number-3">4.1</span> Control Design</h3> <h3 id="org22d12df"><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-orged52a69" class="outline-4"> <div id="outline-container-org0b48ca9" class="outline-4">
<h4 id="orged52a69"><span class="section-number-4">4.1.1</span> Plant</h4> <h4 id="org0b48ca9"><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:
@ -1314,8 +1080,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div> </div>
</div> </div>
<div id="outline-container-org44b5b14" class="outline-4"> <div id="outline-container-org59030a3" class="outline-4">
<h4 id="org44b5b14"><span class="section-number-4">4.1.2</span> Control Design</h4> <h4 id="org59030a3"><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.
@ -1339,8 +1105,8 @@ The obtained loop gains are shown in figure <a href="#org3568457">36</a>.
</div> </div>
</div> </div>
<div id="outline-container-orgfb28f7d" class="outline-4"> <div id="outline-container-org59cf352" class="outline-4">
<h4 id="orgfb28f7d"><span class="section-number-4">4.1.3</span> Diagonal Controller</h4> <h4 id="org59cf352"><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.
@ -1361,12 +1127,12 @@ We save the controller for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgdc93329" class="outline-3"> <div id="outline-container-org76bbcf0" class="outline-3">
<h3 id="orgdc93329"><span class="section-number-3">4.2</span> Tomography Experiment</h3> <h3 id="org76bbcf0"><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-orgaf91898" class="outline-4"> <div id="outline-container-orge2c011b" class="outline-4">
<h4 id="orgaf91898"><span class="section-number-4">4.2.1</span> Initialize the Simulation</h4> <h4 id="orge2c011b"><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.
@ -1414,8 +1180,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-orge68c2e6" class="outline-4"> <div id="outline-container-org8cb0050" class="outline-4">
<h4 id="orge68c2e6"><span class="section-number-4">4.2.2</span> Compare with Undamped system</h4> <h4 id="org8cb0050"><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="orgfe01054" class="figure"> <div id="orgfe01054" class="figure">
@ -1441,8 +1207,8 @@ save(<span class="org-string">'./mat/active_damping_tomo_exp.mat'</span>, <span
</div> </div>
</div> </div>
<div id="outline-container-orgdd6b994" class="outline-3"> <div id="outline-container-org5f85708" class="outline-3">
<h3 id="orgdd6b994"><span class="section-number-3">4.3</span> Conclusion</h3> <h3 id="org5f85708"><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>
@ -1474,12 +1240,12 @@ In Inertial Control, a feedback is applied between the measured <b>absolute</b>
</p> </p>
</div> </div>
<div id="outline-container-org78934a1" class="outline-3"> <div id="outline-container-org9f4c2b3" class="outline-3">
<h3 id="org78934a1"><span class="section-number-3">5.1</span> Control Design</h3> <h3 id="org9f4c2b3"><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-orga97b3aa" class="outline-4"> <div id="outline-container-org9ec605a" class="outline-4">
<h4 id="orga97b3aa"><span class="section-number-4">5.1.1</span> Plant</h4> <h4 id="org9ec605a"><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:
@ -1503,8 +1269,8 @@ Let&rsquo;s look at the transfer function from actuator forces in the nano-hexap
</div> </div>
</div> </div>
<div id="outline-container-org92b0a5f" class="outline-4"> <div id="outline-container-org94a1419" class="outline-4">
<h4 id="org92b0a5f"><span class="section-number-4">5.1.2</span> Control Design</h4> <h4 id="org94a1419"><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="#orga2f6fdb">41</a>. The controller is defined below and the obtained loop gain is shown in figure <a href="#orga2f6fdb">41</a>.
@ -1524,8 +1290,8 @@ The controller is defined below and the obtained loop gain is shown in figure <a
</div> </div>
</div> </div>
<div id="outline-container-org9e08e48" class="outline-4"> <div id="outline-container-orgc596f9b" class="outline-4">
<h4 id="org9e08e48"><span class="section-number-4">5.1.3</span> Diagonal Controller</h4> <h4 id="orgc596f9b"><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.
@ -1546,8 +1312,8 @@ We save the controller for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org054aff8" class="outline-3"> <div id="outline-container-orgdc8e915" class="outline-3">
<h3 id="org054aff8"><span class="section-number-3">5.2</span> Conclusion</h3> <h3 id="orgdc8e915"><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>
@ -1723,9 +1489,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
</p> </p>
</div> </div>
<div id="outline-container-org6a968ef" class="outline-4"> <div id="outline-container-orga028903" class="outline-4">
<h4 id="org6a968ef">Function Description</h4> <h4 id="orga028903">Function Description</h4>
<div class="outline-text-4" id="text-org6a968ef"> <div class="outline-text-4" id="text-orga028903">
<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>
@ -1733,9 +1499,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
</div> </div>
</div> </div>
<div id="outline-container-orgc14eed3" class="outline-4"> <div id="outline-container-orgbda1bf4" class="outline-4">
<h4 id="orgc14eed3">Optional Parameters</h4> <h4 id="orgbda1bf4">Optional Parameters</h4>
<div class="outline-text-4" id="text-orgc14eed3"> <div class="outline-text-4" id="text-orgbda1bf4">
<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>
@ -1746,9 +1512,9 @@ This Matlab function is accessible <a href="src/prepareLinearizeIdentification.m
</div> </div>
</div> </div>
<div id="outline-container-orgc7a07c5" class="outline-4"> <div id="outline-container-org2131c58" class="outline-4">
<h4 id="orgc7a07c5">Initialize the Simulation</h4> <h4 id="org2131c58">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-orgc7a07c5"> <div class="outline-text-4" id="text-org2131c58">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
</p> </p>
@ -1821,9 +1587,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</p> </p>
</div> </div>
<div id="outline-container-org34e8f09" class="outline-4"> <div id="outline-container-org889b896" class="outline-4">
<h4 id="org34e8f09">Function Description</h4> <h4 id="org889b896">Function Description</h4>
<div class="outline-text-4" id="text-org34e8f09"> <div class="outline-text-4" id="text-org889b896">
<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>
@ -1831,9 +1597,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</div> </div>
</div> </div>
<div id="outline-container-org82d8c08" class="outline-4"> <div id="outline-container-orgf77fd6f" class="outline-4">
<h4 id="org82d8c08">Optional Parameters</h4> <h4 id="orgf77fd6f">Optional Parameters</h4>
<div class="outline-text-4" id="text-org82d8c08"> <div class="outline-text-4" id="text-orgf77fd6f">
<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>
@ -1845,9 +1611,9 @@ This Matlab function is accessible <a href="src/prepareTomographyExperiment.m">h
</div> </div>
</div> </div>
<div id="outline-container-org2ece687" class="outline-4"> <div id="outline-container-org45b5800" class="outline-4">
<h4 id="org2ece687">Initialize the Simulation</h4> <h4 id="org45b5800">Initialize the Simulation</h4>
<div class="outline-text-4" id="text-org2ece687"> <div class="outline-text-4" id="text-org45b5800">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
</p> </p>
@ -1915,7 +1681,7 @@ 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: 2020-03-26 jeu. 17:25</p> <p class="date">Created: 2020-04-17 ven. 09:36</p>
</div> </div>
</body> </body>
</html> </html>

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@ -4,237 +4,25 @@
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -259,14 +47,14 @@
<li><a href="#org101bfbc">3. High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</a> <li><a href="#org101bfbc">3. High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</a>
<ul> <ul>
<li><a href="#org259240d">3.1. Identification of the damped plant</a></li> <li><a href="#org259240d">3.1. Identification of the damped plant</a></li>
<li><a href="#orgb574395">3.2. Obtained Plant</a></li> <li><a href="#orgfc86b4c">3.2. Obtained Plant</a></li>
<li><a href="#orgdea5e17">3.3. Controller Design and Loop Gain</a></li> <li><a href="#orgdea5e17">3.3. Controller Design and Loop Gain</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org58f9f32">4. Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</a> <li><a href="#org58f9f32">4. Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</a>
<ul> <ul>
<li><a href="#org82ca884">4.1. Identification of the linearized plant</a></li> <li><a href="#org82ca884">4.1. Identification of the linearized plant</a></li>
<li><a href="#org3b0d2c2">4.2. Obtained Plant</a></li> <li><a href="#org6f5b22e">4.2. Obtained Plant</a></li>
<li><a href="#org839cdb3">4.3. Controller Design</a></li> <li><a href="#org839cdb3">4.3. Controller Design</a></li>
</ul> </ul>
</li> </li>
@ -495,8 +283,8 @@ isstable(Gl)
</div> </div>
</div> </div>
<div id="outline-container-orgb574395" class="outline-3"> <div id="outline-container-orgfc86b4c" class="outline-3">
<h3 id="orgb574395"><span class="section-number-3">3.2</span> Obtained Plant</h3> <h3 id="orgfc86b4c"><span class="section-number-3">3.2</span> Obtained Plant</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
The obtain plant is shown in Figure <a href="#org455eb07">5</a>. The obtain plant is shown in Figure <a href="#org455eb07">5</a>.
@ -593,8 +381,8 @@ isstable(Gx)
</div> </div>
</div> </div>
<div id="outline-container-org3b0d2c2" class="outline-3"> <div id="outline-container-org6f5b22e" class="outline-3">
<h3 id="org3b0d2c2"><span class="section-number-3">4.2</span> Obtained Plant</h3> <h3 id="org6f5b22e"><span class="section-number-3">4.2</span> Obtained Plant</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<div id="orge364e46" class="figure"> <div id="orge364e46" class="figure">
@ -704,7 +492,7 @@ Ts = t(2)<span class="org-type">-</span>t(1);
</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: 2020-04-01 mer. 16:16</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -271,26 +37,26 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#org1f22cdb">1. Decentralized Control</a> <li><a href="#org1f22cdb">1. Decentralized Control</a>
<ul> <ul>
<li><a href="#orgcd58f5e">1.1. Control Schematic</a></li> <li><a href="#org01937c0">1.1. Control Schematic</a></li>
<li><a href="#org4318f13">1.2. Initialize the Simscape Model</a></li> <li><a href="#orgc9e3b66">1.2. Initialize the Simscape Model</a></li>
<li><a href="#org42afc36">1.3. Identification of the plant</a></li> <li><a href="#org42afc36">1.3. Identification of the plant</a></li>
<li><a href="#org871560e">1.4. Plant Analysis</a></li> <li><a href="#org871560e">1.4. Plant Analysis</a></li>
<li><a href="#orgdf3c9aa">1.5. Controller Design</a></li> <li><a href="#org296e3de">1.5. Controller Design</a></li>
<li><a href="#org753f2c4">1.6. Simulation</a></li> <li><a href="#orgb7afa1e">1.6. Simulation</a></li>
<li><a href="#orgd8c14ee">1.7. Results</a></li> <li><a href="#orgbb1dc16">1.7. Results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgfa4be92">2. HAC-LAC (IFF) Decentralized Control</a> <li><a href="#orgfa4be92">2. HAC-LAC (IFF) Decentralized Control</a>
<ul> <ul>
<li><a href="#org744f1a3">2.1. Control Schematic</a></li> <li><a href="#orgbc4af09">2.1. Control Schematic</a></li>
<li><a href="#org0e6472e">2.2. Initialize the Simscape Model</a></li> <li><a href="#org5ac6c37">2.2. Initialize the Simscape Model</a></li>
<li><a href="#org0903106">2.3. Initialization</a></li> <li><a href="#org0903106">2.3. Initialization</a></li>
<li><a href="#orge739f61">2.4. Identification for IFF</a></li> <li><a href="#orge739f61">2.4. Identification for IFF</a></li>
<li><a href="#org08b6a99">2.5. Integral Force Feedback Controller</a></li> <li><a href="#org08b6a99">2.5. Integral Force Feedback Controller</a></li>
<li><a href="#org06b5c75">2.6. Identification of the damped plant</a></li> <li><a href="#org06b5c75">2.6. Identification of the damped plant</a></li>
<li><a href="#orgf258d8b">2.7. Controller Design</a></li> <li><a href="#org85a0730">2.7. Controller Design</a></li>
<li><a href="#org5f74b9e">2.8. Simulation</a></li> <li><a href="#org58ffd80">2.8. Simulation</a></li>
<li><a href="#org42ecd75">2.9. Results</a></li> <li><a href="#orga01ccc6">2.9. Results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org21a9294">3. Conclusion</a></li> <li><a href="#org21a9294">3. Conclusion</a></li>
@ -306,11 +72,11 @@ In this document, we apply some decentralized control to the NASS and see what l
<h2 id="org1f22cdb"><span class="section-number-2">1</span> Decentralized Control</h2> <h2 id="org1f22cdb"><span class="section-number-2">1</span> Decentralized Control</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div> </div>
<div id="outline-container-orgcd58f5e" class="outline-3"> <div id="outline-container-org01937c0" class="outline-3">
<h3 id="orgcd58f5e"><span class="section-number-3">1.1</span> Control Schematic</h3> <h3 id="org01937c0"><span class="section-number-3">1.1</span> Control Schematic</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
The control architecture is shown in Figure <a href="#org5b991df">1</a>. The control architecture is shown in Figure <a href="#org5b9133f">1</a>.
</p> </p>
<p> <p>
@ -326,7 +92,7 @@ The signals are:
</ul> </ul>
<div id="org5b991df" class="figure"> <div id="org5b9133f" class="figure">
<p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" /> <p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Decentralized control for reference tracking</p> <p><span class="figure-number">Figure 1: </span>Decentralized control for reference tracking</p>
@ -334,8 +100,8 @@ The signals are:
</div> </div>
</div> </div>
<div id="outline-container-org4318f13" class="outline-3"> <div id="outline-container-orgc9e3b66" class="outline-3">
<h3 id="org4318f13"><span class="section-number-3">1.2</span> Initialize the Simscape Model</h3> <h3 id="orgc9e3b66"><span class="section-number-3">1.2</span> Initialize the Simscape Model</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -449,8 +215,8 @@ We can see that:
</div> </div>
</div> </div>
<div id="outline-container-orgdf3c9aa" class="outline-3"> <div id="outline-container-org296e3de" class="outline-3">
<h3 id="orgdf3c9aa"><span class="section-number-3">1.5</span> Controller Design</h3> <h3 id="org296e3de"><span class="section-number-3">1.5</span> Controller Design</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<p> <p>
The controller consists of: The controller consists of:
@ -496,8 +262,8 @@ We add a minus sign to the controller as it is not included in the Simscape mode
</div> </div>
</div> </div>
<div id="outline-container-org753f2c4" class="outline-3"> <div id="outline-container-orgb7afa1e" class="outline-3">
<h3 id="org753f2c4"><span class="section-number-3">1.6</span> Simulation</h3> <h3 id="orgb7afa1e"><span class="section-number-3">1.6</span> Simulation</h3>
<div class="outline-text-3" id="text-1-6"> <div class="outline-text-3" id="text-1-6">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>); <pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-L'</span>);
@ -523,8 +289,8 @@ save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-orgd8c14ee" class="outline-3"> <div id="outline-container-orgbb1dc16" class="outline-3">
<h3 id="orgd8c14ee"><span class="section-number-3">1.7</span> Results</h3> <h3 id="orgbb1dc16"><span class="section-number-3">1.7</span> Results</h3>
<div class="outline-text-3" id="text-1-7"> <div class="outline-text-3" id="text-1-7">
<p> <p>
The reference path and the position of the mobile platform are shown in Figure <a href="#org247b3a0">4</a>. The reference path and the position of the mobile platform are shown in Figure <a href="#org247b3a0">4</a>.
@ -554,11 +320,11 @@ We here add an Active Damping Loop (Integral Force Feedback) prior to using the
</p> </p>
</div> </div>
<div id="outline-container-org744f1a3" class="outline-3"> <div id="outline-container-orgbc4af09" class="outline-3">
<h3 id="org744f1a3"><span class="section-number-3">2.1</span> Control Schematic</h3> <h3 id="orgbc4af09"><span class="section-number-3">2.1</span> Control Schematic</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
The control architecture is shown in Figure <a href="#org5b991df">1</a>. The control architecture is shown in Figure <a href="#org5b9133f">1</a>.
</p> </p>
<p> <p>
@ -574,7 +340,7 @@ The signals are:
</ul> </ul>
<div id="orgda1b906" class="figure"> <div id="org657383b" class="figure">
<p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" /> <p><img src="figs/decentralized_reference_tracking_L.png" alt="decentralized_reference_tracking_L.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Decentralized control for reference tracking</p> <p><span class="figure-number">Figure 5: </span>Decentralized control for reference tracking</p>
@ -582,8 +348,8 @@ The signals are:
</div> </div>
</div> </div>
<div id="outline-container-org0e6472e" class="outline-3"> <div id="outline-container-org5ac6c37" class="outline-3">
<h3 id="org0e6472e"><span class="section-number-3">2.2</span> Initialize the Simscape Model</h3> <h3 id="org5ac6c37"><span class="section-number-3">2.2</span> Initialize the Simscape Model</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -719,8 +485,8 @@ Gd.OutputName = {<span class="org-string">'El1'</span>, <span class="org-string"
</div> </div>
</div> </div>
<div id="outline-container-orgf258d8b" class="outline-3"> <div id="outline-container-org85a0730" class="outline-3">
<h3 id="orgf258d8b"><span class="section-number-3">2.7</span> Controller Design</h3> <h3 id="org85a0730"><span class="section-number-3">2.7</span> Controller Design</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300; <pre class="src src-matlab">wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>300;
@ -748,8 +514,8 @@ Kl = diag(1<span class="org-type">./</span>diag(abs(freqresp(Gd, wc)))) <span cl
</div> </div>
<div id="outline-container-org5f74b9e" class="outline-3"> <div id="outline-container-org58ffd80" class="outline-3">
<h3 id="org5f74b9e"><span class="section-number-3">2.8</span> Simulation</h3> <h3 id="org58ffd80"><span class="section-number-3">2.8</span> Simulation</h3>
<div class="outline-text-3" id="text-2-8"> <div class="outline-text-3" id="text-2-8">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>); <pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'ref-track-iff-L'</span>);
@ -775,8 +541,8 @@ save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-org42ecd75" class="outline-3"> <div id="outline-container-orga01ccc6" class="outline-3">
<h3 id="org42ecd75"><span class="section-number-3">2.9</span> Results</h3> <h3 id="orga01ccc6"><span class="section-number-3">2.9</span> Results</h3>
</div> </div>
</div> </div>
<div id="outline-container-org21a9294" class="outline-2"> <div id="outline-container-org21a9294" class="outline-2">
@ -785,7 +551,7 @@ save(<span class="org-string">'./mat/tomo_exp_decentalized.mat'</span>, <span cl
</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: 2020-03-26 jeu. 17:25</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
</body> </body>
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@ -1,263 +1,28 @@
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<h1 class="title">Force Control applied on the Simscape Model</h1> <h1 class="title">Force Control applied on the Simscape Model</h1>
<p> <p>
Cascade Control where the inner loop goal is to control the total wrench (forces and torques) applied to the upper part of the nano-hexapod. Cascade Control where the inner loop goal is to control the total wrench (forces and torques) applied to the upper part of the nano-hexapod.
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256
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -281,13 +47,13 @@ for the JavaScript code in this tag.
<li><a href="#org19b83b7">2.1. Definition of the values</a></li> <li><a href="#org19b83b7">2.1. Definition of the values</a></li>
<li><a href="#org0e9811a">2.2. Control using \(d\)</a> <li><a href="#org0e9811a">2.2. Control using \(d\)</a>
<ul> <ul>
<li><a href="#org9828aed">2.2.1. Control Architecture</a></li> <li><a href="#org47fb453">2.2.1. Control Architecture</a></li>
<li><a href="#org5a120e1">2.2.2. Analytical Analysis</a></li> <li><a href="#org5a120e1">2.2.2. Analytical Analysis</a></li>
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<li><a href="#org4c74e08">2.3.1. Control Architecture</a></li> <li><a href="#org691c845">2.3.1. Control Architecture</a></li>
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@ -297,7 +63,7 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#orgfab8395">2.5.1. Analytical analysis</a></li> <li><a href="#orgfab8395">2.5.1. Analytical analysis</a></li>
<li><a href="#org625e3c2">2.5.2. Control implementation</a></li> <li><a href="#org625e3c2">2.5.2. Control implementation</a></li>
<li><a href="#org3db77f5">2.5.3. Results</a></li> <li><a href="#org38d941f">2.5.3. Results</a></li>
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@ -312,7 +78,7 @@ for the JavaScript code in this tag.
<li><a href="#org50054f2">5.4. Generalized Weighted plant</a></li> <li><a href="#org50054f2">5.4. Generalized Weighted plant</a></li>
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@ -608,8 +374,8 @@ Gpz = connect(Gn, S, Wsplit, Tw, Tmu, Sw, {<span class="org-string">'Fd'</span>,
<h3 id="org0e9811a"><span class="section-number-3">2.2</span> Control using \(d\)</h3> <h3 id="org0e9811a"><span class="section-number-3">2.2</span> Control using \(d\)</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
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<div class="outline-text-4" id="text-2-2-1"> <div class="outline-text-4" id="text-2-2-1">
<p> <p>
Let&rsquo;s consider a feedback loop using \(d\) as shown in Figure <a href="#orgb50386a">4</a>. Let&rsquo;s consider a feedback loop using \(d\) as shown in Figure <a href="#orgb50386a">4</a>.
@ -692,8 +458,8 @@ And \(\epsilon = r - x\):
<h3 id="orga741e48"><span class="section-number-3">2.3</span> Control using \(F_m\)</h3> <h3 id="orga741e48"><span class="section-number-3">2.3</span> Control using \(F_m\)</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
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<h4 id="org4c74e08"><span class="section-number-4">2.3.1</span> Control Architecture</h4> <h4 id="org691c845"><span class="section-number-4">2.3.1</span> Control Architecture</h4>
<div class="outline-text-4" id="text-2-3-1"> <div class="outline-text-4" id="text-2-3-1">
<p> <p>
Let&rsquo;s consider a feedback loop using \(Fm\) as shown in Figure <a href="#org5012ef2">5</a>. Let&rsquo;s consider a feedback loop using \(Fm\) as shown in Figure <a href="#org5012ef2">5</a>.
@ -1004,8 +770,8 @@ Gpz_fb_iff = connect(Gpz_iff, Kpz_iff, R, Sfb, F, {<span class="org-string">'r'<
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<h4 id="org3db77f5"><span class="section-number-4">2.5.3</span> Results</h4> <h4 id="org38d941f"><span class="section-number-4">2.5.3</span> Results</h4>
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<div id="org2b4e783" class="figure"> <div id="org2b4e783" class="figure">
@ -1486,8 +1252,8 @@ Gvc_fb_dvf = connect(Gvc_dvf, <span class="org-type">-</span>Kvc_dvf, R, Sfb, F,
</div> </div>
</div> </div>
<div id="outline-container-org5211e8c" class="outline-3"> <div id="outline-container-org387a405" class="outline-3">
<h3 id="org5211e8c"><span class="section-number-3">5.7</span> Results</h3> <h3 id="org387a405"><span class="section-number-3">5.7</span> Results</h3>
</div> </div>
<div id="outline-container-orgb18d7df" class="outline-3"> <div id="outline-container-orgb18d7df" class="outline-3">
<h3 id="orgb18d7df"><span class="section-number-3">5.8</span> Requirements</h3> <h3 id="orgb18d7df"><span class="section-number-3">5.8</span> Requirements</h3>
@ -1528,7 +1294,7 @@ Gvc_fb_dvf = connect(Gvc_dvf, <span class="org-type">-</span>Kvc_dvf, R, Sfb, F,
</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: 2020-03-26 jeu. 17:25</p> <p class="date">Created: 2020-04-17 ven. 09:36</p>
</div> </div>
</body> </body>
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324
docs/control_voice_coil.html
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -249,10 +37,10 @@
<ul> <ul>
<li><a href="#orge379987">1. HAC-LAC + Cascade Control Topology</a> <li><a href="#orge379987">1. HAC-LAC + Cascade Control Topology</a>
<ul> <ul>
<li><a href="#org6d5d6b2">1.1. Initialization</a></li> <li><a href="#orgf283080">1.1. Initialization</a></li>
<li><a href="#orgf95b045">1.2. Low Authority Control - Integral Force Feedback \(\bm{K}_\text{IFF}\)</a> <li><a href="#orgf95b045">1.2. Low Authority Control - Integral Force Feedback \(\bm{K}_\text{IFF}\)</a>
<ul> <ul>
<li><a href="#orge9b2f08">1.2.1. Identification</a></li> <li><a href="#orgac9efbf">1.2.1. Identification</a></li>
<li><a href="#org203d651">1.2.2. Plant</a></li> <li><a href="#org203d651">1.2.2. Plant</a></li>
<li><a href="#orgccc21d2">1.2.3. Root Locus</a></li> <li><a href="#orgccc21d2">1.2.3. Root Locus</a></li>
<li><a href="#org1a8ee8a">1.2.4. Controller and Loop Gain</a></li> <li><a href="#org1a8ee8a">1.2.4. Controller and Loop Gain</a></li>
@ -261,49 +49,49 @@
<li><a href="#org2a44e66">1.3. High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</a> <li><a href="#org2a44e66">1.3. High Authority Control in the joint space - \(\bm{K}_\mathcal{L}\)</a>
<ul> <ul>
<li><a href="#org989c2e9">1.3.1. Identification of the damped plant</a></li> <li><a href="#org989c2e9">1.3.1. Identification of the damped plant</a></li>
<li><a href="#org45829b7">1.3.2. Obtained Plant</a></li> <li><a href="#org8d7c208">1.3.2. Obtained Plant</a></li>
<li><a href="#orgd1632cf">1.3.3. Controller Design and Loop Gain</a></li> <li><a href="#orgd1632cf">1.3.3. Controller Design and Loop Gain</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org0cd0c63">1.4. Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</a> <li><a href="#org0cd0c63">1.4. Primary Controller in the task space - \(\bm{K}_\mathcal{X}\)</a>
<ul> <ul>
<li><a href="#orga960106">1.4.1. Identification of the linearized plant</a></li> <li><a href="#orga960106">1.4.1. Identification of the linearized plant</a></li>
<li><a href="#org40a9335">1.4.2. Obtained Plant</a></li> <li><a href="#org6b17d02">1.4.2. Obtained Plant</a></li>
<li><a href="#org16f56fa">1.4.3. Controller Design</a></li> <li><a href="#org16f56fa">1.4.3. Controller Design</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org0b05a3a">1.5. Simulation</a></li> <li><a href="#orga259533">1.5. Simulation</a></li>
<li><a href="#org16024e0">1.6. Results</a> <li><a href="#org16024e0">1.6. Results</a>
<ul> <ul>
<li><a href="#orge126fd7">1.6.1. Load the simulation results</a></li> <li><a href="#orgf2436dc">1.6.1. Load the simulation results</a></li>
<li><a href="#org0f974ff">1.6.2. Control effort</a></li> <li><a href="#org0f974ff">1.6.2. Control effort</a></li>
<li><a href="#org83a367c">1.6.3. Load the simulation results</a></li> <li><a href="#org8e90e5a">1.6.3. Load the simulation results</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org74d9dc7">1.7. Compliance of the nano-hexapod</a> <li><a href="#org74d9dc7">1.7. Compliance of the nano-hexapod</a>
<ul> <ul>
<li><a href="#orgbdd14c0">1.7.1. Identification</a></li> <li><a href="#orgc6f70c3">1.7.1. Identification</a></li>
<li><a href="#org1a1ad20">1.7.2. Obtained Compliance</a></li> <li><a href="#org1a1ad20">1.7.2. Obtained Compliance</a></li>
<li><a href="#org5b81db9">1.7.3. Comparison with Piezo</a></li> <li><a href="#org5b81db9">1.7.3. Comparison with Piezo</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3652c0c">1.8. Robustness to Payload Variability</a> <li><a href="#org36ac22b">1.8. Robustness to Payload Variability</a>
<ul> <ul>
<li><a href="#orgecf0445">1.8.1. Initialization</a></li> <li><a href="#orgcaec167">1.8.1. Initialization</a></li>
<li><a href="#org0d97c55">1.8.2. Low Authority Control</a></li> <li><a href="#org0d97c55">1.8.2. Low Authority Control</a></li>
<li><a href="#orgab3ab98">1.8.3. High Authority Control</a></li> <li><a href="#orgab3ab98">1.8.3. High Authority Control</a></li>
<li><a href="#org176695a">1.8.4. Primary Plant</a></li> <li><a href="#org176695a">1.8.4. Primary Plant</a></li>
<li><a href="#org049fbc5">1.8.5. Simulation</a></li> <li><a href="#org9406388">1.8.5. Simulation</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</li> </li>
<li><a href="#orgd649256">2. Other analysis</a> <li><a href="#orgd649256">2. Other analysis</a>
<ul> <ul>
<li><a href="#orgcc14bbe">2.1. Robustness to Payload Variability</a></li> <li><a href="#org3c7ca09">2.1. Robustness to Payload Variability</a></li>
<li><a href="#org18b00fa">2.2. Direct HAC control in the task space - \(\bm{K}_\mathcal{X}\)</a> <li><a href="#org18b00fa">2.2. Direct HAC control in the task space - \(\bm{K}_\mathcal{X}\)</a>
<ul> <ul>
<li><a href="#org14729d2">2.2.1. Identification</a></li> <li><a href="#org5fd28fd">2.2.1. Identification</a></li>
<li><a href="#org1387536">2.2.2. Obtained Plant in the Task Space</a></li> <li><a href="#org1387536">2.2.2. Obtained Plant in the Task Space</a></li>
<li><a href="#org50b9f75">2.2.3. Obtained Plant in the Joint Space</a></li> <li><a href="#org50b9f75">2.2.3. Obtained Plant in the Joint Space</a></li>
<li><a href="#org19db2cd">2.2.4. Controller Design in the Joint Space</a></li> <li><a href="#org19db2cd">2.2.4. Controller Design in the Joint Space</a></li>
@ -311,7 +99,7 @@
</li> </li>
<li><a href="#org5e26e70">2.3. On the usefulness of the High Authority Control loop / Linearization loop</a> <li><a href="#org5e26e70">2.3. On the usefulness of the High Authority Control loop / Linearization loop</a>
<ul> <ul>
<li><a href="#orga867ed3">2.3.1. Identification</a></li> <li><a href="#org63f831b">2.3.1. Identification</a></li>
<li><a href="#orgfab8847">2.3.2. Plant in the Task space</a></li> <li><a href="#orgfab8847">2.3.2. Plant in the Task space</a></li>
<li><a href="#org18aeea5">2.3.3. Plant in the Leg&rsquo;s space</a></li> <li><a href="#org18aeea5">2.3.3. Plant in the Leg&rsquo;s space</a></li>
</ul> </ul>
@ -319,7 +107,7 @@
<li><a href="#org015f992">2.4. DVF instead of IFF?</a> <li><a href="#org015f992">2.4. DVF instead of IFF?</a>
<ul> <ul>
<li><a href="#org17cfb9d">2.4.1. Initialization and Identification</a></li> <li><a href="#org17cfb9d">2.4.1. Initialization and Identification</a></li>
<li><a href="#org1144ed5">2.4.2. Obtained Plant</a></li> <li><a href="#orgc3f6788">2.4.2. Obtained Plant</a></li>
<li><a href="#org51c8027">2.4.3. Controller</a></li> <li><a href="#org51c8027">2.4.3. Controller</a></li>
<li><a href="#org33637f1">2.4.4. HAC Identification</a></li> <li><a href="#org33637f1">2.4.4. HAC Identification</a></li>
<li><a href="#orgec66083">2.4.5. Conclusion</a></li> <li><a href="#orgec66083">2.4.5. Conclusion</a></li>
@ -342,8 +130,8 @@
</div> </div>
</div> </div>
<div id="outline-container-org6d5d6b2" class="outline-3"> <div id="outline-container-orgf283080" class="outline-3">
<h3 id="org6d5d6b2"><span class="section-number-3">1.1</span> Initialization</h3> <h3 id="orgf283080"><span class="section-number-3">1.1</span> Initialization</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -416,8 +204,8 @@ Kiff = tf(zeros(6));
<a id="org224edef"></a> <a id="org224edef"></a>
</p> </p>
</div> </div>
<div id="outline-container-orge9b2f08" class="outline-4"> <div id="outline-container-orgac9efbf" class="outline-4">
<h4 id="orge9b2f08"><span class="section-number-4">1.2.1</span> Identification</h4> <h4 id="orgac9efbf"><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>
Let&rsquo;s first identify the plant for the IFF controller. Let&rsquo;s first identify the plant for the IFF controller.
@ -542,8 +330,8 @@ isstable(Gl)
</div> </div>
</div> </div>
<div id="outline-container-org45829b7" class="outline-4"> <div id="outline-container-org8d7c208" class="outline-4">
<h4 id="org45829b7"><span class="section-number-4">1.3.2</span> Obtained Plant</h4> <h4 id="org8d7c208"><span class="section-number-4">1.3.2</span> Obtained Plant</h4>
<div class="outline-text-4" id="text-1-3-2"> <div class="outline-text-4" id="text-1-3-2">
<p> <p>
The obtained dynamics is shown in Figure <a href="#orgd1818fd">5</a>. The obtained dynamics is shown in Figure <a href="#orgd1818fd">5</a>.
@ -640,8 +428,8 @@ Gpl.OutputName = {<span class="org-string">'El1'</span>, <span class="org-strin
</div> </div>
</div> </div>
<div id="outline-container-org40a9335" class="outline-4"> <div id="outline-container-org6b17d02" class="outline-4">
<h4 id="org40a9335"><span class="section-number-4">1.4.2</span> Obtained Plant</h4> <h4 id="org6b17d02"><span class="section-number-4">1.4.2</span> Obtained Plant</h4>
<div class="outline-text-4" id="text-1-4-2"> <div class="outline-text-4" id="text-1-4-2">
<div id="org8e042d5" class="figure"> <div id="org8e042d5" class="figure">
@ -697,8 +485,8 @@ And now we include the Jacobian inside the controller.
</div> </div>
</div> </div>
<div id="outline-container-org0b05a3a" class="outline-3"> <div id="outline-container-orga259533" class="outline-3">
<h3 id="org0b05a3a"><span class="section-number-3">1.5</span> Simulation</h3> <h3 id="orga259533"><span class="section-number-3">1.5</span> Simulation</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<p> <p>
Let&rsquo;s first save the 3 controllers for further analysis: Let&rsquo;s first save the 3 controllers for further analysis:
@ -734,8 +522,8 @@ save(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="o
<h3 id="org16024e0"><span class="section-number-3">1.6</span> Results</h3> <h3 id="org16024e0"><span class="section-number-3">1.6</span> Results</h3>
<div class="outline-text-3" id="text-1-6"> <div class="outline-text-3" id="text-1-6">
</div> </div>
<div id="outline-container-orge126fd7" class="outline-4"> <div id="outline-container-orgf2436dc" class="outline-4">
<h4 id="orge126fd7"><span class="section-number-4">1.6.1</span> Load the simulation results</h4> <h4 id="orgf2436dc"><span class="section-number-4">1.6.1</span> Load the simulation results</h4>
<div class="outline-text-4" id="text-1-6-1"> <div class="outline-text-4" id="text-1-6-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
@ -757,8 +545,8 @@ load(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="o
</div> </div>
</div> </div>
<div id="outline-container-org83a367c" class="outline-4"> <div id="outline-container-org8e90e5a" class="outline-4">
<h4 id="org83a367c"><span class="section-number-4">1.6.3</span> Load the simulation results</h4> <h4 id="org8e90e5a"><span class="section-number-4">1.6.3</span> Load the simulation results</h4>
<div class="outline-text-4" id="text-1-6-3"> <div class="outline-text-4" id="text-1-6-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">n_av = 4; <pre class="src src-matlab">n_av = 4;
@ -805,8 +593,8 @@ Ts = t(2)<span class="org-type">-</span>t(1);
<h3 id="org74d9dc7"><span class="section-number-3">1.7</span> Compliance of the nano-hexapod</h3> <h3 id="org74d9dc7"><span class="section-number-3">1.7</span> Compliance of the nano-hexapod</h3>
<div class="outline-text-3" id="text-1-7"> <div class="outline-text-3" id="text-1-7">
</div> </div>
<div id="outline-container-orgbdd14c0" class="outline-4"> <div id="outline-container-orgc6f70c3" class="outline-4">
<h4 id="orgbdd14c0"><span class="section-number-4">1.7.1</span> Identification</h4> <h4 id="orgc6f70c3"><span class="section-number-4">1.7.1</span> Identification</h4>
<div class="outline-text-4" id="text-1-7-1"> <div class="outline-text-4" id="text-1-7-1">
<p> <p>
Let&rsquo;s identify the Compliance of the NASS: Let&rsquo;s identify the Compliance of the NASS:
@ -942,12 +730,12 @@ Gc_pz.OutputName = {<span class="org-string">'Ex'</span>, <span class="org-strin
</div> </div>
<div id="outline-container-org3652c0c" class="outline-3"> <div id="outline-container-org36ac22b" class="outline-3">
<h3 id="org3652c0c"><span class="section-number-3">1.8</span> Robustness to Payload Variability</h3> <h3 id="org36ac22b"><span class="section-number-3">1.8</span> Robustness to Payload Variability</h3>
<div class="outline-text-3" id="text-1-8"> <div class="outline-text-3" id="text-1-8">
</div> </div>
<div id="outline-container-orgecf0445" class="outline-4"> <div id="outline-container-orgcaec167" class="outline-4">
<h4 id="orgecf0445"><span class="section-number-4">1.8.1</span> Initialization</h4> <h4 id="orgcaec167"><span class="section-number-4">1.8.1</span> Initialization</h4>
<div class="outline-text-4" id="text-1-8-1"> <div class="outline-text-4" id="text-1-8-1">
<p> <p>
Let&rsquo;s change the payload mass, and see if the controller design for a payload mass of 1 still gives good performance. Let&rsquo;s change the payload mass, and see if the controller design for a payload mass of 1 still gives good performance.
@ -1174,8 +962,8 @@ Kp = Kp<span class="org-type">.*</span>diag(1<span class="org-type">./</span>dia
</div> </div>
</div> </div>
<div id="outline-container-org049fbc5" class="outline-4"> <div id="outline-container-org9406388" class="outline-4">
<h4 id="org049fbc5"><span class="section-number-4">1.8.5</span> Simulation</h4> <h4 id="org9406388"><span class="section-number-4">1.8.5</span> Simulation</h4>
<div class="outline-text-4" id="text-1-8-5"> <div class="outline-text-4" id="text-1-8-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>); <pre class="src src-matlab">load(<span class="org-string">'mat/conf_simulink.mat'</span>);
@ -1210,8 +998,8 @@ save(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="o
<h2 id="orgd649256"><span class="section-number-2">2</span> Other analysis</h2> <h2 id="orgd649256"><span class="section-number-2">2</span> Other analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> </div>
<div id="outline-container-orgcc14bbe" class="outline-3"> <div id="outline-container-org3c7ca09" class="outline-3">
<h3 id="orgcc14bbe"><span class="section-number-3">2.1</span> Robustness to Payload Variability</h3> <h3 id="org3c7ca09"><span class="section-number-3">2.1</span> Robustness to Payload Variability</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<ul class="org-ul"> <ul class="org-ul">
<li class="off"><code>[&#xa0;]</code> For 3/masses (1kg, 10kg, 50kg), plot each of the 3 plants</li> <li class="off"><code>[&#xa0;]</code> For 3/masses (1kg, 10kg, 50kg), plot each of the 3 plants</li>
@ -1230,8 +1018,8 @@ save(<span class="org-string">'./mat/cascade_hac_lac.mat'</span>, <span class="o
</div> </div>
</div> </div>
<div id="outline-container-org14729d2" class="outline-4"> <div id="outline-container-org5fd28fd" class="outline-4">
<h4 id="org14729d2"><span class="section-number-4">2.2.1</span> Identification</h4> <h4 id="org5fd28fd"><span class="section-number-4">2.2.1</span> Identification</h4>
<div class="outline-text-4" id="text-2-2-1"> <div class="outline-text-4" id="text-2-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-iff'</span>); <pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-iff'</span>);
@ -1346,8 +1134,8 @@ We can do that in two different ways:
</div> </div>
</div> </div>
<div id="outline-container-orga867ed3" class="outline-4"> <div id="outline-container-org63f831b" class="outline-4">
<h4 id="orga867ed3"><span class="section-number-4">2.3.1</span> Identification</h4> <h4 id="org63f831b"><span class="section-number-4">2.3.1</span> Identification</h4>
<div class="outline-text-4" id="text-2-3-1"> <div class="outline-text-4" id="text-2-3-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-iff'</span>); <pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-iff'</span>);
@ -1435,8 +1223,8 @@ G_dvf.OutputName = {<span class="org-string">'Dlm1'</span>, <span class="org-str
</div> </div>
</div> </div>
<div id="outline-container-org1144ed5" class="outline-4"> <div id="outline-container-orgc3f6788" class="outline-4">
<h4 id="org1144ed5"><span class="section-number-4">2.4.2</span> Obtained Plant</h4> <h4 id="orgc3f6788"><span class="section-number-4">2.4.2</span> Obtained Plant</h4>
</div> </div>
<div id="outline-container-org51c8027" class="outline-4"> <div id="outline-container-org51c8027" class="outline-4">
<h4 id="org51c8027"><span class="section-number-4">2.4.3</span> Controller</h4> <h4 id="org51c8027"><span class="section-number-4">2.4.3</span> Controller</h4>
@ -1503,7 +1291,7 @@ DVF can be used instead of IFF.
</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: 2020-04-01 mer. 16:16</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
</body> </body>
</html> </html>

247
docs/disturbances.html
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@ -4,237 +4,25 @@
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<title>Identification of the disturbances</title> <title>Identification of the disturbances</title>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -393,7 +181,6 @@ io(io_i) = linio([mdl, <span class="org-string">'/Disturbances'</span>], 1, <spa
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Granite/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute motion - Granite</span> io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Granite/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute motion - Granite</span>
io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion - Hexapod</span> io(io_i) = linio([mdl, <span class="org-string">'/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Absolute Motion - Hexapod</span>
<span class="org-comment">% io(io_i) = linio([mdl, '/Vm'], 1, 'openoutput'); io_i = io_i + 1; % Relative Velocity hexapod/granite</span>
<span class="org-comment">% Run the linearization</span> <span class="org-comment">% Run the linearization</span>
G = linearize(mdl, io, 0); G = linearize(mdl, io, 0);
@ -493,6 +280,18 @@ tyx = load(<span class="org-string">'./mat/pxe_ty_r.mat'</span>, <span class="or
</pre> </pre>
</div> </div>
<p>
Because some 50Hz and harmonics were present in the ground motion measurement, we remove these peaks with the following code:
</p>
<div class="org-src-container">
<pre class="src src-matlab">f0s = [50, 100, 150, 200, 250, 350, 450];
<span class="org-keyword">for</span> <span class="org-variable-name">f0</span> = <span class="org-constant">f0s</span>
<span class="org-constant">i</span> = find(gm.f <span class="org-type">&gt;</span> f0<span class="org-type">-</span>0.5 <span class="org-type">&amp;</span> gm.f <span class="org-type">&lt;</span> f0<span class="org-type">+</span>0.5);
gm.psd_gm(<span class="org-constant">i</span>) = linspace(gm.psd_gm(<span class="org-constant">i</span>(1)), gm.psd_gm(<span class="org-constant">i</span>(end)), length(<span class="org-constant">i</span>));
<span class="org-keyword">end</span>
</pre>
</div>
<p> <p>
We now compute the relative velocity between the hexapod and the granite due to ground motion. We now compute the relative velocity between the hexapod and the granite due to ground motion.
</p> </p>
@ -768,7 +567,7 @@ Let&rsquo;s now compare the effect of those perturbations on the position error
</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: 2020-03-17 mar. 17:31</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
</body> </body>
</html> </html>

448
docs/experiments.html
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@ -4,227 +4,17 @@
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<title>Simulation of Scientific Experiments</title> <title>Simulation of Scientific Experiments</title>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -240,30 +30,37 @@
<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="#org0ba0ddd">2.1. Simulation Setup</a></li> <li><a href="#orgdebc736">2.1. Simulation Setup</a></li>
<li><a href="#org140576f">2.2. Analysis</a></li> <li><a href="#orge0e2e88">2.2. Analysis</a></li>
<li><a href="#org26e3394">2.3. Conclusion</a></li> <li><a href="#org38ba07f">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="#org3da7cb0">3.1. Simulation Setup</a></li> <li><a href="#orgc2a0926">3.1. Simulation Setup</a></li>
<li><a href="#orgdb56a7f">3.2. Analysis</a></li> <li><a href="#org388be58">3.2. Analysis</a></li>
<li><a href="#org722f52a">3.3. Conclusion</a></li> <li><a href="#org51b3617">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="#org7202245">4. Tomography Experiment with Ty raster scans</a>
<ul> <ul>
<li><a href="#org6137b17">4.1. Simulation Setup</a></li> <li><a href="#org94c3461">4.1. Simulation Setup</a></li>
<li><a href="#org92c4f21">4.2. Analysis</a></li> <li><a href="#org65d4246">4.2. Analysis</a></li>
<li><a href="#org92f12cd">4.3. Conclusion</a></li> <li><a href="#org41a2a1d">4.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org8fa1632">5. Raster Scans with the translation stage</a> <li><a href="#org72f01ab">5. Tomography when the micro-hexapod is not centered</a>
<ul> <ul>
<li><a href="#org4110173">5.1. Simulation Setup</a></li> <li><a href="#org8a5fae6">5.1. Simulation Setup</a></li>
<li><a href="#org1e50cb1">5.2. Analysis</a></li> <li><a href="#orgf8b4f39">5.2. Analysis</a></li>
<li><a href="#org98199a0">5.3. Conclusion</a></li> <li><a href="#orgdd34703">5.3. Conclusion</a></li>
</ul>
</li>
<li><a href="#org8fa1632">6. Raster Scans with the translation stage</a>
<ul>
<li><a href="#orge3f0741">6.1. Simulation Setup</a></li>
<li><a href="#org1836f98">6.2. Analysis</a></li>
<li><a href="#org8cf54cb">6.3. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -291,8 +88,8 @@ The document in organized as follow:
<li>In section <a href="#orgfc7d050">1</a> the Simscape model is initialized</li> <li>In section <a href="#orgfc7d050">1</a> the Simscape model is initialized</li>
<li>In section <a href="#org3effbb8">2</a> a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included</li> <li>In section <a href="#org3effbb8">2</a> a tomography experiment is performed where the sample is aligned with the rotation axis. No disturbance is included</li>
<li>In section <a href="#org4e7f626">3</a>, the same is done but with disturbance included</li> <li>In section <a href="#org4e7f626">3</a>, the same is done but with disturbance included</li>
<li>In section <a href="#orgb31e3fb">4</a> the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included</li> <li>In section <a href="#orgb31e3fb">5</a> the micro-hexapod translate the sample such that its center of mass is no longer aligned with the rotation axis. No disturbance is included</li>
<li>In section <a href="#org6aaeb53">5</a>, scans with the translation stage are simulated with no perturbation included</li> <li>In section <a href="#org6aaeb53">6</a>, scans with the translation stage are simulated with no perturbation included</li>
</ul> </ul>
<div id="outline-container-org03b2a76" class="outline-2"> <div id="outline-container-org03b2a76" class="outline-2">
@ -329,15 +126,6 @@ initializeSample(<span class="org-string">'mass'</span>, 1);
</pre> </pre>
</div> </div>
<p>
We initialize the reference path for all the stages.
All stage is set to its zero position except the Spindle which is rotating at 60rpm.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
</pre>
</div>
<p> <p>
No controller is used (Open Loop). No controller is used (Open Loop).
</p> </p>
@ -347,7 +135,7 @@ No controller is used (Open Loop).
</div> </div>
<p> <p>
And we put some gravity. We don&rsquo;t gravity.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>); <pre class="src src-matlab">initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
@ -375,8 +163,8 @@ In this section, a tomography experiment is performed with the sample aligned wi
No disturbance is included. No disturbance is included.
</p> </p>
</div> </div>
<div id="outline-container-org0ba0ddd" class="outline-3"> <div id="outline-container-orgdebc736" class="outline-3">
<h3 id="org0ba0ddd"><span class="section-number-3">2.1</span> Simulation Setup</h3> <h3 id="orgdebc736"><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.
@ -393,6 +181,15 @@ And we initialize the disturbances to be equal to zero.
</pre> </pre>
</div> </div>
<p>
We initialize the reference path for all the stages.
All stage is set to its zero position except the Spindle which is rotating at 60rpm.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
</pre>
</div>
<p> <p>
We simulate the model. We simulate the model.
</p> </p>
@ -412,8 +209,8 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-org140576f" class="outline-3"> <div id="outline-container-orge0e2e88" class="outline-3">
<h3 id="org140576f"><span class="section-number-3">2.2</span> Analysis</h3> <h3 id="orge0e2e88"><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">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
@ -429,8 +226,8 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-org26e3394" class="outline-3"> <div id="outline-container-org38ba07f" class="outline-3">
<h3 id="org26e3394"><span class="section-number-3">2.3</span> Conclusion</h3> <h3 id="org38ba07f"><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>
@ -454,8 +251,8 @@ In this section, we also perform a tomography experiment with the sample&rsquo;s
However this time, we include perturbations such as ground motion and stage vibrations. However this time, we include perturbations such as ground motion and stage vibrations.
</p> </p>
</div> </div>
<div id="outline-container-org3da7cb0" class="outline-3"> <div id="outline-container-orgc2a0926" class="outline-3">
<h3 id="org3da7cb0"><span class="section-number-3">3.1</span> Simulation Setup</h3> <h3 id="orgc2a0926"><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.
@ -465,13 +262,22 @@ We now activate the disturbances.
<span class="org-string">'Dwx'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - X direction</span> <span class="org-string">'Dwx'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
<span class="org-string">'Dwy'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span> <span class="org-string">'Dwy'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
<span class="org-string">'Dwz'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span> <span class="org-string">'Dwz'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
<span class="org-string">'Fty_x'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - X direction</span> <span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
<span class="org-string">'Fty_z'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span> <span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
<span class="org-string">'Frz_z'</span>, <span class="org-constant">true</span> ...<span class="org-comment"> % Spindle - Z direction</span> <span class="org-string">'Frz_z'</span>, <span class="org-constant">true</span> ...<span class="org-comment"> % Spindle - Z direction</span>
); );
</pre> </pre>
</div> </div>
<p>
We initialize the reference path for all the stages.
All stage is set to its zero position except the Spindle which is rotating at 60rpm.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
</pre>
</div>
<p> <p>
We simulate the model. We simulate the model.
</p> </p>
@ -491,8 +297,8 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-orgdb56a7f" class="outline-3"> <div id="outline-container-org388be58" class="outline-3">
<h3 id="orgdb56a7f"><span class="section-number-3">3.2</span> Analysis</h3> <h3 id="org388be58"><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">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>, <span class="org-string">'tomo_align_no_dist'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
@ -508,12 +314,12 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-org722f52a" class="outline-3"> <div id="outline-container-org51b3617" class="outline-3">
<h3 id="org722f52a"><span class="section-number-3">3.3</span> Conclusion</h3> <h3 id="org51b3617"><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>
Error motion is what expected from the disturbance measurements. Here, no vibration is included in the X and Y directions.
</p> </p>
</div> </div>
@ -521,10 +327,90 @@ Error motion is what expected from the disturbance measurements.
</div> </div>
</div> </div>
<div id="outline-container-org72f01ab" class="outline-2"> <div id="outline-container-org7202245" class="outline-2">
<h2 id="org72f01ab"><span class="section-number-2">4</span> Tomography when the micro-hexapod is not centered</h2> <h2 id="org7202245"><span class="section-number-2">4</span> Tomography Experiment with Ty raster scans</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<p> <p>
<a id="orgd4f0240"></a>
</p>
<p>
In this section, we also perform a tomography experiment with scans of the Translation stage.
All the perturbations are included.
</p>
</div>
<div id="outline-container-org94c3461" class="outline-3">
<h3 id="org94c3461"><span class="section-number-3">4.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-4-1">
<p>
We now activate the disturbances.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances(...
<span class="org-string">'Dwx'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
<span class="org-string">'Dwy'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
<span class="org-string">'Dwz'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
<span class="org-string">'Fty_x'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
<span class="org-string">'Fty_z'</span>, <span class="org-constant">true</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
<span class="org-string">'Frz_z'</span>, <span class="org-constant">true</span> ...<span class="org-comment"> % Spindle - Z direction</span>
);
</pre>
</div>
<p>
We initialize the reference path for all the stages.
The Spindle which is rotating at 60rpm and the translation stage not moving as it would take a long time to simulate.
However, vibrations of the Ty stage are included.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
</pre>
</div>
<p>
We simulate the model.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
</pre>
</div>
<p>
And we save the obtained data.
</p>
<div class="org-src-container">
<pre class="src src-matlab">scans_rz_align_dist = simout;
save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'scans_rz_align_dist'</span>, <span class="org-string">'-append'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org65d4246" class="outline-3">
<h3 id="org65d4246"><span class="section-number-3">4.2</span> Analysis</h3>
<div class="outline-text-3" id="text-4-2">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'scans_rz_align_dist'</span>);
</pre>
</div>
<div id="org38e229c" class="figure">
<p><img src="figs/exp_scans_rz_dist.png" alt="exp_scans_rz_dist.png" />
</p>
<p><span class="figure-number">Figure 3: </span>X-Y-Z translations and rotations of the sample w.r.t. the granite when performing tomography experiment and scans with the translation stage at the same time</p>
</div>
</div>
</div>
<div id="outline-container-org41a2a1d" class="outline-3">
<h3 id="org41a2a1d"><span class="section-number-3">4.3</span> Conclusion</h3>
</div>
</div>
<div id="outline-container-org72f01ab" class="outline-2">
<h2 id="org72f01ab"><span class="section-number-2">5</span> Tomography when the micro-hexapod is not centered</h2>
<div class="outline-text-2" id="text-5">
<p>
<a id="orgb31e3fb"></a> <a id="orgb31e3fb"></a>
</p> </p>
<p> <p>
@ -536,9 +422,9 @@ This is due to the fact that the micro-hexapod has performed some displacement.
No disturbances are included. No disturbances are included.
</p> </p>
</div> </div>
<div id="outline-container-org6137b17" class="outline-3"> <div id="outline-container-org8a5fae6" class="outline-3">
<h3 id="org6137b17"><span class="section-number-3">4.1</span> Simulation Setup</h3> <h3 id="org8a5fae6"><span class="section-number-3">5.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-5-1">
<p> <p>
We first set the wanted translation of the Micro Hexapod. We first set the wanted translation of the Micro Hexapod.
</p> </p>
@ -597,9 +483,9 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-org92c4f21" class="outline-3"> <div id="outline-container-orgf8b4f39" class="outline-3">
<h3 id="org92c4f21"><span class="section-number-3">4.2</span> Analysis</h3> <h3 id="orgf8b4f39"><span class="section-number-3">5.2</span> Analysis</h3>
<div class="outline-text-3" id="text-4-2"> <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">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_not_align'</span>, <span class="org-string">'tomo_align_no_dist'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_not_align'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
</pre> </pre>
@ -609,14 +495,14 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
<div id="orgb824a01" class="figure"> <div id="orgb824a01" class="figure">
<p><img src="figs/exp_tomo_offset.png" alt="exp_tomo_offset.png" /> <p><img src="figs/exp_tomo_offset.png" alt="exp_tomo_offset.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset.png">png</a>, <a href="./figs/exp_tomo_offset.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 4: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset.png">png</a>, <a href="./figs/exp_tomo_offset.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org92f12cd" class="outline-3"> <div id="outline-container-orgdd34703" class="outline-3">
<h3 id="org92f12cd"><span class="section-number-3">4.3</span> Conclusion</h3> <h3 id="orgdd34703"><span class="section-number-3">5.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-5-3">
<div class="important"> <div class="important">
<p> <p>
The main motion error are 1Hz X-Y translations and constant Ry error. The main motion error are 1Hz X-Y translations and constant Ry error.
@ -629,8 +515,8 @@ This is mainly due to finite stiffness of the elements.
</div> </div>
<div id="outline-container-org8fa1632" class="outline-2"> <div id="outline-container-org8fa1632" class="outline-2">
<h2 id="org8fa1632"><span class="section-number-2">5</span> Raster Scans with the translation stage</h2> <h2 id="org8fa1632"><span class="section-number-2">6</span> Raster Scans with the translation stage</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-6">
<p> <p>
<a id="org6aaeb53"></a> <a id="org6aaeb53"></a>
</p> </p>
@ -638,9 +524,9 @@ This is mainly due to finite stiffness of the elements.
In this section, scans with the translation stage are performed. In this section, scans with the translation stage are performed.
</p> </p>
</div> </div>
<div id="outline-container-org4110173" class="outline-3"> <div id="outline-container-orge3f0741" class="outline-3">
<h3 id="org4110173"><span class="section-number-3">5.1</span> Simulation Setup</h3> <h3 id="orge3f0741"><span class="section-number-3">6.1</span> Simulation Setup</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-6-1">
<p> <p>
We initialize the stages. We initialize the stages.
</p> </p>
@ -725,9 +611,9 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
</div> </div>
</div> </div>
<div id="outline-container-org1e50cb1" class="outline-3"> <div id="outline-container-org1836f98" class="outline-3">
<h3 id="org1e50cb1"><span class="section-number-3">5.2</span> Analysis</h3> <h3 id="org1836f98"><span class="section-number-3">6.2</span> Analysis</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-6-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'ty_scan_triangle'</span>, <span class="org-string">'ty_scan_sinus'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'ty_scan_triangle'</span>, <span class="org-string">'ty_scan_sinus'</span>);
</pre> </pre>
@ -737,14 +623,14 @@ save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span cl
<div id="org888f0bf" class="figure"> <div id="org888f0bf" class="figure">
<p><img src="figs/exp_ty_scan.png" alt="exp_ty_scan.png" /> <p><img src="figs/exp_ty_scan.png" alt="exp_ty_scan.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan.png">png</a>, <a href="./figs/exp_ty_scan.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 5: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan.png">png</a>, <a href="./figs/exp_ty_scan.pdf">pdf</a>)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org98199a0" class="outline-3"> <div id="outline-container-org8cf54cb" class="outline-3">
<h3 id="org98199a0"><span class="section-number-3">5.3</span> Conclusion</h3> <h3 id="org8cf54cb"><span class="section-number-3">6.3</span> Conclusion</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-6-3">
<div class="important"> <div class="important">
<p> <p>
Scans with the translation stage induces some errors in the Y direction and Rx translations. Scans with the translation stage induces some errors in the Y direction and Rx translations.
@ -762,7 +648,7 @@ Thus, this should be preferred.
</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: 2020-03-17 mar. 12:32</p> <p class="date">Created: 2020-04-17 ven. 10:25</p>
</div> </div>
</body> </body>
</html> </html>

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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -237,16 +27,332 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgdc168b9">1. computeReferencePose</a></li> <li><a href="#org3fa0f20">1. describeNassSetup</a>
<li><a href="#org493ab7f">2. Compute the Sample Position Error w.r.t. the NASS</a></li> <ul>
<li><a href="#org3615302">Function description</a></li>
<li><a href="#org3b8c4f7">Simscape Configuration</a></li>
<li><a href="#org5b65749">Disturbances</a></li>
<li><a href="#org59f7825">References</a></li>
<li><a href="#org90b1ac8">Controller</a></li>
<li><a href="#orgdd5b7a5">Micro-Station</a></li>
<li><a href="#org1687c05">Metrology</a></li>
<li><a href="#orgee5944e">Nano Hexapod</a></li>
<li><a href="#orga499c17">Sample</a></li>
</ul>
</li>
<li><a href="#orgdc168b9">2. computeReferencePose</a></li>
<li><a href="#org493ab7f">3. Compute the Sample Position Error w.r.t. the NASS</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgdc168b9" class="outline-2"> <div id="outline-container-org3fa0f20" class="outline-2">
<h2 id="orgdc168b9"><span class="section-number-2">1</span> computeReferencePose</h2> <h2 id="org3fa0f20"><span class="section-number-2">1</span> describeNassSetup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="org0b9cc9d"></a>
</p>
</div>
<div id="outline-container-org3615302" class="outline-3">
<h3 id="org3615302">Function description</h3>
<div class="outline-text-3" id="text-org3615302">
<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">describeNassSetup</span>()
<span class="org-comment">% describeNassSetup -</span>
<span class="org-comment">%</span>
<span class="org-comment">% Syntax: [] = describeNassSetup()</span>
<span class="org-comment">%</span>
<span class="org-comment">% Inputs:</span>
<span class="org-comment">% - -</span>
<span class="org-comment">%</span>
<span class="org-comment">% Outputs:</span>
<span class="org-comment">% - -</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org3b8c4f7" class="outline-3">
<h3 id="org3b8c4f7">Simscape Configuration</h3>
<div class="outline-text-3" id="text-org3b8c4f7">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/conf_simscape.mat'</span>, <span class="org-string">'conf_simscape'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Simscape Configuration:\n'</span>);
<span class="org-keyword">if</span> conf_simscape.type <span class="org-type">==</span> 1
fprintf(<span class="org-string">'- Gravity is included\n'</span>);
<span class="org-keyword">else</span>
fprintf(<span class="org-string">'- Gravity is not included\n'</span>);
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org5b65749" class="outline-3">
<h3 id="org5b65749">Disturbances</h3>
<div class="outline-text-3" id="text-org5b65749">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/nass_disturbances.mat'</span>, <span class="org-string">'args'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Disturbances:\n'</span>);
<span class="org-keyword">if</span> <span class="org-type">~</span>args.enable
fprintf(<span class="org-string">'- No disturbance is included\n'</span>);
<span class="org-keyword">else</span>
<span class="org-keyword">if</span> args.Dwx <span class="org-type">&amp;&amp;</span> args.Dwy <span class="org-type">&amp;&amp;</span> args.Dwz
fprintf(<span class="org-string">'- Ground motion\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> args.Fty_x <span class="org-type">&amp;&amp;</span> args.Fty_z
fprintf(<span class="org-string">'- Vibrations of the Translation Stage\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> args.Frz_z
fprintf(<span class="org-string">'- Vibrations of the Spindle\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org59f7825" class="outline-3">
<h3 id="org59f7825">References</h3>
<div class="outline-text-3" id="text-org59f7825">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/nass_references.mat'</span>, <span class="org-string">'args'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Reference Tracking:\n'</span>);
fprintf(<span class="org-string">'- Translation Stage:\n'</span>);
<span class="org-keyword">switch</span> <span class="org-constant">args.Dy_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
fprintf(<span class="org-string">' - Constant Position\n'</span>);
fprintf(<span class="org-string">' - Dy = %.0f [mm]\n'</span>, args.Dy_amplitude<span class="org-type">*</span>1e3);
<span class="org-keyword">case</span> <span class="org-string">'triangular'</span>
fprintf(<span class="org-string">' - Triangular Path\n'</span>);
fprintf(<span class="org-string">' - Amplitude = %.0f [mm]\n'</span>, args.Dy_amplitude<span class="org-type">*</span>1e3);
fprintf(<span class="org-string">' - Period = %.0f [s]\n'</span>, args.Dy_period);
<span class="org-keyword">case</span> <span class="org-string">'sinusoidal'</span>
fprintf(<span class="org-string">' - Sinusoidal Path\n'</span>);
fprintf(<span class="org-string">' - Amplitude = %.0f [mm]\n'</span>, args.Dy_amplitude<span class="org-type">*</span>1e3);
fprintf(<span class="org-string">' - Period = %.0f [s]\n'</span>, args.Dy_period);
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'- Tilt Stage:\n'</span>);
<span class="org-keyword">switch</span> <span class="org-constant">args.Ry_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
fprintf(<span class="org-string">' - Constant Position\n'</span>);
fprintf(<span class="org-string">' - Ry = %.0f [mm]\n'</span>, args.Ry_amplitude<span class="org-type">*</span>1e3);
<span class="org-keyword">case</span> <span class="org-string">'triangular'</span>
fprintf(<span class="org-string">' - Triangular Path\n'</span>);
fprintf(<span class="org-string">' - Amplitude = %.0f [mm]\n'</span>, args.Ry_amplitude<span class="org-type">*</span>1e3);
fprintf(<span class="org-string">' - Period = %.0f [s]\n'</span>, args.Ry_period);
<span class="org-keyword">case</span> <span class="org-string">'sinusoidal'</span>
fprintf(<span class="org-string">' - Sinusoidal Path\n'</span>);
fprintf(<span class="org-string">' - Amplitude = %.0f [mm]\n'</span>, args.Ry_amplitude<span class="org-type">*</span>1e3);
fprintf(<span class="org-string">' - Period = %.0f [s]\n'</span>, args.Ry_period);
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'- Spindle:\n'</span>);
<span class="org-keyword">switch</span> <span class="org-constant">args.Rz_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
fprintf(<span class="org-string">' - Constant Position\n'</span>);
fprintf(<span class="org-string">' - Rz = %.0f [deg]\n'</span>, 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>args.Rz_amplitude);
<span class="org-keyword">case</span> { <span class="org-string">'rotating'</span>, <span class="org-string">'rotating-not-filtered'</span> }
fprintf(<span class="org-string">' - Rotating\n'</span>);
fprintf(<span class="org-string">' - Speed = %.0f [rpm]\n'</span>, 60<span class="org-type">/</span>Rz_period);
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'- Micro Hexapod:\n'</span>);
<span class="org-keyword">switch</span> <span class="org-constant">args.Dh_type</span>
<span class="org-keyword">case</span> <span class="org-string">'constant'</span>
fprintf(<span class="org-string">' - Constant Position\n'</span>);
fprintf(<span class="org-string">' - Dh = %.0f, %.0f, %.0f [mm]\n'</span>, args.Dh_pos(1), args.Dh_pos(2), args.Dh_pos(3));
fprintf(<span class="org-string">' - Rh = %.0f, %.0f, %.0f [deg]\n'</span>, args.Dh_pos(4), args.Dh_pos(5), args.Dh_pos(6));
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org90b1ac8" class="outline-3">
<h3 id="org90b1ac8">Controller</h3>
<div class="outline-text-3" id="text-org90b1ac8">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/controller.mat'</span>, <span class="org-string">'controller'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Controller:\n'</span>);
fprintf(<span class="org-string">'- %s\n'</span>, controller.name);
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgdd5b7a5" class="outline-3">
<h3 id="orgdd5b7a5">Micro-Station</h3>
<div class="outline-text-3" id="text-orgdd5b7a5">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'ground'</span>, <span class="org-string">'granite'</span>, <span class="org-string">'ty'</span>, <span class="org-string">'ry'</span>, <span class="org-string">'rz'</span>, <span class="org-string">'micro_hexapod'</span>, <span class="org-string">'axisc'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Micro Station:\n'</span>);
<span class="org-keyword">if</span> granite.type <span class="org-type">==</span> 1 <span class="org-type">&amp;&amp;</span> ...
ty.type <span class="org-type">==</span> 1 <span class="org-type">&amp;&amp;</span> ...
ry.type <span class="org-type">==</span> 1 <span class="org-type">&amp;&amp;</span> ...
rz.type <span class="org-type">==</span> 1 <span class="org-type">&amp;&amp;</span> ...
micro_hexapod.type <span class="org-type">==</span> 1;
fprintf(<span class="org-string">'- All stages are rigid\n'</span>);
<span class="org-keyword">elseif</span> granite.type <span class="org-type">==</span> 2 <span class="org-type">&amp;&amp;</span> ...
ty.type <span class="org-type">==</span> 2 <span class="org-type">&amp;&amp;</span> ...
ry.type <span class="org-type">==</span> 2 <span class="org-type">&amp;&amp;</span> ...
rz.type <span class="org-type">==</span> 2 <span class="org-type">&amp;&amp;</span> ...
micro_hexapod.type <span class="org-type">==</span> 2;
fprintf(<span class="org-string">'- All stages are flexible\n'</span>);
<span class="org-keyword">else</span>
<span class="org-keyword">if</span> granite.type <span class="org-type">==</span> 1 <span class="org-type">||</span> granite.type <span class="org-type">==</span> 4
fprintf(<span class="org-string">'- Granite is rigid\n'</span>);
<span class="org-keyword">else</span>
fprintf(<span class="org-string">'- Granite is flexible\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> ty.type <span class="org-type">==</span> 1 <span class="org-type">||</span> ty.type <span class="org-type">==</span> 4
fprintf(<span class="org-string">'- Translation Stage is rigid\n'</span>);
<span class="org-keyword">else</span>
fprintf(<span class="org-string">'- Translation Stage is flexible\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> ry.type <span class="org-type">==</span> 1 <span class="org-type">||</span> ry.type <span class="org-type">==</span> 4
fprintf(<span class="org-string">'- Tilt Stage is rigid\n'</span>);
<span class="org-keyword">else</span>
fprintf(<span class="org-string">'- Tilt Stage is flexible\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> rz.type <span class="org-type">==</span> 1 <span class="org-type">||</span> rz.type <span class="org-type">==</span> 4
fprintf(<span class="org-string">'- Spindle is rigid\n'</span>);
<span class="org-keyword">else</span>
fprintf(<span class="org-string">'- Spindle is flexible\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">if</span> micro_hexapod.type <span class="org-type">==</span> 1 <span class="org-type">||</span> micro_hexapod.type <span class="org-type">==</span> 4
fprintf(<span class="org-string">'- Micro Hexapod is rigid\n'</span>);
<span class="org-keyword">else</span>
fprintf(<span class="org-string">'- Micro Hexapod is flexible\n'</span>);
<span class="org-keyword">end</span>
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org1687c05" class="outline-3">
<h3 id="org1687c05">Metrology</h3>
<div class="outline-text-3" id="text-org1687c05">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'mirror'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Reference Mirror:\n'</span>);
<span class="org-keyword">if</span> mirror.type <span class="org-type">==</span> 2;
fprintf(<span class="org-string">'- flexible fixation\n'</span>);
fprintf(<span class="org-string">'- w = %.0f [Hz]\n'</span>, mirror.freq(1));
<span class="org-keyword">else</span>
fprintf(<span class="org-string">'- rigidly attached to the nano-hexapod\n'</span>);
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'- m = %.0f [kg]\n'</span>, mirror.mass);
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgee5944e" class="outline-3">
<h3 id="orgee5944e">Nano Hexapod</h3>
<div class="outline-text-3" id="text-orgee5944e">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Nano Hexapod:\n'</span>);
<span class="org-keyword">if</span> nano_hexapod.type <span class="org-type">==</span> 0;
fprintf(<span class="org-string">'- no included\n'</span>);
<span class="org-keyword">elseif</span> nano_hexapod.type <span class="org-type">==</span> 1 <span class="org-type">||</span> nano_hexapod.type <span class="org-type">==</span> 3;
fprintf(<span class="org-string">'- rigid\n'</span>);
<span class="org-keyword">elseif</span> nano_hexapod.type <span class="org-type">==</span> 2;
fprintf(<span class="org-string">'- flexible\n'</span>);
fprintf(<span class="org-string">'- Ki = %.0g [N/m]\n'</span>, nano_hexapod.Ki(1));
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-orga499c17" class="outline-3">
<h3 id="orga499c17">Sample</h3>
<div class="outline-text-3" id="text-orga499c17">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/stages.mat'</span>, <span class="org-string">'sample'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fprintf(<span class="org-string">'Sample:\n'</span>);
<span class="org-keyword">if</span> sample.type <span class="org-type">==</span> 0;
fprintf(<span class="org-string">'- no included\n'</span>);
<span class="org-keyword">elseif</span> sample.type <span class="org-type">==</span> 1 <span class="org-type">||</span> sample.type <span class="org-type">==</span> 3;
fprintf(<span class="org-string">'- rigid\n'</span>);
fprintf(<span class="org-string">'- mass = %.0f [kg]\n'</span>, sample.mass);
fprintf(<span class="org-string">'- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n'</span>, sample.inertia(1), sample.inertia(2), sample.inertia(3));
<span class="org-keyword">elseif</span> sample.type <span class="org-type">==</span> 2;
fprintf(<span class="org-string">'- flexible\n'</span>);
fprintf(<span class="org-string">'- mass = %.0f [kg]\n'</span>, sample.mass);
fprintf(<span class="org-string">'- moment of inertia = %.2f, %.2f, %.2f [kg m2]\n'</span>, sample.inertia(1), sample.inertia(2), sample.inertia(3));
<span class="org-comment">% fprintf('- Kt = %.0g, %.0g, %.0g [N/m]\n', sample.K(1), sample.K(2), sample.K(3));</span>
<span class="org-comment">% fprintf('- Kr = %.0g, %.0g, %.0g [Nm/rad]\n', sample.K(4), sample.K(5), sample.K(6));</span>
fprintf(<span class="org-string">'- wt(x,y,z) = %.0f, %.0f, %.0f [Hz]\n'</span>, 1<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>sqrt(sample.K(1)<span class="org-type">/</span>sample.mass), 1<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>sqrt(sample.K(1)<span class="org-type">/</span>sample.mass), 1<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>sqrt(sample.K(1)<span class="org-type">/</span>sample.mass));
fprintf(<span class="org-string">'- wr(x,y,z) = %.0f, %.0f, %.0f [Hz]\n'</span>, 1<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>sqrt(sample.K(4)<span class="org-type">/</span>sample.inertia(1)), 1<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>sqrt(sample.K(5)<span class="org-type">/</span>sample.inertia(2)), 1<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>sqrt(sample.K(6)<span class="org-type">/</span>sample.inertia(3)));
<span class="org-keyword">end</span>
fprintf(<span class="org-string">'\n'</span>);
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgdc168b9" class="outline-2">
<h2 id="orgdc168b9"><span class="section-number-2">2</span> computeReferencePose</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org98cbe6e"></a> <a id="org98cbe6e"></a>
</p> </p>
@ -338,8 +444,8 @@ This Matlab function is accessible <a href="..//src/computeReferencePose.m">here
</div> </div>
<div id="outline-container-org493ab7f" class="outline-2"> <div id="outline-container-org493ab7f" class="outline-2">
<h2 id="org493ab7f"><span class="section-number-2">2</span> Compute the Sample Position Error w.r.t. the NASS</h2> <h2 id="org493ab7f"><span class="section-number-2">3</span> Compute the Sample Position Error w.r.t. the NASS</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="org6dcd4fb"></a> <a id="org6dcd4fb"></a>
</p> </p>
@ -376,7 +482,7 @@ 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>
<p class="date">Created: 2020-03-17 mar. 17:28</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
</body> </body>
</html> </html>

234
docs/identification.html
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@ -4,237 +4,25 @@
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -815,7 +603,7 @@ 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>
<p class="date">Created: 2020-04-01 mer. 16:14</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
</body> </body>
</html> </html>

227
docs/index.html
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@ -4,233 +4,23 @@
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<h1 class="title">Simscape Model of the Nano-Active-Stabilization-System</h1> <h1 class="title">Simscape Model of the Nano-Active-Stabilization-System</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -256,7 +46,6 @@
</ul> </ul>
</div> </div>
</div> </div>
<p> <p>
Here are links to the documents related to the Simscape model of the Nano-Active-Stabilization-System. Here are links to the documents related to the Simscape model of the Nano-Active-Stabilization-System.
</p> </p>
@ -444,7 +233,7 @@ These functions are all defined <a href="./functions.html">here</a>.
</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: 2020-04-07 mar. 14:55</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
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234
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@ -572,7 +360,7 @@ 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>
<p class="date">Created: 2020-03-06 ven. 15:09</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
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<h1 class="title">Study of the Metrology Frame</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgf049208">1. Flexibility of the reference mirror</a>
<ul>
<li><a href="#orgaec148c">1.1. Initialization</a></li>
<li><a href="#orgaeca24e">1.2. Rigid fixation between the metrology frame and the nano-hexapod</a></li>
<li><a href="#orgbe194f6">1.3. Flexible fixation between the metrology frame and the nano-hexapod</a></li>
<li><a href="#org385c252">1.4. Comparison</a></li>
<li><a href="#orgbe63408">1.5. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgf049208" class="outline-2">
<h2 id="orgf049208"><span class="section-number-2">1</span> Flexibility of the reference mirror</h2>
<div class="outline-text-2" id="text-1">
<p>
In this section we wish to see how a flexibility between the nano-hexapod&rsquo;s top platform and the reference mirror will change the plant dynamics and limits the performance.
</p>
<p>
First, we identify the dynamics of the system for an infinitely rigid reference mirror, and then for a reference mirror with a limited resonance frequency.
</p>
<p>
We will compare the two dynamics and conclude.
</p>
</div>
<div id="outline-container-orgaec148c" class="outline-3">
<h3 id="orgaec148c"><span class="section-number-3">1.1</span> Initialization</h3>
<div class="outline-text-3" id="text-1-1">
<p>
We initialize all the stages with the default parameters.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeGround();
initializeGranite();
initializeTy();
initializeRy();
initializeRz();
initializeMicroHexapod();
initializeAxisc();
initializeNanoHexapod();
</pre>
</div>
<p>
We first consider a rigid Sample to simplify the analysis.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgaeca24e" class="outline-3">
<h3 id="orgaeca24e"><span class="section-number-3">1.2</span> Rigid fixation between the metrology frame and the nano-hexapod</h3>
<div class="outline-text-3" id="text-1-2">
<p>
Let&rsquo;s first consider a rigid reference mirror and we identify the dynamics of the system.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeMirror(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgbe194f6" class="outline-3">
<h3 id="orgbe194f6"><span class="section-number-3">1.3</span> Flexible fixation between the metrology frame and the nano-hexapod</h3>
<div class="outline-text-3" id="text-1-3">
<p>
We now initialize a reference mirror with a main resonance frequency at \(200\ [Hz]\).
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeMirror(<span class="org-string">'type'</span>, <span class="org-string">'flexible'</span>, <span class="org-string">'freq'</span>, 200<span class="org-type">*</span>ones(6,1));
</pre>
</div>
<p>
And we re identify the plant dynamics.
</p>
</div>
</div>
<div id="outline-container-org385c252" class="outline-3">
<h3 id="org385c252"><span class="section-number-3">1.4</span> Comparison</h3>
<div class="outline-text-3" id="text-1-4">
<p>
The obtained transfer functions from \(\mathcal{F}_z\) to \(\mathcal{X}_z\) when considering a rigid reference mirror and a flexible one are shown in Figure <a href="#orgfa25dbd">1</a>.
</p>
<div id="orgfa25dbd" class="figure">
<p><img src="figs/effect_mirror_flexibility_fz_dz.png" alt="effect_mirror_flexibility_fz_dz.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Effect of the mirror flexibility on the transfer function from \(\mathcal{F}_z\) to \(\mathcal{X}_z\)</p>
</div>
</div>
</div>
<div id="outline-container-orgbe63408" class="outline-3">
<h3 id="orgbe63408"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5">
<div class="important">
<p>
A flexibility between the nano-hexapod top platform and the reference mirror will appear in the plant as two complex conjugate poles at the frequency of the resonance of the mirror on top of the nano-hexapod.
This induces 180 degrees of phase drop on the plant and will limit the attainable controller bandwidth.
</p>
<p>
This phase drop appears whatever the nano-hexapod stiffness.
Thus, care should be taken when designing the fixation of the reference mirror on top of the nano-hexapod.
</p>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-17 ven. 09:35</p>
</div>
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<h1 class="title">Motion and Force Requirements for the Nano-Hexapod</h1> <h1 class="title">Motion and Force Requirements for the Nano-Hexapod</h1>
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@ -360,7 +155,7 @@ F = m<span class="org-type">*</span>d<span class="org-type">*</span>w<span class
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<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
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<h2>Table of Contents</h2> <h2>Table of Contents</h2>
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<ul> <ul>
<li><a href="#orgb09af41">1. Low Authority Control - Decentralized Integral Force Feedback</a> <li><a href="#org99c5b6d">1. Low Authority Control - Decentralized Direct Velocity Feedback</a>
<ul> <ul>
<li><a href="#orgf3f8aed">1.1. Initialization</a></li> <li><a href="#orgf3f8aed">1.1. Initialization</a></li>
<li><a href="#org93676a4">1.2. Identification</a></li> <li><a href="#orgc5a1e81">1.2. Identification</a></li>
<li><a href="#org1f2e125">1.3. Controller Design</a></li> <li><a href="#orgfef1a3f">1.3. Controller Design</a></li>
<li><a href="#org3c73014">1.4. Effect of the Low Authority Control on the Primary Plant</a></li>
<li><a href="#orgee5dbee">1.5. Effect of the Low Authority Control on the Sensibility to Disturbances</a></li>
<li><a href="#org27f255e">1.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf825c29">2. Primary Control</a> <li><a href="#org81dc0a8">2. Primary Control in the leg space</a>
<ul> <ul>
<li><a href="#org611a860">2.1. Identification</a></li> <li><a href="#org1e7a412">2.1. Plant in the leg space</a></li>
<li><a href="#orgfef1a3f">2.2. Controller Design</a></li> <li><a href="#orgf39520c">2.2. Control in the leg space</a></li>
<li><a href="#org16d192f">2.3. Sensibility to Disturbances and Noise Budget</a></li>
<li><a href="#org84f68cc">2.4. Simulations</a></li>
<li><a href="#orgbeadec8">2.5. Results</a></li>
<li><a href="#org87fa1ac">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#org9bd2bf8">3. Primary Control in the task space</a>
<ul>
<li><a href="#org07b4a9d">3.1. Plant in the task space</a></li>
<li><a href="#org7d888f9">3.2. Control in the task space</a>
<ul>
<li><a href="#orgb28634b">3.2.1. Stability</a></li>
</ul>
</li>
<li><a href="#org57e2cfd">3.3. Simulation</a></li>
<li><a href="#org882e1ac">3.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org84f68cc">3. Simulations</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgb09af41" class="outline-2"> <div id="outline-container-org99c5b6d" class="outline-2">
<h2 id="orgb09af41"><span class="section-number-2">1</span> Low Authority Control - Decentralized Integral Force Feedback</h2> <h2 id="org99c5b6d"><span class="section-number-2">1</span> Low Authority Control - Decentralized Direct Velocity Feedback</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p>
<a id="orgfec42cb"></a>
</p>
<div id="org7f11a74" class="figure">
<p><img src="figs/control_architecture_dvf.png" alt="control_architecture_dvf.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Low Authority Control: Decentralized Direct Velocity Feedback</p>
</div>
</div> </div>
<div id="outline-container-orgf3f8aed" class="outline-3"> <div id="outline-container-orgf3f8aed" class="outline-3">
<h3 id="orgf3f8aed"><span class="section-number-3">1.1</span> Initialization</h3> <h3 id="orgf3f8aed"><span class="section-number-3">1.1</span> Initialization</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p>
We initialize all the stages with the default parameters.
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeGround(); <pre class="src src-matlab">initializeGround();
initializeGranite(); initializeGranite();
@ -274,43 +96,45 @@ initializeRz();
initializeMicroHexapod(); initializeMicroHexapod();
initializeAxisc(); initializeAxisc();
initializeMirror(); initializeMirror();
initializeSimscapeConfiguration();
initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'none'</span>);
initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-dvf'</span>);
</pre> </pre>
</div> </div>
<p> <p>
We set the references that corresponds to a tomography experiment. We set the stiffness of the payload fixation:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating-not-filtered'</span>, <span class="org-string">'Rz_period'</span>, 1); <pre class="src src-matlab">Kp = 1e8; <span class="org-comment">% [N/m]</span>
initializeSimscapeConfiguration();
initializeDisturbances(<span class="org-string">'enable'</span>, <span class="org-constant">false</span>);
initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'none'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">initializeController(<span class="org-string">'type'</span>, <span class="org-string">'hac-iff'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org93676a4" class="outline-3"> <div id="outline-container-orgc5a1e81" class="outline-3">
<h3 id="org93676a4"><span class="section-number-3">1.2</span> Identification</h3> <h3 id="orgc5a1e81"><span class="section-number-3">1.2</span> Identification</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Kx = tf(zeros(6)); <pre class="src src-matlab">K = tf(zeros(6));
Kiff = tf(zeros(6)); Kdvf = tf(zeros(6));
</pre> </pre>
</div> </div>
<p>
We identify the system for the following payload masses:
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ms = [1, 10, 50]; <pre class="src src-matlab">Ms = [1, 10, 50];
Gm_iff = {zeros(length(Ms), 1)};
</pre> </pre>
</div> </div>
<p>
The nano-hexapod has the following leg&rsquo;s stiffness and damping.
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'k'</span>, 1e5, <span class="org-string">'c'</span>, 2e2); <pre class="src src-matlab">initializeNanoHexapod(<span class="org-string">'k'</span>, 1e5, <span class="org-string">'c'</span>, 2e2);
</pre> </pre>
@ -318,45 +142,494 @@ Gm_iff = {zeros(length(Ms), 1)};
</div> </div>
</div> </div>
<div id="outline-container-org1f2e125" class="outline-3"> <div id="outline-container-orgfef1a3f" class="outline-3">
<h3 id="org1f2e125"><span class="section-number-3">1.3</span> Controller Design</h3> <h3 id="orgfef1a3f"><span class="section-number-3">1.3</span> Controller Design</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
Root Locus The obtain dynamics from actuators forces \(\tau_i\) to the relative motion of the legs \(d\mathcal{L}_i\) is shown in Figure <a href="#orgdb7af3b">2</a> for the three considered payload masses.
</p> </p>
<div id="orgf657dfe" class="figure"> <p>
<p><img src="figs/opt_stiff_iff_root_locus.png" alt="opt_stiff_iff_root_locus.png" /> The Root Locus is shown in Figure <a href="#org5814b4f">3</a> and wee see that we have unconditional stability.
</p> </p>
<p><span class="figure-number">Figure 1: </span>Root Locus for the</p>
<p>
In order to choose the gain such that we obtain good damping for all the three payload masses, we plot the damping ration of the modes as a function of the gain for all three payload masses in Figure <a href="#orgb16b2c3">4</a>.
</p>
<div id="orgdb7af3b" class="figure">
<p><img src="figs/opt_stiff_dvf_plant.png" alt="opt_stiff_dvf_plant.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Dynamics for the Direct Velocity Feedback active damping for three payload masses</p>
</div>
<div id="org5814b4f" class="figure">
<p><img src="figs/opt_stiff_dvf_root_locus.png" alt="opt_stiff_dvf_root_locus.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Root Locus for the DVF controll for three payload masses</p>
</div> </div>
<p> <p>
Damping as function of the gain Damping as function of the gain
</p> </p>
<div id="orgb16b2c3" class="figure">
<p><img src="figs/opt_stiff_dvf_damping_gain.png" alt="opt_stiff_dvf_damping_gain.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Damping ratio of the poles as a function of the DVF gain</p>
</div>
<p>
Finally, we use the following controller for the Decentralized Direct Velocity Feedback:
</p>
<div class="org-src-container">
<pre class="src src-matlab">Kdvf = 5e3<span class="org-type">*</span>s<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1e3)<span class="org-type">*</span>eye(6);
</pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgf825c29" class="outline-2">
<h2 id="orgf825c29"><span class="section-number-2">2</span> Primary Control</h2> <div id="outline-container-org3c73014" class="outline-3">
<h3 id="org3c73014"><span class="section-number-3">1.4</span> Effect of the Low Authority Control on the Primary Plant</h3>
<div class="outline-text-3" id="text-1-4">
<p>
Let&rsquo;s identify the dynamics from actuator forces \(\bm{\tau}\) to displacement as measured by the metrology \(\bm{\mathcal{X}}\):
\[ \bm{G}(s) = \frac{\bm{\mathcal{X}}}{\bm{\tau}} \]
We do so both when the DVF is applied and when it is not applied.
</p>
<p>
Then, we compute the transfer function from forces applied by the actuators \(\bm{\mathcal{F}}\) to the measured position error in the frame of the nano-hexapod \(\bm{\epsilon}_{\mathcal{X}_n}\):
\[ \bm{G}_\mathcal{X}(s) = \frac{\bm{\epsilon}_{\mathcal{X}_n}}{\bm{\mathcal{F}}} = \bm{G}(s) \bm{J}^{-T} \]
The obtained dynamics is shown in Figure <a href="#org45c1265">5</a>.
</p>
<p>
And we compute the transfer function from actuator forces \(\bm{\tau}\) to position error of each leg \(\bm{\epsilon}_\mathcal{L}\):
\[ \bm{G}_\mathcal{L} = \frac{\bm{\epsilon}_\mathcal{L}}{\bm{\tau}} = \bm{J} \bm{G}(s) \]
The obtained dynamics is shown in Figure <a href="#org069e296">6</a>.
</p>
<div id="org45c1265" class="figure">
<p><img src="figs/opt_stiff_primary_plant_damped_X.png" alt="opt_stiff_primary_plant_damped_X.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Primary plant in the task space with (dashed) and without (solid) Direct Velocity Feedback</p>
</div>
<div id="org069e296" class="figure">
<p><img src="figs/opt_stiff_primary_plant_damped_L.png" alt="opt_stiff_primary_plant_damped_L.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Primary plant in the space of the legs with (dashed) and without (solid) Direct Velocity Feedback</p>
</div>
<p>
The coupling (off diagonal elements) of \(\bm{G}_\mathcal{X}\) are shown in Figure <a href="#orgbb4e497">7</a> both when DVF is applied and when it is not.
</p>
<p>
The coupling does not change a lot with DVF.
</p>
<p>
The coupling in the space of the legs \(\bm{G}_\mathcal{L}\) are shown in Figure <a href="#orgc43d759">8</a>.
The magnitude of the coupling around the resonance of the nano-hexapod (where the coupling is the highest) is considerably reduced when DVF is applied.
</p>
<div id="orgbb4e497" class="figure">
<p><img src="figs/opt_stiff_primary_plant_damped_coupling_X.png" alt="opt_stiff_primary_plant_damped_coupling_X.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Coupling in the primary plant in the task with (dashed) and without (solid) Direct Velocity Feedback</p>
</div>
<div id="orgc43d759" class="figure">
<p><img src="figs/opt_stiff_primary_plant_damped_coupling_L.png" alt="opt_stiff_primary_plant_damped_coupling_L.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Coupling in the primary plant in the space of the legs with (dashed) and without (solid) Direct Velocity Feedback</p>
</div>
</div>
</div>
<div id="outline-container-orgee5dbee" class="outline-3">
<h3 id="orgee5dbee"><span class="section-number-3">1.5</span> Effect of the Low Authority Control on the Sensibility to Disturbances</h3>
<div class="outline-text-3" id="text-1-5">
<p>
We may now see how Decentralized Direct Velocity Feedback changes the sensibility to disturbances, namely:
</p>
<ul class="org-ul">
<li>Ground motion</li>
<li>Spindle and Translation stage vibrations</li>
<li>Direct forces applied to the sample</li>
</ul>
<p>
To simplify the analysis, we here only consider the vertical direction, thus, we will look at the transfer functions:
</p>
<ul class="org-ul">
<li>from vertical ground motion \(D_{w,z}\) to the vertical position error of the sample \(E_z\)</li>
<li>from vertical vibration forces of the spindle \(F_{R_z,z}\) to \(E_z\)</li>
<li>from vertical vibration forces of the translation stage \(F_{T_y,z}\) to \(E_z\)</li>
<li>from vertical direct forces (such as cable forces) \(F_{d,z}\) to \(E_z\)</li>
</ul>
<p>
The norm of these transfer functions are shown in Figure <a href="#org199898b">9</a>.
</p>
<div id="org199898b" class="figure">
<p><img src="figs/opt_stiff_sensibility_dist_dvf.png" alt="opt_stiff_sensibility_dist_dvf.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Norm of the transfer function from vertical disturbances to vertical position error with (dashed) and without (solid) Direct Velocity Feedback applied</p>
</div>
</div>
</div>
<div id="outline-container-org27f255e" class="outline-3">
<h3 id="org27f255e"><span class="section-number-3">1.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-6">
<div class="important">
<p>
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org81dc0a8" class="outline-2">
<h2 id="org81dc0a8"><span class="section-number-2">2</span> Primary Control in the leg space</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> <p>
<div id="outline-container-org611a860" class="outline-3"> <a id="orgd0beb6a"></a>
<h3 id="org611a860"><span class="section-number-3">2.1</span> Identification</h3> </p>
<p>
In this section we implement the control architecture shown in Figure <a href="#org7d5c8bc">10</a> consisting of:
</p>
<ul class="org-ul">
<li>an inner loop with a decentralized direct velocity feedback control</li>
<li>an outer loop where the controller \(\bm{K}_\mathcal{L}\) is designed in the frame of the legs</li>
</ul>
<div id="org7d5c8bc" class="figure">
<p><img src="figs/control_architecture_hac_dvf_pos_L.png" alt="control_architecture_hac_dvf_pos_L.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Cascade Control Architecture. The inner loop consist of a decentralized Direct Velocity Feedback. The outer loop consist of position control in the leg&rsquo;s space</p>
</div> </div>
<div id="outline-container-orgfef1a3f" class="outline-3"> <p>
<h3 id="orgfef1a3f"><span class="section-number-3">2.2</span> Controller Design</h3> The controller for decentralized direct velocity feedback is the one designed in Section <a href="#orgfec42cb">1</a>.
</p>
</div>
<div id="outline-container-org1e7a412" class="outline-3">
<h3 id="org1e7a412"><span class="section-number-3">2.1</span> Plant in the leg space</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We now loop at the transfer function matrix from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) for the design of \(\bm{K}_\mathcal{L}\).
</p>
<p>
The diagonal elements of the transfer function matrix from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) for the three considered masses are shown in Figure <a href="#org23d23ae">11</a>.
</p>
<p>
The plant dynamics below \(100\ [Hz]\) is only slightly dependent on the payload mass.
</p>
<div id="org23d23ae" class="figure">
<p><img src="figs/opt_stiff_primary_plant_L.png" alt="opt_stiff_primary_plant_L.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Diagonal elements of the transfer function matrix from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) for the three considered masses</p>
</div>
</div> </div>
</div> </div>
<div id="outline-container-org84f68cc" class="outline-2">
<h2 id="org84f68cc"><span class="section-number-2">3</span> Simulations</h2> <div id="outline-container-orgf39520c" class="outline-3">
<h3 id="orgf39520c"><span class="section-number-3">2.2</span> Control in the leg space</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We design a diagonal controller with all the same diagonal elements.
</p>
<p>
The requirements for the controller are:
</p>
<ul class="org-ul">
<li>Crossover frequency of around 100Hz</li>
<li>Stable for all the considered payload masses</li>
<li>Sufficient phase and gain margin</li>
<li>Integral action at low frequency</li>
</ul>
<p>
The design controller is as follows:
</p>
<ul class="org-ul">
<li>Lead centered around the crossover</li>
<li>An integrator below 10Hz</li>
<li>A low pass filter at 250Hz</li>
</ul>
<p>
The loop gain is shown in Figure <a href="#orgbcc0acb">12</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">h = 2.0;
Kl = 2e7 <span class="org-type">*</span> eye(6) <span class="org-type">*</span> ...
1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>200<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>200<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10) <span class="org-type">*</span> ...
1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>300);
</pre>
</div>
<div id="orgbcc0acb" class="figure">
<p><img src="figs/opt_stiff_primary_loop_gain_L.png" alt="opt_stiff_primary_loop_gain_L.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Loop gain for the primary plant</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/stages.mat'</span>, <span class="org-string">'nano_hexapod'</span>);
K = Kl<span class="org-type">*</span>nano_hexapod.J<span class="org-type">*</span>diag([1, 1, 1, 1, 1, 0]);
</pre>
</div>
<p>
Check the MIMO stability
</p>
</div>
</div>
<div id="outline-container-org16d192f" class="outline-3">
<h3 id="org16d192f"><span class="section-number-3">2.3</span> Sensibility to Disturbances and Noise Budget</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We identify the transfer function from disturbances to the position error of the sample when the HAC-LAC control is applied.
</p>
<p>
We compare the norm of these transfer function for the vertical direction when no control is applied and when HAC-LAC control is applied: Figure <a href="#org9650e03">13</a>.
</p>
<div id="org9650e03" class="figure">
<p><img src="figs/opt_stiff_primary_control_L_senbility_dist.png" alt="opt_stiff_primary_control_L_senbility_dist.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Sensibility to disturbances when the HAC-LAC control is applied</p>
</div>
<p>
Then, we load the Power Spectral Density of the perturbations and we look at the obtained PSD of the displacement error in the vertical direction due to the disturbances:
</p>
<ul class="org-ul">
<li>Figure <a href="#org32928e0">14</a>: Amplitude Spectral Density of the vertical position error due to both the vertical ground motion and the vertical vibrations of the spindle</li>
<li>Figure <a href="#org7fda8f7">15</a>: Comparison of the Amplitude Spectral Density of the vertical position error in Open Loop and with the HAC-DVF Control</li>
<li>Figure <a href="#org073608b">16</a>: Comparison of the Cumulative Amplitude Spectrum of the vertical position error in Open Loop and with the HAC-DVF Control</li>
</ul>
<div id="org32928e0" class="figure">
<p><img src="figs/opt_stiff_primary_control_L_psd_dist.png" alt="opt_stiff_primary_control_L_psd_dist.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the vertical position error of the sample when the HAC-DVF control is applied due to both the ground motion and spindle vibrations</p>
</div>
<div id="org7fda8f7" class="figure">
<p><img src="figs/opt_stiff_primary_control_L_psd_tot.png" alt="opt_stiff_primary_control_L_psd_tot.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the vertical position error of the sample in Open-Loop and when the HAC-DVF control is applied</p>
</div>
<div id="org073608b" class="figure">
<p><img src="figs/opt_stiff_primary_control_L_cas_tot.png" alt="opt_stiff_primary_control_L_cas_tot.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Cumulative Amplitude Spectrum of the vertical position error of the sample in Open-Loop and when the HAC-DVF control is applied</p>
</div>
</div>
</div>
<div id="outline-container-org84f68cc" class="outline-3">
<h3 id="org84f68cc"><span class="section-number-3">2.4</span> Simulations</h3>
<div class="outline-text-3" id="text-2-4">
<p>
Let&rsquo;s now simulate a tomography experiment.
To do so, we include all disturbances except vibrations of the translation stage.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeDisturbances();
initializeSimscapeConfiguration(<span class="org-string">'gravity'</span>, <span class="org-constant">false</span>);
initializeLoggingConfiguration(<span class="org-string">'log'</span>, <span class="org-string">'all'</span>);
</pre>
</div>
<p>
And we run the simulation for all three payload Masses.
</p>
</div>
</div>
<div id="outline-container-orgbeadec8" class="outline-3">
<h3 id="orgbeadec8"><span class="section-number-3">2.5</span> Results</h3>
<div class="outline-text-3" id="text-2-5">
<p>
Let&rsquo;s now see how this controller performs.
</p>
<p>
First, we compute the Power Spectral Density of the sample&rsquo;s position error and we compare it with the open loop case in Figure <a href="#org6cab6ef">17</a>.
</p>
<p>
Similarly, the Cumulative Amplitude Spectrum is shown in Figure <a href="#org33e9f1a">18</a>.
</p>
<p>
Finally, the time domain position error signals are shown in Figure <a href="#orgf0f1950">19</a>.
</p>
<div id="org6cab6ef" class="figure">
<p><img src="figs/opt_stiff_hac_dvf_L_psd_disp_error.png" alt="opt_stiff_hac_dvf_L_psd_disp_error.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the position error in Open Loop and with the HAC-LAC controller</p>
</div>
<div id="org33e9f1a" class="figure">
<p><img src="figs/opt_stiff_hac_dvf_L_cas_disp_error.png" alt="opt_stiff_hac_dvf_L_cas_disp_error.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Cumulative Amplitude Spectrum of the position error in Open Loop and with the HAC-LAC controller</p>
</div>
<div id="orgf0f1950" class="figure">
<p><img src="figs/opt_stiff_hac_dvf_L_pos_error.png" alt="opt_stiff_hac_dvf_L_pos_error.png" />
</p>
<p><span class="figure-number">Figure 19: </span>Position Error of the sample during a tomography experiment when no control is applied and with the HAC-DVF control architecture</p>
</div>
</div>
</div>
<div id="outline-container-org87fa1ac" class="outline-3">
<h3 id="org87fa1ac"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<p>
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org9bd2bf8" class="outline-2">
<h2 id="org9bd2bf8"><span class="section-number-2">3</span> Primary Control in the task space</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="orge9c2f9a"></a>
</p>
<p>
In this section, the control architecture shown in Figure <a href="#org7e70ccc">20</a> is applied and consists of:
</p>
<ul class="org-ul">
<li>an inner Low Authority Control loop consisting of a decentralized direct velocity control controller</li>
<li>an outer loop with the primary controller \(\bm{K}_\mathcal{X}\) designed in the task space</li>
</ul>
<div id="org7e70ccc" class="figure">
<p><img src="figs/control_architecture_hac_dvf_pos_X.png" alt="control_architecture_hac_dvf_pos_X.png" />
</p>
<p><span class="figure-number">Figure 20: </span>HAC-LAC architecture</p>
</div>
</div>
<div id="outline-container-org07b4a9d" class="outline-3">
<h3 id="org07b4a9d"><span class="section-number-3">3.1</span> Plant in the task space</h3>
<div class="outline-text-3" id="text-3-1">
<p>
Let&rsquo;s look \(\bm{G}_\mathcal{X}(s)\).
</p>
</div>
</div>
<div id="outline-container-org7d888f9" class="outline-3">
<h3 id="org7d888f9"><span class="section-number-3">3.2</span> Control in the task space</h3>
<div class="outline-text-3" id="text-3-2">
<div class="org-src-container">
<pre class="src src-matlab">Kx = tf(zeros(6));
h = 2.5;
Kx<span class="org-type">(1,1) </span>= 3e7 <span class="org-type">*</span> ...
1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
Kx<span class="org-type">(2,2) </span>= Kx(1,1);
h = 2.5;
Kx<span class="org-type">(3,3) </span>= 3e7 <span class="org-type">*</span> ...
1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">h = 1.5;
Kx<span class="org-type">(4,4) </span>= 5e5 <span class="org-type">*</span> ...
1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
Kx<span class="org-type">(5,5) </span>= Kx(4,4);
h = 1.5;
Kx<span class="org-type">(6,6) </span>= 5e4 <span class="org-type">*</span> ...
1<span class="org-type">/</span>h<span class="org-type">*</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>30<span class="org-type">/</span>h) <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>30<span class="org-type">*</span>h) <span class="org-type">+</span> 1) <span class="org-type">*</span> ...
(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1 <span class="org-type">+</span> 1)<span class="org-type">/</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>1);
</pre>
</div>
</div>
<div id="outline-container-orgb28634b" class="outline-4">
<h4 id="orgb28634b"><span class="section-number-4">3.2.1</span> Stability</h4>
<div class="outline-text-4" id="text-3-2-1">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(Ms)</span>
isstable(feedback(Gm_x{<span class="org-constant">i</span>}<span class="org-type">*</span>Kx, eye(6), <span class="org-type">-</span>1))
<span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org57e2cfd" class="outline-3">
<h3 id="org57e2cfd"><span class="section-number-3">3.3</span> Simulation</h3>
</div>
<div id="outline-container-org882e1ac" class="outline-3">
<h3 id="org882e1ac"><span class="section-number-3">3.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-4">
<div class="important">
<p>
</p>
</div>
</div>
</div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-08 mer. 17:22</p> <p class="date">Created: 2020-04-17 ven. 10:25</p>
</div> </div>
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<h1 class="title">Determination of the optimal nano-hexapod&rsquo;s stiffness for reducing the effect of disturbances</h1> <h1 class="title">Determination of the optimal nano-hexapod&rsquo;s stiffness for reducing the effect of disturbances</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -257,7 +43,7 @@
<li><a href="#org78dd34d">2.3. Sensitivity to Stages vibration (Filtering)</a></li> <li><a href="#org78dd34d">2.3. Sensitivity to Stages vibration (Filtering)</a></li>
<li><a href="#orgd4ea2f4">2.4. Effect of Ground motion (Transmissibility).</a></li> <li><a href="#orgd4ea2f4">2.4. Effect of Ground motion (Transmissibility).</a></li>
<li><a href="#org0448746">2.5. Direct Forces (Compliance).</a></li> <li><a href="#org0448746">2.5. Direct Forces (Compliance).</a></li>
<li><a href="#org08f24cd">2.6. Conclusion</a></li> <li><a href="#org626fe57">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org6527e58">3. Effect of granite stiffness</a> <li><a href="#org6527e58">3. Effect of granite stiffness</a>
@ -270,7 +56,7 @@
</li> </li>
<li><a href="#org9215f81">3.2. Soft Granite</a></li> <li><a href="#org9215f81">3.2. Soft Granite</a></li>
<li><a href="#org8878556">3.3. Effect of the Granite transfer function</a></li> <li><a href="#org8878556">3.3. Effect of the Granite transfer function</a></li>
<li><a href="#orgbc8931e">3.4. Conclusion</a></li> <li><a href="#orgf388e39">3.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org8a88fb0">4. Open Loop Budget Error</a> <li><a href="#org8a88fb0">4. Open Loop Budget Error</a>
@ -278,7 +64,7 @@
<li><a href="#org6bd588f">4.1. Noise Budgeting - Theory</a></li> <li><a href="#org6bd588f">4.1. Noise Budgeting - Theory</a></li>
<li><a href="#orgcc86f59">4.2. Power Spectral Densities</a></li> <li><a href="#orgcc86f59">4.2. Power Spectral Densities</a></li>
<li><a href="#orgef96b89">4.3. Cumulative Amplitude Spectrum</a></li> <li><a href="#orgef96b89">4.3. Cumulative Amplitude Spectrum</a></li>
<li><a href="#org18bab44">4.4. Conclusion</a></li> <li><a href="#org0be3c47">4.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org34c0f38">5. Closed Loop Budget Error</a> <li><a href="#org34c0f38">5. Closed Loop Budget Error</a>
@ -287,7 +73,7 @@
<li><a href="#orgf2d36a1">5.2. Reduction thanks to feedback - Required bandwidth</a></li> <li><a href="#orgf2d36a1">5.2. Reduction thanks to feedback - Required bandwidth</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd9198a1">6. Conclusion</a></li> <li><a href="#org08f4548">6. Conclusion</a></li>
</ul> </ul>
</div> </div>
</div> </div>
@ -497,8 +283,8 @@ The effect of direct forces/torques applied on the sample (cable forces for inst
</div> </div>
</div> </div>
<div id="outline-container-org08f24cd" class="outline-3"> <div id="outline-container-org626fe57" class="outline-3">
<h3 id="org08f24cd"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org626fe57"><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>
@ -678,8 +464,8 @@ From Figures <a href="#orgc4c14fb">11</a> and <a href="#org533cc4b">12</a>, we s
</div> </div>
</div> </div>
<div id="outline-container-orgbc8931e" class="outline-3"> <div id="outline-container-orgf388e39" class="outline-3">
<h3 id="orgbc8931e"><span class="section-number-3">3.4</span> Conclusion</h3> <h3 id="orgf388e39"><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>
@ -848,8 +634,8 @@ The black dashed line corresponds to the performance objective of a sample vibra
</div> </div>
</div> </div>
<div id="outline-container-org18bab44" class="outline-3"> <div id="outline-container-org0be3c47" class="outline-3">
<h3 id="org18bab44"><span class="section-number-3">4.4</span> Conclusion</h3> <h3 id="org0be3c47"><span class="section-number-3">4.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-4-4"> <div class="outline-text-3" id="text-4-4">
<div class="important"> <div class="important">
<p> <p>
@ -975,13 +761,13 @@ The obtained required bandwidth (approximate upper and lower bounds) to obtained
<thead> <thead>
<tr> <tr>
<th scope="col" class="org-left">Nano-Hexapod stiffness [N/m]</th> <th scope="col" class="org-left">Nano-Hexapod stiffness [N/m]</th>
<th scope="col" class="org-right">10<sup>3</sup></th> <th scope="col" class="org-right">10^3</th>
<th scope="col" class="org-right">10<sup>4</sup></th> <th scope="col" class="org-right">10^4</th>
<th scope="col" class="org-right">10<sup>5</sup></th> <th scope="col" class="org-right">10^5</th>
<th scope="col" class="org-right">10<sup>6</sup></th> <th scope="col" class="org-right">10^6</th>
<th scope="col" class="org-right">10<sup>7</sup></th> <th scope="col" class="org-right">10^7</th>
<th scope="col" class="org-right">10<sup>8</sup></th> <th scope="col" class="org-right">10^8</th>
<th scope="col" class="org-right">10<sup>9</sup></th> <th scope="col" class="org-right">10^9</th>
</tr> </tr>
</thead> </thead>
<tbody> <tbody>
@ -1012,8 +798,8 @@ The obtained required bandwidth (approximate upper and lower bounds) to obtained
</div> </div>
</div> </div>
<div id="outline-container-orgd9198a1" class="outline-2"> <div id="outline-container-org08f4548" class="outline-2">
<h2 id="orgd9198a1"><span class="section-number-2">6</span> Conclusion</h2> <h2 id="org08f4548"><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">
<div class="important"> <div class="important">
<p> <p>
@ -1031,7 +817,7 @@ From Figure <a href="#orgd677910">23</a> and Table <a href="#org5ab4860">1</a>,
</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: 2020-04-08 mer. 17:20</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -250,17 +38,17 @@
<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="#org4efa9f2">2.1. Prepare the Simulation</a></li> <li><a href="#org824599b">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="#orga90edfe">2.3. Conclusion</a></li> <li><a href="#org127e189">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="#orgcbcbd60">3.1. Prepare the Simulation</a></li> <li><a href="#orgf76b12a">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="#orgc1b5b33">3.4. Conclusion</a></li> <li><a href="#org1528ce4">3.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -348,8 +136,8 @@ 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-org4efa9f2" class="outline-3"> <div id="outline-container-org824599b" class="outline-3">
<h3 id="org4efa9f2"><span class="section-number-3">2.1</span> Prepare the Simulation</h3> <h3 id="org824599b"><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>.
@ -519,8 +307,8 @@ ans =
</div> </div>
</div> </div>
<div id="outline-container-orga90edfe" class="outline-3"> <div id="outline-container-org127e189" class="outline-3">
<h3 id="orga90edfe"><span class="section-number-3">2.3</span> Conclusion</h3> <h3 id="org127e189"><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>
@ -548,8 +336,8 @@ 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-orgcbcbd60" class="outline-3"> <div id="outline-container-orgf76b12a" class="outline-3">
<h3 id="orgcbcbd60"><span class="section-number-3">3.1</span> Prepare the Simulation</h3> <h3 id="orgf76b12a"><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>.
@ -873,8 +661,8 @@ Verify that the pose error is small.
</div> </div>
</div> </div>
<div id="outline-container-orgc1b5b33" class="outline-3"> <div id="outline-container-org1528ce4" class="outline-3">
<h3 id="orgc1b5b33"><span class="section-number-3">3.4</span> Conclusion</h3> <h3 id="org1528ce4"><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>
@ -888,7 +676,7 @@ 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: 2020-03-06 ven. 15:09</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
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<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-03-06 ven. 15:09</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
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<h1 class="title">Simulink Project for the NASS</h1> <h1 class="title">Simulink Project for the NASS</h1>
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@ -300,7 +89,7 @@ The project also permits to automatically add defined folder to the path when th
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<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-03-06 ven. 15:10</p> <p class="date">Created: 2020-04-17 ven. 09:36</p>
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@ -1,262 +1,28 @@
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -271,9 +37,9 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#orgac25f89">1. <code>initializeFramesPositions</code>: Initialize the positions of frames {A}, {B}, {F} and {M}</a> <li><a href="#orgac25f89">1. <code>initializeFramesPositions</code>: Initialize the positions of frames {A}, {B}, {F} and {M}</a>
<ul> <ul>
<li><a href="#org17eec4d">1.1. Function description</a></li> <li><a href="#org5cdd36d">1.1. Function description</a></li>
<li><a href="#org93cf646">1.2. Documentation</a></li> <li><a href="#orge837700">1.2. Documentation</a></li>
<li><a href="#org142c995">1.3. Optional Parameters</a></li> <li><a href="#org312e9a7">1.3. Optional Parameters</a></li>
<li><a href="#org3622825">1.4. Initialize the Stewart structure</a></li> <li><a href="#org3622825">1.4. Initialize the Stewart structure</a></li>
<li><a href="#org7d50d54">1.5. Compute the position of each frame</a></li> <li><a href="#org7d50d54">1.5. Compute the position of each frame</a></li>
</ul> </ul>
@ -282,27 +48,27 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#org65fc289">2.1. <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</a> <li><a href="#org65fc289">2.1. <code>generateCubicConfiguration</code>: Generate a Cubic Configuration</a>
<ul> <ul>
<li><a href="#org7e1a61c">2.1.1. Function description</a></li> <li><a href="#org5a5b987">2.1.1. Function description</a></li>
<li><a href="#org9d47e7c">2.1.2. Documentation</a></li> <li><a href="#org40ea23a">2.1.2. Documentation</a></li>
<li><a href="#orgf3ef9f0">2.1.3. Optional Parameters</a></li> <li><a href="#org37651aa">2.1.3. Optional Parameters</a></li>
<li><a href="#orge94a885">2.1.4. Position of the Cube</a></li> <li><a href="#orge94a885">2.1.4. Position of the Cube</a></li>
<li><a href="#orge025784">2.1.5. Compute the pose</a></li> <li><a href="#org789a28b">2.1.5. Compute the pose</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgccb31c6">2.2. <code>generateGeneralConfiguration</code>: Generate a Very General Configuration</a> <li><a href="#orgccb31c6">2.2. <code>generateGeneralConfiguration</code>: Generate a Very General Configuration</a>
<ul> <ul>
<li><a href="#org7c192dc">2.2.1. Function description</a></li> <li><a href="#org0ba3fa4">2.2.1. Function description</a></li>
<li><a href="#org542739a">2.2.2. Documentation</a></li> <li><a href="#org839cae7">2.2.2. Documentation</a></li>
<li><a href="#org2f3445e">2.2.3. Optional Parameters</a></li> <li><a href="#org2e06fba">2.2.3. Optional Parameters</a></li>
<li><a href="#orga173176">2.2.4. Compute the pose</a></li> <li><a href="#orgfac23f3">2.2.4. Compute the pose</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</li> </li>
<li><a href="#org9944c04">3. <code>computeJointsPose</code>: Compute the Pose of the Joints</a> <li><a href="#org9944c04">3. <code>computeJointsPose</code>: Compute the Pose of the Joints</a>
<ul> <ul>
<li><a href="#org8036919">3.1. Function description</a></li> <li><a href="#org465ebb2">3.1. Function description</a></li>
<li><a href="#orgae953ca">3.2. Documentation</a></li> <li><a href="#orgc11609b">3.2. Documentation</a></li>
<li><a href="#orge87b302">3.3. Compute the position of the Joints</a></li> <li><a href="#orge87b302">3.3. Compute the position of the Joints</a></li>
<li><a href="#org3a7e3c5">3.4. Compute the strut length and orientation</a></li> <li><a href="#org3a7e3c5">3.4. Compute the strut length and orientation</a></li>
<li><a href="#org9e1258f">3.5. Compute the orientation of the Joints</a></li> <li><a href="#org9e1258f">3.5. Compute the orientation of the Joints</a></li>
@ -310,14 +76,14 @@ for the JavaScript code in this tag.
</li> </li>
<li><a href="#orgae8d0dc">4. <code>initializeStrutDynamics</code>: Add Stiffness and Damping properties of each strut</a> <li><a href="#orgae8d0dc">4. <code>initializeStrutDynamics</code>: Add Stiffness and Damping properties of each strut</a>
<ul> <ul>
<li><a href="#org422cb52">4.1. Function description</a></li> <li><a href="#org9af8ca0">4.1. Function description</a></li>
<li><a href="#orge6db36d">4.2. Optional Parameters</a></li> <li><a href="#org335e959">4.2. Optional Parameters</a></li>
<li><a href="#org3c2e550">4.3. Add Stiffness and Damping properties of each strut</a></li> <li><a href="#org3c2e550">4.3. Add Stiffness and Damping properties of each strut</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org9e8cbfa">5. <code>computeJacobian</code>: Compute the Jacobian Matrix</a> <li><a href="#org9e8cbfa">5. <code>computeJacobian</code>: Compute the Jacobian Matrix</a>
<ul> <ul>
<li><a href="#org0e1dad9">5.1. Function description</a></li> <li><a href="#org64e795c">5.1. Function description</a></li>
<li><a href="#org9bcd9b9">5.2. Compute Jacobian Matrix</a></li> <li><a href="#org9bcd9b9">5.2. Compute Jacobian Matrix</a></li>
<li><a href="#orgf08eda6">5.3. Compute Stiffness Matrix</a></li> <li><a href="#orgf08eda6">5.3. Compute Stiffness Matrix</a></li>
<li><a href="#orgd164132">5.4. Compute Compliance Matrix</a></li> <li><a href="#orgd164132">5.4. Compute Compliance Matrix</a></li>
@ -327,16 +93,16 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#org4674203">6.1. <code>initializeCylindricalPlatforms</code>: Initialize the geometry of the Fixed and Mobile Platforms</a> <li><a href="#org4674203">6.1. <code>initializeCylindricalPlatforms</code>: Initialize the geometry of the Fixed and Mobile Platforms</a>
<ul> <ul>
<li><a href="#org3f9ec54">6.1.1. Function description</a></li> <li><a href="#org1af6832">6.1.1. Function description</a></li>
<li><a href="#org079557b">6.1.2. Optional Parameters</a></li> <li><a href="#org12a2c2b">6.1.2. Optional Parameters</a></li>
<li><a href="#org2965fe8">6.1.3. Create the <code>platforms</code> struct</a></li> <li><a href="#org2965fe8">6.1.3. Create the <code>platforms</code> struct</a></li>
<li><a href="#org7e1a4d4">6.1.4. Save the <code>platforms</code> struct</a></li> <li><a href="#org7e1a4d4">6.1.4. Save the <code>platforms</code> struct</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org6b4f1ca">6.2. <code>initializeCylindricalStruts</code>: Define the mass and moment of inertia of cylindrical struts</a> <li><a href="#org6b4f1ca">6.2. <code>initializeCylindricalStruts</code>: Define the mass and moment of inertia of cylindrical struts</a>
<ul> <ul>
<li><a href="#orgfa4c069">6.2.1. Function description</a></li> <li><a href="#org407cf8c">6.2.1. Function description</a></li>
<li><a href="#org5a83934">6.2.2. Optional Parameters</a></li> <li><a href="#org420f14e">6.2.2. Optional Parameters</a></li>
<li><a href="#org3f9f0ef">6.2.3. Create the <code>struts</code> structure</a></li> <li><a href="#org3f9f0ef">6.2.3. Create the <code>struts</code> structure</a></li>
</ul> </ul>
</li> </li>
@ -346,16 +112,16 @@ for the JavaScript code in this tag.
<ul> <ul>
<li><a href="#org03168fc">7.1. <code>inverseKinematics</code>: Compute Inverse Kinematics</a> <li><a href="#org03168fc">7.1. <code>inverseKinematics</code>: Compute Inverse Kinematics</a>
<ul> <ul>
<li><a href="#org76e188e">7.1.1. Function description</a></li> <li><a href="#orgb7853bd">7.1.1. Function description</a></li>
<li><a href="#org137ad87">7.1.2. Optional Parameters</a></li> <li><a href="#orge9021eb">7.1.2. Optional Parameters</a></li>
<li><a href="#orgbdc5fb1">7.1.3. Theory</a></li> <li><a href="#orgbdc5fb1">7.1.3. Theory</a></li>
<li><a href="#org8b70a76">7.1.4. Compute</a></li> <li><a href="#org8b70a76">7.1.4. Compute</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf4ebfa3">7.2. <code>forwardKinematicsApprox</code>: Compute the Forward Kinematics</a> <li><a href="#orgf4ebfa3">7.2. <code>forwardKinematicsApprox</code>: Compute the Forward Kinematics</a>
<ul> <ul>
<li><a href="#org1b067b0">7.2.1. Function description</a></li> <li><a href="#org37e6edf">7.2.1. Function description</a></li>
<li><a href="#org8283c6b">7.2.2. Optional Parameters</a></li> <li><a href="#org6441308">7.2.2. Optional Parameters</a></li>
<li><a href="#orgf17cab9">7.2.3. Computation</a></li> <li><a href="#orgf17cab9">7.2.3. Computation</a></li>
</ul> </ul>
</li> </li>
@ -443,8 +209,8 @@ This Matlab function is accessible <a href="src/initializeFramesPositions.m">her
</p> </p>
</div> </div>
<div id="outline-container-org17eec4d" class="outline-3"> <div id="outline-container-org5cdd36d" class="outline-3">
<h3 id="org17eec4d"><span class="section-number-3">1.1</span> Function description</h3> <h3 id="org5cdd36d"><span class="section-number-3">1.1</span> Function description</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<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">[stewart]</span> = <span class="org-function-name">initializeFramesPositions</span>(<span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">initializeFramesPositions</span>(<span class="org-variable-name">args</span>)
@ -468,8 +234,8 @@ This Matlab function is accessible <a href="src/initializeFramesPositions.m">her
</div> </div>
</div> </div>
<div id="outline-container-org93cf646" class="outline-3"> <div id="outline-container-orge837700" class="outline-3">
<h3 id="org93cf646"><span class="section-number-3">1.2</span> Documentation</h3> <h3 id="orge837700"><span class="section-number-3">1.2</span> Documentation</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<div id="orgebd0f49" class="figure"> <div id="orgebd0f49" class="figure">
@ -480,8 +246,8 @@ This Matlab function is accessible <a href="src/initializeFramesPositions.m">her
</div> </div>
</div> </div>
<div id="outline-container-org142c995" class="outline-3"> <div id="outline-container-org312e9a7" class="outline-3">
<h3 id="org142c995"><span class="section-number-3">1.3</span> Optional Parameters</h3> <h3 id="org312e9a7"><span class="section-number-3">1.3</span> Optional Parameters</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
@ -536,8 +302,8 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
</p> </p>
</div> </div>
<div id="outline-container-org7e1a61c" class="outline-4"> <div id="outline-container-org5a5b987" class="outline-4">
<h4 id="org7e1a61c"><span class="section-number-4">2.1.1</span> Function description</h4> <h4 id="org5a5b987"><span class="section-number-4">2.1.1</span> Function description</h4>
<div class="outline-text-4" id="text-2-1-1"> <div class="outline-text-4" id="text-2-1-1">
<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">[stewart]</span> = <span class="org-function-name">generateCubicConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">generateCubicConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
@ -563,8 +329,8 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
</div> </div>
</div> </div>
<div id="outline-container-org9d47e7c" class="outline-4"> <div id="outline-container-org40ea23a" class="outline-4">
<h4 id="org9d47e7c"><span class="section-number-4">2.1.2</span> Documentation</h4> <h4 id="org40ea23a"><span class="section-number-4">2.1.2</span> Documentation</h4>
<div class="outline-text-4" id="text-2-1-2"> <div class="outline-text-4" id="text-2-1-2">
<div id="org70070f0" class="figure"> <div id="org70070f0" class="figure">
@ -575,8 +341,8 @@ This Matlab function is accessible <a href="src/generateCubicConfiguration.m">he
</div> </div>
</div> </div>
<div id="outline-container-orgf3ef9f0" class="outline-4"> <div id="outline-container-org37651aa" class="outline-4">
<h4 id="orgf3ef9f0"><span class="section-number-4">2.1.3</span> Optional Parameters</h4> <h4 id="org37651aa"><span class="section-number-4">2.1.3</span> Optional Parameters</h4>
<div class="outline-text-4" id="text-2-1-3"> <div class="outline-text-4" id="text-2-1-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
@ -618,8 +384,8 @@ CCm = [Cc(<span class="org-type">:</span>,2), Cc(<span class="org-type">:</span>
</div> </div>
</div> </div>
<div id="outline-container-orge025784" class="outline-4"> <div id="outline-container-org789a28b" class="outline-4">
<h4 id="orge025784"><span class="section-number-4">2.1.5</span> Compute the pose</h4> <h4 id="org789a28b"><span class="section-number-4">2.1.5</span> Compute the pose</h4>
<div class="outline-text-4" id="text-2-1-5"> <div class="outline-text-4" id="text-2-1-5">
<p> <p>
We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector from \({}^{C}C_{f}\) to \({}^{C}C_{m}\)). We can compute the vector of each leg \({}^{C}\hat{\bm{s}}_{i}\) (unit vector from \({}^{C}C_{f}\) to \({}^{C}C_{m}\)).
@ -653,8 +419,8 @@ This Matlab function is accessible <a href="src/generateGeneralConfiguration.m">
</p> </p>
</div> </div>
<div id="outline-container-org7c192dc" class="outline-4"> <div id="outline-container-org0ba3fa4" class="outline-4">
<h4 id="org7c192dc"><span class="section-number-4">2.2.1</span> Function description</h4> <h4 id="org0ba3fa4"><span class="section-number-4">2.2.1</span> Function description</h4>
<div class="outline-text-4" id="text-2-2-1"> <div class="outline-text-4" id="text-2-2-1">
<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">[stewart]</span> = <span class="org-function-name">generateGeneralConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">generateGeneralConfiguration</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
@ -680,8 +446,8 @@ This Matlab function is accessible <a href="src/generateGeneralConfiguration.m">
</div> </div>
</div> </div>
<div id="outline-container-org542739a" class="outline-4"> <div id="outline-container-org839cae7" class="outline-4">
<h4 id="org542739a"><span class="section-number-4">2.2.2</span> Documentation</h4> <h4 id="org839cae7"><span class="section-number-4">2.2.2</span> Documentation</h4>
<div class="outline-text-4" id="text-2-2-2"> <div class="outline-text-4" id="text-2-2-2">
<p> <p>
Joints are positions on a circle centered with the Z axis of {F} and {M} and at a chosen distance from {F} and {M}. Joints are positions on a circle centered with the Z axis of {F} and {M} and at a chosen distance from {F} and {M}.
@ -690,8 +456,8 @@ The radius of the circles can be chosen as well as the angles where the joints a
</div> </div>
</div> </div>
<div id="outline-container-org2f3445e" class="outline-4"> <div id="outline-container-org2e06fba" class="outline-4">
<h4 id="org2f3445e"><span class="section-number-4">2.2.3</span> Optional Parameters</h4> <h4 id="org2e06fba"><span class="section-number-4">2.2.3</span> Optional Parameters</h4>
<div class="outline-text-4" id="text-2-2-3"> <div class="outline-text-4" id="text-2-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
@ -708,8 +474,8 @@ The radius of the circles can be chosen as well as the angles where the joints a
</div> </div>
</div> </div>
<div id="outline-container-orga173176" class="outline-4"> <div id="outline-container-orgfac23f3" class="outline-4">
<h4 id="orga173176"><span class="section-number-4">2.2.4</span> Compute the pose</h4> <h4 id="orgfac23f3"><span class="section-number-4">2.2.4</span> Compute the pose</h4>
<div class="outline-text-4" id="text-2-2-4"> <div class="outline-text-4" id="text-2-2-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">stewart.Fa = zeros(3,6); <pre class="src src-matlab">stewart.Fa = zeros(3,6);
@ -741,8 +507,8 @@ This Matlab function is accessible <a href="src/computeJointsPose.m">here</a>.
</p> </p>
</div> </div>
<div id="outline-container-org8036919" class="outline-3"> <div id="outline-container-org465ebb2" class="outline-3">
<h3 id="org8036919"><span class="section-number-3">3.1</span> Function description</h3> <h3 id="org465ebb2"><span class="section-number-3">3.1</span> Function description</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"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">computeJointsPose</span>(<span class="org-variable-name">stewart</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">computeJointsPose</span>(<span class="org-variable-name">stewart</span>)
@ -774,8 +540,8 @@ This Matlab function is accessible <a href="src/computeJointsPose.m">here</a>.
</div> </div>
</div> </div>
<div id="outline-container-orgae953ca" class="outline-3"> <div id="outline-container-orgc11609b" class="outline-3">
<h3 id="orgae953ca"><span class="section-number-3">3.2</span> Documentation</h3> <h3 id="orgc11609b"><span class="section-number-3">3.2</span> Documentation</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<div id="org20f7106" class="figure"> <div id="org20f7106" class="figure">
@ -849,8 +615,8 @@ This Matlab function is accessible <a href="src/initializeStrutDynamics.m">here<
</p> </p>
</div> </div>
<div id="outline-container-org422cb52" class="outline-3"> <div id="outline-container-org9af8ca0" class="outline-3">
<h3 id="org422cb52"><span class="section-number-3">4.1</span> Function description</h3> <h3 id="org9af8ca0"><span class="section-number-3">4.1</span> Function description</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"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">initializeStrutDynamics</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">initializeStrutDynamics</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
@ -872,8 +638,8 @@ This Matlab function is accessible <a href="src/initializeStrutDynamics.m">here<
</div> </div>
</div> </div>
<div id="outline-container-orge6db36d" class="outline-3"> <div id="outline-container-org335e959" class="outline-3">
<h3 id="orge6db36d"><span class="section-number-3">4.2</span> Optional Parameters</h3> <h3 id="org335e959"><span class="section-number-3">4.2</span> Optional Parameters</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">arguments <pre class="src src-matlab">arguments
@ -910,8 +676,8 @@ This Matlab function is accessible <a href="src/computeJacobian.m">here</a>.
</p> </p>
</div> </div>
<div id="outline-container-org0e1dad9" class="outline-3"> <div id="outline-container-org64e795c" class="outline-3">
<h3 id="org0e1dad9"><span class="section-number-3">5.1</span> Function description</h3> <h3 id="org64e795c"><span class="section-number-3">5.1</span> Function description</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"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">computeJacobian</span>(<span class="org-variable-name">stewart</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">computeJacobian</span>(<span class="org-variable-name">stewart</span>)
@ -981,8 +747,8 @@ This Matlab function is accessible <a href="src/initializeCylindricalPlatforms.m
</p> </p>
</div> </div>
<div id="outline-container-org3f9ec54" class="outline-4"> <div id="outline-container-org1af6832" class="outline-4">
<h4 id="org3f9ec54"><span class="section-number-4">6.1.1</span> Function description</h4> <h4 id="org1af6832"><span class="section-number-4">6.1.1</span> Function description</h4>
<div class="outline-text-4" id="text-6-1-1"> <div class="outline-text-4" id="text-6-1-1">
<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">[stewart]</span> = <span class="org-function-name">initializeCylindricalPlatforms</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">initializeCylindricalPlatforms</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
@ -1015,8 +781,8 @@ This Matlab function is accessible <a href="src/initializeCylindricalPlatforms.m
</div> </div>
</div> </div>
<div id="outline-container-org079557b" class="outline-4"> <div id="outline-container-org12a2c2b" class="outline-4">
<h4 id="org079557b"><span class="section-number-4">6.1.2</span> Optional Parameters</h4> <h4 id="org12a2c2b"><span class="section-number-4">6.1.2</span> Optional Parameters</h4>
<div class="outline-text-4" id="text-6-1-2"> <div class="outline-text-4" id="text-6-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
@ -1080,8 +846,8 @@ This Matlab function is accessible <a href="src/initializeCylindricalStruts.m">h
</p> </p>
</div> </div>
<div id="outline-container-orgfa4c069" class="outline-4"> <div id="outline-container-org407cf8c" class="outline-4">
<h4 id="orgfa4c069"><span class="section-number-4">6.2.1</span> Function description</h4> <h4 id="org407cf8c"><span class="section-number-4">6.2.1</span> Function description</h4>
<div class="outline-text-4" id="text-6-2-1"> <div class="outline-text-4" id="text-6-2-1">
<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">[stewart]</span> = <span class="org-function-name">initializeCylindricalStruts</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[stewart]</span> = <span class="org-function-name">initializeCylindricalStruts</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
@ -1114,8 +880,8 @@ This Matlab function is accessible <a href="src/initializeCylindricalStruts.m">h
</div> </div>
</div> </div>
<div id="outline-container-org5a83934" class="outline-4"> <div id="outline-container-org420f14e" class="outline-4">
<h4 id="org5a83934"><span class="section-number-4">6.2.2</span> Optional Parameters</h4> <h4 id="org420f14e"><span class="section-number-4">6.2.2</span> Optional Parameters</h4>
<div class="outline-text-4" id="text-6-2-2"> <div class="outline-text-4" id="text-6-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
@ -1184,8 +950,8 @@ This Matlab function is accessible <a href="src/inverseKinematics.m">here</a>.
</p> </p>
</div> </div>
<div id="outline-container-org76e188e" class="outline-4"> <div id="outline-container-orgb7853bd" class="outline-4">
<h4 id="org76e188e"><span class="section-number-4">7.1.1</span> Function description</h4> <h4 id="orgb7853bd"><span class="section-number-4">7.1.1</span> Function description</h4>
<div class="outline-text-4" id="text-7-1-1"> <div class="outline-text-4" id="text-7-1-1">
<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">[Li, dLi]</span> = <span class="org-function-name">inverseKinematics</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[Li, dLi]</span> = <span class="org-function-name">inverseKinematics</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
@ -1209,8 +975,8 @@ This Matlab function is accessible <a href="src/inverseKinematics.m">here</a>.
</div> </div>
</div> </div>
<div id="outline-container-org137ad87" class="outline-4"> <div id="outline-container-orge9021eb" class="outline-4">
<h4 id="org137ad87"><span class="section-number-4">7.1.2</span> Optional Parameters</h4> <h4 id="orge9021eb"><span class="section-number-4">7.1.2</span> Optional Parameters</h4>
<div class="outline-text-4" id="text-7-1-2"> <div class="outline-text-4" id="text-7-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
@ -1287,8 +1053,8 @@ This Matlab function is accessible <a href="src/forwardKinematicsApprox.m">here<
</p> </p>
</div> </div>
<div id="outline-container-org1b067b0" class="outline-4"> <div id="outline-container-org37e6edf" class="outline-4">
<h4 id="org1b067b0"><span class="section-number-4">7.2.1</span> Function description</h4> <h4 id="org37e6edf"><span class="section-number-4">7.2.1</span> Function description</h4>
<div class="outline-text-4" id="text-7-2-1"> <div class="outline-text-4" id="text-7-2-1">
<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">[P, R]</span> = <span class="org-function-name">forwardKinematicsApprox</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>) <pre class="src src-matlab"><span class="org-keyword">function</span> <span class="org-variable-name">[P, R]</span> = <span class="org-function-name">forwardKinematicsApprox</span>(<span class="org-variable-name">stewart</span>, <span class="org-variable-name">args</span>)
@ -1311,8 +1077,8 @@ This Matlab function is accessible <a href="src/forwardKinematicsApprox.m">here<
</div> </div>
</div> </div>
<div id="outline-container-org8283c6b" class="outline-4"> <div id="outline-container-org6441308" class="outline-4">
<h4 id="org8283c6b"><span class="section-number-4">7.2.2</span> Optional Parameters</h4> <h4 id="org6441308"><span class="section-number-4">7.2.2</span> Optional Parameters</h4>
<div class="outline-text-4" id="text-7-2-2"> <div class="outline-text-4" id="text-7-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">arguments <pre class="src src-matlab">arguments
@ -1371,7 +1137,7 @@ We then compute the corresponding rotation matrix.
</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: 2020-04-17 ven. 09:36</p>
</div> </div>
</body> </body>
</html> </html>

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<title>Evaluating the Plant Uncertainty in various experimental conditions</title> <title>Evaluating the Plant Uncertainty in various experimental conditions</title>
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@ -252,13 +39,13 @@
<li><a href="#orga0077c1">2. Variation of the Sample Resonance Frequency</a></li> <li><a href="#orga0077c1">2. Variation of the Sample Resonance Frequency</a></li>
<li><a href="#orgb49a967">3. Variation of the Spindle Angle</a> <li><a href="#orgb49a967">3. Variation of the Spindle Angle</a>
<ul> <ul>
<li><a href="#org63447f1">3.1. Identification</a></li> <li><a href="#org07d9092">3.1. Identification</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org9081b0f">4. Variation of the Spindle Rotation Speed</a> <li><a href="#org9081b0f">4. Variation of the Spindle Rotation Speed</a>
<ul> <ul>
<li><a href="#orgd625617">4.1. Initialization of gravity compensation forces</a></li> <li><a href="#orgd625617">4.1. Initialization of gravity compensation forces</a></li>
<li><a href="#org54babd6">4.2. Identification</a></li> <li><a href="#org027e6cb">4.2. Identification</a></li>
<li><a href="#org70dd336">4.3. Plots</a></li> <li><a href="#org70dd336">4.3. Plots</a></li>
</ul> </ul>
</li> </li>
@ -513,8 +300,8 @@ Let&rsquo;s note \(\omega_m\) the frequency of the resonance of the Payload.
<a id="org58b9cae"></a> <a id="org58b9cae"></a>
</p> </p>
</div> </div>
<div id="outline-container-org63447f1" class="outline-3"> <div id="outline-container-org07d9092" class="outline-3">
<h3 id="org63447f1"><span class="section-number-3">3.1</span> Identification</h3> <h3 id="org07d9092"><span class="section-number-3">3.1</span> Identification</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
We identify the dynamics for the following Tilt stage angles. We identify the dynamics for the following Tilt stage angles.
@ -592,8 +379,8 @@ Finally, we simulate the system and same the forces/torques applied in each join
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org54babd6" class="outline-3"> <div id="outline-container-org027e6cb" class="outline-3">
<h3 id="org54babd6"><span class="section-number-3">4.2</span> Identification</h3> <h3 id="org027e6cb"><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>
We initialize the stages with forces/torques compensating the gravity forces. We initialize the stages with forces/torques compensating the gravity forces.
@ -816,7 +603,7 @@ From all the experimental condition studied, the only ones that have significant
</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: 2020-04-01 mer. 16:16</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
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248
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<h1 class="title">Determination of the optimal nano-hexapod&rsquo;s stiffness</h1> <h1 class="title">Determination of the optimal nano-hexapod&rsquo;s stiffness</h1>
<div id="table-of-contents"> <div id="table-of-contents">
@ -251,7 +37,7 @@
<ul> <ul>
<li><a href="#org157c07d">1. Spindle Rotation Speed</a> <li><a href="#org157c07d">1. Spindle Rotation Speed</a>
<ul> <ul>
<li><a href="#org67607c3">1.1. Initialization</a></li> <li><a href="#orgf8f2ffc">1.1. Initialization</a></li>
<li><a href="#org687bdef">1.2. Identification when rotating at maximum speed</a></li> <li><a href="#org687bdef">1.2. Identification when rotating at maximum speed</a></li>
<li><a href="#org7dcfddb">1.3. Change of dynamics</a></li> <li><a href="#org7dcfddb">1.3. Change of dynamics</a></li>
</ul> </ul>
@ -266,7 +52,7 @@
</li> </li>
<li><a href="#org19559b0">3. Payload &ldquo;Impedance&rdquo; Effect</a> <li><a href="#org19559b0">3. Payload &ldquo;Impedance&rdquo; Effect</a>
<ul> <ul>
<li><a href="#org64a8be3">3.1. Initialization</a></li> <li><a href="#orgd45a5be">3.1. Initialization</a></li>
<li><a href="#org73f1c6e">3.2. Identification of the dynamics while change the payload dynamics</a></li> <li><a href="#org73f1c6e">3.2. Identification of the dynamics while change the payload dynamics</a></li>
<li><a href="#orgd7a519b">3.3. Change of dynamics for the primary controller</a> <li><a href="#orgd7a519b">3.3. Change of dynamics for the primary controller</a>
<ul> <ul>
@ -323,8 +109,8 @@ The rotation speed will have an effect due to the Coriolis effect.
</p> </p>
</div> </div>
<div id="outline-container-org67607c3" class="outline-3"> <div id="outline-container-orgf8f2ffc" class="outline-3">
<h3 id="org67607c3"><span class="section-number-3">1.1</span> Initialization</h3> <h3 id="orgf8f2ffc"><span class="section-number-3">1.1</span> Initialization</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -600,8 +386,8 @@ When the nano-hexapod is stiff (\(k>10^7\ [N/m]\)), the compliance of the micro-
</p> </p>
</div> </div>
<div id="outline-container-org64a8be3" class="outline-3"> <div id="outline-container-orgd45a5be" class="outline-3">
<h3 id="org64a8be3"><span class="section-number-3">3.1</span> Initialization</h3> <h3 id="orgd45a5be"><span class="section-number-3">3.1</span> Initialization</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
We initialize all the stages with the default parameters. We initialize all the stages with the default parameters.
@ -843,7 +629,7 @@ And finally, in Figures <a href="#orge05feb5">21</a> and <a href="#org17c5c95">2
</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: 2020-04-08 mer. 12:12</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
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256
docs/uncertainty_payload.html
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@ -4,239 +4,25 @@
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<title>Effect of Uncertainty on the payload&rsquo;s dynamics on the isolation platform dynamics</title> <title>Effect of Uncertainty on the payload&rsquo;s dynamics on the isolation platform dynamics</title>
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -251,17 +37,17 @@
<ul> <ul>
<li><a href="#orgcc5f0ec">1. Simple Introductory Example</a> <li><a href="#orgcc5f0ec">1. Simple Introductory Example</a>
<ul> <ul>
<li><a href="#org1f20d62">1.1. Equations of motion</a></li> <li><a href="#orgf75e223">1.1. Equations of motion</a></li>
<li><a href="#org4efccbf">1.2. Initialization of the payload dynamics</a></li> <li><a href="#org4efccbf">1.2. Initialization of the payload dynamics</a></li>
<li><a href="#orgb400ca3">1.3. Initialization of the isolation platform</a></li> <li><a href="#orgb400ca3">1.3. Initialization of the isolation platform</a></li>
<li><a href="#orgd0dd88b">1.4. Comparison</a></li> <li><a href="#orgd0dd88b">1.4. Comparison</a></li>
<li><a href="#org1637b13">1.5. Conclusion</a></li> <li><a href="#orgd1e600e">1.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org1f8e63e">2. Generalization to arbitrary dynamics</a> <li><a href="#org1f8e63e">2. Generalization to arbitrary dynamics</a>
<ul> <ul>
<li><a href="#orgc4fa63e">2.1. Introduction</a></li> <li><a href="#orgc4fa63e">2.1. Introduction</a></li>
<li><a href="#orgd6da9a7">2.2. Equations of motion</a></li> <li><a href="#org5ed1517">2.2. Equations of motion</a></li>
<li><a href="#orge217a33">2.3. Impedance \(G^\prime(s)\) of a mass-spring-damper payload</a></li> <li><a href="#orge217a33">2.3. Impedance \(G^\prime(s)\) of a mass-spring-damper payload</a></li>
<li><a href="#org0ee44da">2.4. First Analytical analysis</a></li> <li><a href="#org0ee44da">2.4. First Analytical analysis</a></li>
<li><a href="#orgfe81c1c">2.5. Impedance of the Payload and Dynamical Uncertainty</a></li> <li><a href="#orgfe81c1c">2.5. Impedance of the Payload and Dynamical Uncertainty</a></li>
@ -274,7 +60,7 @@
<li><a href="#org9086831">2.8.3. Effect of the platform&rsquo;s mass \(m\)</a></li> <li><a href="#org9086831">2.8.3. Effect of the platform&rsquo;s mass \(m\)</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3a1ebf1">2.9. Conclusion</a></li> <li><a href="#org3f697cc">2.9. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -328,8 +114,8 @@ The goal is to stabilize \(x\) using \(F\) in spite of uncertainty on the payloa
</div> </div>
</div> </div>
<div id="outline-container-org1f20d62" class="outline-3"> <div id="outline-container-orgf75e223" class="outline-3">
<h3 id="org1f20d62"><span class="section-number-3">1.1</span> Equations of motion</h3> <h3 id="orgf75e223"><span class="section-number-3">1.1</span> Equations of motion</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
If we write the equation of motion of the system in Figure <a href="#orgaa77a57">1</a>, we obtain: If we write the equation of motion of the system in Figure <a href="#orgaa77a57">1</a>, we obtain:
@ -436,8 +222,8 @@ The obtained dynamics from \(F\) to \(x\) for the three isolation platform are s
</div> </div>
</div> </div>
<div id="outline-container-org1637b13" class="outline-3"> <div id="outline-container-orgd1e600e" class="outline-3">
<h3 id="org1637b13"><span class="section-number-3">1.5</span> Conclusion</h3> <h3 id="orgd1e600e"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<div class="important"> <div class="important">
<p> <p>
@ -489,8 +275,8 @@ Now let&rsquo;s consider the system consisting of a mass-spring-system (the isol
</div> </div>
</div> </div>
<div id="outline-container-orgd6da9a7" class="outline-3"> <div id="outline-container-org5ed1517" class="outline-3">
<h3 id="orgd6da9a7"><span class="section-number-3">2.2</span> Equations of motion</h3> <h3 id="org5ed1517"><span class="section-number-3">2.2</span> Equations of motion</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We have to following equations of motion: We have to following equations of motion:
@ -946,8 +732,8 @@ Let&rsquo;s fix \(k = 10^7\ [N/m]\), \(\xi = \frac{c}{2\sqrt{km}} = 0.1\) and se
</div> </div>
</div> </div>
<div id="outline-container-org3a1ebf1" class="outline-3"> <div id="outline-container-org3f697cc" class="outline-3">
<h3 id="org3a1ebf1"><span class="section-number-3">2.9</span> Conclusion</h3> <h3 id="org3f697cc"><span class="section-number-3">2.9</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-9"> <div class="outline-text-3" id="text-2-9">
<div class="important"> <div class="important">
<p> <p>
@ -971,7 +757,7 @@ In that case, maximizing the stiffness of the payload is a good idea.
</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: 2020-04-07 mar. 16:17</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -249,17 +37,17 @@
<ul> <ul>
<li><a href="#orgbe6e0b8">1. Simple Introductory Example</a> <li><a href="#orgbe6e0b8">1. Simple Introductory Example</a>
<ul> <ul>
<li><a href="#org283e8c3">1.1. Equations of motion</a></li> <li><a href="#orgf4562a5">1.1. Equations of motion</a></li>
<li><a href="#org8bd2a4a">1.2. Initialization of the support dynamics</a></li> <li><a href="#org8bd2a4a">1.2. Initialization of the support dynamics</a></li>
<li><a href="#orgefb9b71">1.3. Initialization of the isolation platform</a></li> <li><a href="#orgefb9b71">1.3. Initialization of the isolation platform</a></li>
<li><a href="#org3bc4ad1">1.4. Comparison</a></li> <li><a href="#org3bc4ad1">1.4. Comparison</a></li>
<li><a href="#orgd28ebd8">1.5. Conclusion</a></li> <li><a href="#org2a9bf99">1.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orge1d3484">2. Generalization to arbitrary dynamics</a> <li><a href="#orge1d3484">2. Generalization to arbitrary dynamics</a>
<ul> <ul>
<li><a href="#org3948d1f">2.1. Introduction</a></li> <li><a href="#org3948d1f">2.1. Introduction</a></li>
<li><a href="#org28c48e3">2.2. Equations of motion</a></li> <li><a href="#org3d4902a">2.2. Equations of motion</a></li>
<li><a href="#orgc20cabb">2.3. Compliance of the Support</a></li> <li><a href="#orgc20cabb">2.3. Compliance of the Support</a></li>
<li><a href="#org67810a4">2.4. Equivalent Inverse Multiplicative Uncertainty</a></li> <li><a href="#org67810a4">2.4. Equivalent Inverse Multiplicative Uncertainty</a></li>
<li><a href="#orge950395">2.5. Effect of the Isolation platform Stiffness</a></li> <li><a href="#orge950395">2.5. Effect of the Isolation platform Stiffness</a></li>
@ -270,7 +58,7 @@
<li><a href="#orgd2fc303">2.6.3. Effect of the platform&rsquo;s mass \(m\)</a></li> <li><a href="#orgd2fc303">2.6.3. Effect of the platform&rsquo;s mass \(m\)</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org718f0f1">2.7. Conclusion</a></li> <li><a href="#org999e1c5">2.7. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -324,8 +112,8 @@ The goal is to stabilize \(x\) using \(F\) in spite of uncertainty on the suppor
</div> </div>
</div> </div>
<div id="outline-container-org283e8c3" class="outline-3"> <div id="outline-container-orgf4562a5" class="outline-3">
<h3 id="org283e8c3"><span class="section-number-3">1.1</span> Equations of motion</h3> <h3 id="orgf4562a5"><span class="section-number-3">1.1</span> Equations of motion</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
If we write the equation of motion of the system in Figure <a href="#org41bc770">1</a>, we obtain: If we write the equation of motion of the system in Figure <a href="#org41bc770">1</a>, we obtain:
@ -429,8 +217,8 @@ The obtained dynamics from \(F\) to \(x\) for the three isolation platform are s
</div> </div>
</div> </div>
<div id="outline-container-orgd28ebd8" class="outline-3"> <div id="outline-container-org2a9bf99" class="outline-3">
<h3 id="orgd28ebd8"><span class="section-number-3">1.5</span> Conclusion</h3> <h3 id="org2a9bf99"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<div class="important"> <div class="important">
<p> <p>
@ -475,8 +263,8 @@ Now let&rsquo;s consider the system consisting of a mass-spring-system (the isol
</div> </div>
</div> </div>
<div id="outline-container-org28c48e3" class="outline-3"> <div id="outline-container-org3d4902a" class="outline-3">
<h3 id="org28c48e3"><span class="section-number-3">2.2</span> Equations of motion</h3> <h3 id="org3d4902a"><span class="section-number-3">2.2</span> Equations of motion</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We have to following equations of motion: We have to following equations of motion:
@ -812,8 +600,8 @@ Let&rsquo;s fix \(k = 10^7\ [N/m]\), \(\xi = \frac{c}{2\sqrt{km}} = 0.1\) and se
</div> </div>
</div> </div>
<div id="outline-container-org718f0f1" class="outline-3"> <div id="outline-container-org999e1c5" class="outline-3">
<h3 id="org718f0f1"><span class="section-number-3">2.7</span> Conclusion</h3> <h3 id="org999e1c5"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<div class="important"> <div class="important">
<p> <p>
@ -841,7 +629,7 @@ Thus, if a stiff isolation platform is used, the recommendation is to have the l
</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: 2020-04-01 mer. 16:14</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -250,69 +38,69 @@
<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="#org006e24f">2.1. Init</a></li> <li><a href="#org4609941">2.1. Init</a></li>
<li><a href="#org4fbbce9">2.2. Identification</a></li> <li><a href="#org294eb39">2.2. Identification</a></li>
<li><a href="#org49ca9ab">2.3. Sensitivity to Disturbances</a></li> <li><a href="#org7a1cc07">2.3. Sensitivity to Disturbances</a></li>
<li><a href="#org346ebf3">2.4. Noise Budget</a></li> <li><a href="#orga53aea9">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="#org33c3829">3. Integral Force Feedback</a> <li><a href="#org1cbdf7c">3. Integral Force Feedback</a>
<ul> <ul>
<li><a href="#org326d925">3.1. Control Design</a></li> <li><a href="#org2eefec2">3.1. Control Design</a></li>
<li><a href="#org86f3473">3.2. Identification</a></li> <li><a href="#org1a0f43f">3.2. Identification</a></li>
<li><a href="#org68c471e">3.3. Sensitivity to Disturbance</a></li> <li><a href="#orgc9a5688">3.3. Sensitivity to Disturbance</a></li>
<li><a href="#org5edf015">3.4. Damped Plant</a></li> <li><a href="#org681a4b5">3.4. Damped Plant</a></li>
<li><a href="#orgfc93a1c">3.5. Conclusion</a></li> <li><a href="#org7dff1b8">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="#org5704583">4.1. Control Design</a></li> <li><a href="#orgb8526dc">4.1. Control Design</a></li>
<li><a href="#orga436aa7">4.2. Identification</a></li> <li><a href="#org08507fd">4.2. Identification</a></li>
<li><a href="#org133268a">4.3. Sensitivity to Disturbance</a></li> <li><a href="#org0f3fad3">4.3. Sensitivity to Disturbance</a></li>
<li><a href="#org2f974d4">4.4. Damped Plant</a></li> <li><a href="#org652a3fa">4.4. Damped Plant</a></li>
<li><a href="#orgfdbd543">4.5. Conclusion</a></li> <li><a href="#orgae3868e">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="#org2050b01">5.1. Control Design</a></li> <li><a href="#orgf39d565">5.1. Control Design</a></li>
<li><a href="#orgc946d88">5.2. Identification</a></li> <li><a href="#org5546bc6">5.2. Identification</a></li>
<li><a href="#orgde4b14e">5.3. Sensitivity to Disturbance</a></li> <li><a href="#orgd944a62">5.3. Sensitivity to Disturbance</a></li>
<li><a href="#org640c7d9">5.4. Damped Plant</a></li> <li><a href="#org7dee42a">5.4. Damped Plant</a></li>
<li><a href="#org94e9d5f">5.5. Conclusion</a></li> <li><a href="#orgd0c02fb">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="#org1bfaed7">6.1. Identification</a></li> <li><a href="#orgb02fbb6">6.1. Identification</a></li>
<li><a href="#orgf32651c">6.2. Control Design</a></li> <li><a href="#orge2bfe04">6.2. Control Design</a></li>
<li><a href="#orgc7383cd">6.3. Identification</a></li> <li><a href="#org53cc9c6">6.3. Identification</a></li>
<li><a href="#org34de1fd">6.4. Sensitivity to Disturbance</a></li> <li><a href="#orgd6515d0">6.4. Sensitivity to Disturbance</a></li>
<li><a href="#org609c873">6.5. Damped Plant</a></li> <li><a href="#orgc6d991d">6.5. Damped Plant</a></li>
<li><a href="#org3c4f6ff">6.6. Conclusion</a></li> <li><a href="#org8c680f2">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="#orge08556d">7.2. Sensitivity to Disturbance</a></li> <li><a href="#orgcb13f9e">7.2. Sensitivity to Disturbance</a></li>
<li><a href="#orgfff33b9">7.3. Noise Budget</a></li> <li><a href="#org5cadbe8">7.3. Noise Budget</a></li>
<li><a href="#orgc582849">7.4. Damped Plant</a></li> <li><a href="#org8fede67">7.4. Damped Plant</a></li>
<li><a href="#orgde3c3e7">7.5. Conclusion</a></li> <li><a href="#orgd8ddad5">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="#orge0ae68a">8.1. Init</a></li> <li><a href="#org33240ce">8.1. Init</a></li>
<li><a href="#orgd0cdd7a">8.2. Identification</a></li> <li><a href="#org1533141">8.2. Identification</a></li>
<li><a href="#orgea2fb03">8.3. Sensitivity to Disturbances</a></li> <li><a href="#orgb814bd8">8.3. Sensitivity to Disturbances</a></li>
<li><a href="#org88de5a5">8.4. Noise Budget</a></li> <li><a href="#org790a719">8.4. Noise Budget</a></li>
<li><a href="#org241513b">8.5. Integral Force Feedback</a></li> <li><a href="#orgfa698bd">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="#orgb7cef4c">8.7. Noise Budget</a></li> <li><a href="#org1ecc3e1">8.7. Noise Budget</a></li>
<li><a href="#orga9d9dce">8.8. Conclusion</a></li> <li><a href="#org229e708">8.8. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -410,8 +198,8 @@ 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-org006e24f" class="outline-3"> <div id="outline-container-org4609941" class="outline-3">
<h3 id="org006e24f"><span class="section-number-3">2.1</span> Init</h3> <h3 id="org4609941"><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.
@ -423,8 +211,8 @@ All the controllers are set to 0 (Open Loop).
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-org4fbbce9" class="outline-3"> <div id="outline-container-org294eb39" class="outline-3">
<h3 id="org4fbbce9"><span class="section-number-3">2.2</span> Identification</h3> <h3 id="org294eb39"><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.
@ -487,8 +275,8 @@ Finally, we save the identified system dynamics for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-org49ca9ab" class="outline-3"> <div id="outline-container-org7a1cc07" class="outline-3">
<h3 id="org49ca9ab"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3> <h3 id="org7a1cc07"><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:
@ -515,8 +303,8 @@ We show several plots representing the sensitivity to disturbances:
</div> </div>
</div> </div>
<div id="outline-container-org346ebf3" class="outline-3"> <div id="outline-container-orga53aea9" class="outline-3">
<h3 id="org346ebf3"><span class="section-number-3">2.4</span> Noise Budget</h3> <h3 id="orga53aea9"><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.
@ -575,8 +363,8 @@ It corresponds to the plant to control.
</div> </div>
</div> </div>
<div id="outline-container-org33c3829" class="outline-2"> <div id="outline-container-org1cbdf7c" class="outline-2">
<h2 id="org33c3829"><span class="section-number-2">3</span> Integral Force Feedback</h2> <h2 id="org1cbdf7c"><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>
@ -588,8 +376,8 @@ 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-org326d925" class="outline-3"> <div id="outline-container-org2eefec2" class="outline-3">
<h3 id="org326d925"><span class="section-number-3">3.1</span> Control Design</h3> <h3 id="org2eefec2"><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">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
@ -624,8 +412,8 @@ The controller for each pair of actuator/sensor is:
</div> </div>
</div> </div>
<div id="outline-container-org86f3473" class="outline-3"> <div id="outline-container-org1a0f43f" class="outline-3">
<h3 id="org86f3473"><span class="section-number-3">3.2</span> Identification</h3> <h3 id="org1a0f43f"><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.
@ -708,8 +496,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org68c471e" class="outline-3"> <div id="outline-container-orgc9a5688" class="outline-3">
<h3 id="org68c471e"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3> <h3 id="orgc9a5688"><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">
@ -727,8 +515,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org5edf015" class="outline-3"> <div id="outline-container-org681a4b5" class="outline-3">
<h3 id="org5edf015"><span class="section-number-3">3.4</span> Damped Plant</h3> <h3 id="org681a4b5"><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">
@ -739,8 +527,8 @@ G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-orgfc93a1c" class="outline-3"> <div id="outline-container-org7dff1b8" class="outline-3">
<h3 id="orgfc93a1c"><span class="section-number-3">3.5</span> Conclusion</h3> <h3 id="org7dff1b8"><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>
@ -769,8 +557,8 @@ 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-org5704583" class="outline-3"> <div id="outline-container-orgb8526dc" class="outline-3">
<h3 id="org5704583"><span class="section-number-3">4.1</span> Control Design</h3> <h3 id="orgb8526dc"><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">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
@ -806,8 +594,8 @@ A Low pass Filter is added to make the controller transfer function proper.
</div> </div>
</div> </div>
<div id="outline-container-orga436aa7" class="outline-3"> <div id="outline-container-org08507fd" class="outline-3">
<h3 id="orga436aa7"><span class="section-number-3">4.2</span> Identification</h3> <h3 id="org08507fd"><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.
@ -891,8 +679,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
<div id="outline-container-org133268a" class="outline-3"> <div id="outline-container-org0f3fad3" class="outline-3">
<h3 id="org133268a"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3> <h3 id="org0f3fad3"><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">
@ -910,8 +698,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org2f974d4" class="outline-3"> <div id="outline-container-org652a3fa" class="outline-3">
<h3 id="org2f974d4"><span class="section-number-3">4.4</span> Damped Plant</h3> <h3 id="org652a3fa"><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">
@ -922,8 +710,8 @@ G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-orgfdbd543" class="outline-3"> <div id="outline-container-orgae3868e" class="outline-3">
<h3 id="orgfdbd543"><span class="section-number-3">4.5</span> Conclusion</h3> <h3 id="orgae3868e"><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>
@ -952,8 +740,8 @@ 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-org2050b01" class="outline-3"> <div id="outline-container-orgf39d565" class="outline-3">
<h3 id="org2050b01"><span class="section-number-3">5.1</span> Control Design</h3> <h3 id="orgf39d565"><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">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
@ -981,8 +769,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
</div> </div>
</div> </div>
<div id="outline-container-orgc946d88" class="outline-3"> <div id="outline-container-org5546bc6" class="outline-3">
<h3 id="orgc946d88"><span class="section-number-3">5.2</span> Identification</h3> <h3 id="org5546bc6"><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.
@ -1065,8 +853,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-orgde4b14e" class="outline-3"> <div id="outline-container-orgd944a62" class="outline-3">
<h3 id="orgde4b14e"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3> <h3 id="orgd944a62"><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">
@ -1084,8 +872,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org640c7d9" class="outline-3"> <div id="outline-container-org7dee42a" class="outline-3">
<h3 id="org640c7d9"><span class="section-number-3">5.4</span> Damped Plant</h3> <h3 id="org7dee42a"><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">
@ -1096,8 +884,8 @@ G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org94e9d5f" class="outline-3"> <div id="outline-container-orgd0c02fb" class="outline-3">
<h3 id="org94e9d5f"><span class="section-number-3">5.5</span> Conclusion</h3> <h3 id="orgd0c02fb"><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>
@ -1125,8 +913,8 @@ 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-org1bfaed7" class="outline-3"> <div id="outline-container-orgb02fbb6" class="outline-3">
<h3 id="org1bfaed7"><span class="section-number-3">6.1</span> Identification</h3> <h3 id="orgb02fbb6"><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.
@ -1214,8 +1002,8 @@ G.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comm
</div> </div>
</div> </div>
<div id="outline-container-orgf32651c" class="outline-3"> <div id="outline-container-orge2bfe04" class="outline-3">
<h3 id="orgf32651c"><span class="section-number-3">6.2</span> Control Design</h3> <h3 id="orge2bfe04"><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.
@ -1245,8 +1033,8 @@ The controller for each pair of actuator/sensor is:
</div> </div>
</div> </div>
<div id="outline-container-orgc7383cd" class="outline-3"> <div id="outline-container-org53cc9c6" class="outline-3">
<h3 id="orgc7383cd"><span class="section-number-3">6.3</span> Identification</h3> <h3 id="org53cc9c6"><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.
@ -1330,8 +1118,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div> </div>
</div> </div>
<div id="outline-container-org34de1fd" class="outline-3"> <div id="outline-container-orgd6515d0" class="outline-3">
<h3 id="org34de1fd"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3> <h3 id="orgd6515d0"><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">
@ -1349,8 +1137,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div> </div>
</div> </div>
<div id="outline-container-org609c873" class="outline-3"> <div id="outline-container-orgc6d991d" class="outline-3">
<h3 id="org609c873"><span class="section-number-3">6.5</span> Damped Plant</h3> <h3 id="orgc6d991d"><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">
@ -1361,8 +1149,8 @@ G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div> </div>
</div> </div>
<div id="outline-container-org3c4f6ff" class="outline-3"> <div id="outline-container-org8c680f2" class="outline-3">
<h3 id="org3c4f6ff"><span class="section-number-3">6.6</span> Conclusion</h3> <h3 id="org8c680f2"><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>
@ -1391,8 +1179,8 @@ This gives similar results than with a classical force sensor.
</div> </div>
</div> </div>
<div id="outline-container-orge08556d" class="outline-3"> <div id="outline-container-orgcb13f9e" class="outline-3">
<h3 id="orge08556d"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3> <h3 id="orgcb13f9e"><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">
@ -1425,8 +1213,8 @@ This gives similar results than with a classical force sensor.
</div> </div>
</div> </div>
<div id="outline-container-orgfff33b9" class="outline-3"> <div id="outline-container-org5cadbe8" class="outline-3">
<h3 id="orgfff33b9"><span class="section-number-3">7.3</span> Noise Budget</h3> <h3 id="org5cadbe8"><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.
@ -1493,8 +1281,8 @@ It is important to note that the effect of direct forces applied to the sample a
</div> </div>
</div> </div>
<div id="outline-container-orgc582849" class="outline-3"> <div id="outline-container-org8fede67" class="outline-3">
<h3 id="orgc582849"><span class="section-number-3">7.4</span> Damped Plant</h3> <h3 id="org8fede67"><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">
@ -1505,8 +1293,8 @@ It is important to note that the effect of direct forces applied to the sample a
</div> </div>
</div> </div>
<div id="outline-container-orgde3c3e7" class="outline-3"> <div id="outline-container-orgd8ddad5" class="outline-3">
<h3 id="orgde3c3e7"><span class="section-number-3">7.5</span> Conclusion</h3> <h3 id="orgd8ddad5"><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>
@ -1582,8 +1370,8 @@ 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-orge0ae68a" class="outline-3"> <div id="outline-container-org33240ce" class="outline-3">
<h3 id="orge0ae68a"><span class="section-number-3">8.1</span> Init</h3> <h3 id="org33240ce"><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.
@ -1595,8 +1383,8 @@ All the controllers are set to 0 (Open Loop).
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-orgd0cdd7a" class="outline-3"> <div id="outline-container-org1533141" class="outline-3">
<h3 id="orgd0cdd7a"><span class="section-number-3">8.2</span> Identification</h3> <h3 id="org1533141"><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.
@ -1659,8 +1447,8 @@ Finally, we save the identified system dynamics for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgea2fb03" class="outline-3"> <div id="outline-container-orgb814bd8" class="outline-3">
<h3 id="orgea2fb03"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3> <h3 id="orgb814bd8"><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.
@ -1694,8 +1482,8 @@ We show several plots representing the sensitivity to disturbances:
</div> </div>
</div> </div>
<div id="outline-container-org88de5a5" class="outline-3"> <div id="outline-container-org790a719" class="outline-3">
<h3 id="org88de5a5"><span class="section-number-3">8.4</span> Noise Budget</h3> <h3 id="org790a719"><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.
@ -1744,8 +1532,8 @@ Thus, it may be desirable to use voice coil actuators.
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org241513b" class="outline-3"> <div id="outline-container-orgfa698bd" class="outline-3">
<h3 id="org241513b"><span class="section-number-3">8.5</span> Integral Force Feedback</h3> <h3 id="orgfa698bd"><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;
@ -1840,8 +1628,8 @@ G_vc_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="o
</div> </div>
</div> </div>
<div id="outline-container-orgb7cef4c" class="outline-3"> <div id="outline-container-org1ecc3e1" class="outline-3">
<h3 id="orgb7cef4c"><span class="section-number-3">8.7</span> Noise Budget</h3> <h3 id="org1ecc3e1"><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.
@ -1855,8 +1643,8 @@ We compute the obtain PSD of the displacement \(D\) when using IFF.
</div> </div>
</div> </div>
<div id="outline-container-orga9d9dce" class="outline-3"> <div id="outline-container-org229e708" class="outline-3">
<h3 id="orga9d9dce"><span class="section-number-3">8.8</span> Conclusion</h3> <h3 id="org229e708"><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>
@ -1874,7 +1662,7 @@ 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: 2020-03-13 ven. 17:39</p> <p class="date">Created: 2020-04-17 ven. 09:35</p>
</div> </div>
</body> </body>
</html> </html>

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org/active_damping_uniaxial.org
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#+TITLE: Active Damping with an uni-axial model #+TITLE: Active Damping with an uni-axial model
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* Introduction :ignore: * Introduction :ignore:
First, in section [[sec:undamped_system]], we will looked at the undamped system. First, in section [[sec:undamped_system]], we will looked at the undamped system.

25
org/compensation_gravity_forces.org
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#+TITLE: Compensating the gravity forces to start at steady state #+TITLE: Compensating the gravity forces to start at steady state
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* Introduction :ignore: * Introduction :ignore:
In this file is shown a technique used to compensate the gravity forces at t=0. In this file is shown a technique used to compensate the gravity forces at t=0.

25
org/control.org
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#+TITLE: Control of the Nano-Active-Stabilization-System #+TITLE: Control of the Nano-Active-Stabilization-System
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:END:
* Introduction :ignore: * Introduction :ignore:
The system consist of the following inputs and outputs (Figure [[fig:control_architecture_plant]]): The system consist of the following inputs and outputs (Figure [[fig:control_architecture_plant]]):

25
org/control_active_damping.org
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@ -1,28 +1,5 @@
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* Introduction :ignore: * Introduction :ignore:
The goal of this file is to study the use of active damping for the control of the NASS. The goal of this file is to study the use of active damping for the control of the NASS.

27
org/control_cascade.org
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#+TITLE: Cascade Control applied on the Simscape Model #+TITLE: Cascade Control applied on the Simscape Model
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* Introduction :ignore: * Introduction :ignore:
The control architecture we wish here to study is shown in Figure [[fig:cascade_control_architecture]]. The control architecture we wish here to study is shown in Figure [[fig:cascade_control_architecture]].

25
org/control_decentralized.org
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* Introduction :ignore: * Introduction :ignore:
In this document, we apply some decentralized control to the NASS and see what level of performance can be obtained. In this document, we apply some decentralized control to the NASS and see what level of performance can be obtained.

27
org/control_force.org
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Cascade Control where the inner loop goal is to control the total wrench (forces and torques) applied to the upper part of the nano-hexapod. Cascade Control where the inner loop goal is to control the total wrench (forces and torques) applied to the upper part of the nano-hexapod.

29
org/control_hac_lac.org
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* Introduction :ignore: * Introduction :ignore:
The position $\bm{\mathcal{X}}$ of the Sample with respect to the granite is measured. The position $\bm{\mathcal{X}}$ of the Sample with respect to the granite is measured.

29
org/control_requirements.org
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@ -1,32 +1,5 @@
#+TITLE: Control Requirements #+TITLE: Control Requirements
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* Introduction :ignore: * Introduction :ignore:
The goal here is to write clear specifications for the NASS. The goal here is to write clear specifications for the NASS.

27
org/control_voice_coil.org
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@ -1,30 +1,5 @@
#+TITLE: Control of the NASS with Voice coil actuators #+TITLE: Control of the NASS with Voice coil actuators
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results file raw replace
#+PROPERTY: header-args:latex+ :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports results
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
* Introduction :ignore: * Introduction :ignore:
* HAC-LAC + Cascade Control Topology * HAC-LAC + Cascade Control Topology

25
org/disturbances.org
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@ -1,28 +1,5 @@
#+TITLE: Identification of the disturbances #+TITLE: Identification of the disturbances
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:
* Introduction :ignore: * Introduction :ignore:
:PROPERTIES: :PROPERTIES:

44
org/experiments.org
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@ -1,28 +1,5 @@
#+TITLE: Simulation of Scientific Experiments #+TITLE: Simulation of Scientific Experiments
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:
* Introduction :ignore: * Introduction :ignore:
The goal here is to simulate some scientific experiments with the Simscape model when no control is applied to the nano-hexapod. The goal here is to simulate some scientific experiments with the Simscape model when no control is applied to the nano-hexapod.
@ -299,7 +276,7 @@ And we save the obtained data.
** Conclusion ** Conclusion
#+begin_important #+begin_important
Error motion is what expected from the disturbance measurements. Here, no vibration is included in the X and Y directions.
#+end_important #+end_important
* Tomography Experiment with Ty raster scans * Tomography Experiment with Ty raster scans
@ -320,11 +297,12 @@ We now activate the disturbances.
'Frz_z', true ... % Spindle - Z direction 'Frz_z', true ... % Spindle - Z direction
); );
#+end_src #+end_src
We initialize the reference path for all the stages. We initialize the reference path for all the stages.
The Spindle which is rotating at 60rpm and the translation stage is following a triangular path. The Spindle which is rotating at 60rpm and the translation stage not moving as it would take a long time to simulate.
However, vibrations of the Ty stage are included.
#+begin_src matlab #+begin_src matlab
initializeReferences('Rz_type', 'rotating', 'Rz_period', 1, ... initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
'Dy_type', 'triangular', 'Dy_amplitude', 5e-3, 'Dy_period', 10);
#+end_src #+end_src
We simulate the model. We simulate the model.
@ -387,13 +365,13 @@ And we save the obtained data.
xlim([0.5, inf]); xlim([0.5, inf]);
#+end_src #+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes #+begin_src matlab :tangle no :exports results :results file replace
#+begin_src matlab :var filepath="figs/exp_scans_rz_dist.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") exportFig('figs/exp_scans_rz_dist.pdf', 'width', 'full', 'height', 'full')
<<plt-matlab>>
#+end_src #+end_src
#+NAME: fig:exp_scans_rz_dist #+name: fig:exp_scans_rz_dist
#+CAPTION: X-Y-Z translations and rotations of the sample w.r.t. the granite when performing tomography experiment and scans with the translation stage at the same time ([[./figs/exp_scans_rz_dist.png][png]], [[./figs/exp_scans_rz_dist.pdf][pdf]]) #+CAPTION: X-Y-Z translations and rotations of the sample w.r.t. the granite when performing tomography experiment and scans with the translation stage at the same time
#+RESULTS:
[[file:figs/exp_scans_rz_dist.png]] [[file:figs/exp_scans_rz_dist.png]]
** Conclusion ** Conclusion

25
org/functions.org
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@ -1,28 +1,5 @@
#+TITLE: Matlab Functions used for the NASS Project #+TITLE: Matlab Functions used for the NASS Project
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:
* describeNassSetup * describeNassSetup
:PROPERTIES: :PROPERTIES:

25
org/identification.org
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@ -1,28 +1,5 @@
#+TITLE: Identification #+TITLE: Identification
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle ../matlab/identification.m
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:
* Introduction :ignore: * Introduction :ignore:
The goal here is to tune the Simscape model of the station in order to have a good dynamical representation of the real system. The goal here is to tune the Simscape model of the station in order to have a good dynamical representation of the real system.

25
org/index.org
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@ -1,28 +1,5 @@
#+TITLE: Simscape Model of the Nano-Active-Stabilization-System #+TITLE: Simscape Model of the Nano-Active-Stabilization-System
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:
Here are links to the documents related to the Simscape model of the Nano-Active-Stabilization-System. Here are links to the documents related to the Simscape model of the Nano-Active-Stabilization-System.

25
org/kinematics.org
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@ -1,28 +1,5 @@
#+TITLE: Kinematics of the station #+TITLE: Kinematics of the station
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results raw replace :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports both
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:
* Introduction :ignore: * Introduction :ignore:
In this document, we discuss the way the motion of each stage is defined. In this document, we discuss the way the motion of each stage is defined.

27
org/metrology_frame.org
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@ -1,30 +1,5 @@
#+TITLE: Study of the Metrology Frame #+TITLE: Study of the Metrology Frame
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results file raw replace
#+PROPERTY: header-args:latex+ :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports results
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
* Flexibility of the reference mirror * Flexibility of the reference mirror
** Introduction :ignore: ** Introduction :ignore:

1
org/motion_force_requirements.org
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@ -1,4 +1,5 @@
#+TITLE: Motion and Force Requirements for the Nano-Hexapod #+TITLE: Motion and Force Requirements for the Nano-Hexapod
#+SETUPFILE: ./setup/org-setup-file.org
* Soft Hexapod * Soft Hexapod
As the nano-hexapod is in series with the other stages, it must apply all the force required to move the sample. As the nano-hexapod is in series with the other stages, it must apply all the force required to move the sample.

53
org/optimal_stiffness_control.org
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@ -1,30 +1,5 @@
#+TITLE: Control of the NASS with optimal stiffness #+TITLE: Control of the NASS with optimal stiffness
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results file raw replace
#+PROPERTY: header-args:latex+ :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports results
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
* Introduction :ignore: * Introduction :ignore:
@ -1055,7 +1030,7 @@ exportFig('figs/opt_stiff_primary_control_L_cas_tot.pdf', 'width', 'full', 'heig
Let's now simulate a tomography experiment. Let's now simulate a tomography experiment.
To do so, we include all disturbances except vibrations of the translation stage. To do so, we include all disturbances except vibrations of the translation stage.
#+begin_src matlab #+begin_src matlab
initializeDisturbances('Fty_x', false, 'Fty_z', false); initializeDisturbances();
initializeSimscapeConfiguration('gravity', false); initializeSimscapeConfiguration('gravity', false);
initializeLoggingConfiguration('log', 'all'); initializeLoggingConfiguration('log', 'all');
#+end_src #+end_src
@ -1079,13 +1054,13 @@ And we run the simulation for all three payload Masses.
#+end_src #+end_src
#+begin_src matlab :exports none #+begin_src matlab :exports none
save('./mat/tomo_exp_hac_dvf.mat', 'hac_dvf_L'); save('./mat/tomo_exp_hac_dvf.mat', 'hac_dvf_L', 'Ms');
#+end_src #+end_src
** Results ** Results
#+begin_src matlab :exports none #+begin_src matlab :exports none
load('./mat/experiment_tomography.mat', 'tomo_align_dist'); load('./mat/experiment_tomography.mat', 'scans_rz_align_dist');
load('./mat/tomo_exp_hac_dvf.mat', 'hac_dvf_L'); load('./mat/tomo_exp_hac_dvf.mat', 'hac_dvf_L', 'Ms');
#+end_src #+end_src
Let's now see how this controller performs. Let's now see how this controller performs.
@ -1097,12 +1072,12 @@ Similarly, the Cumulative Amplitude Spectrum is shown in Figure [[fig:opt_stiff_
Finally, the time domain position error signals are shown in Figure [[fig:opt_stiff_hac_dvf_L_pos_error]]. Finally, the time domain position error signals are shown in Figure [[fig:opt_stiff_hac_dvf_L_pos_error]].
#+begin_src matlab :exports none #+begin_src matlab :exports none
n_av = 4; n_av = 4;
han_win = hanning(ceil(length(simout.Em.En.Data(:,1))/n_av)); han_win = hanning(ceil(length(hac_dvf_L{1}.Em.En.Data(:,1))/n_av));
t = simout.Em.En.Time; t = hac_dvf_L{1}.Em.En.Time;
Ts = t(2)-t(1); Ts = t(2)-t(1);
[pxx_ol, f] = pwelch(tomo_align_dist.Em.En.Data, han_win, [], [], 1/Ts); [pxx_ol, f] = pwelch(scans_rz_align_dist.Em.En.Data, han_win, [], [], 1/Ts);
pxx_dvf_L = zeros(length(f), 6, length(Ms)); pxx_dvf_L = zeros(length(f), 6, length(Ms));
for i = 1:length(Ms) for i = 1:length(Ms)
@ -1299,7 +1274,7 @@ exportFig('figs/opt_stiff_hac_dvf_L_cas_disp_error.pdf', 'width', 'full', 'heigh
figure; figure;
ax1 = subplot(2, 3, 1); ax1 = subplot(2, 3, 1);
hold on; hold on;
plot(tomo_align_dist.Em.En.Time, tomo_align_dist.Em.En.Data(:, 1), 'k-') plot(scans_rz_align_dist.Em.En.Time, scans_rz_align_dist.Em.En.Data(:, 1), 'k-')
for i = 1:length(Ms) for i = 1:length(Ms)
set(gca,'ColorOrderIndex',i); set(gca,'ColorOrderIndex',i);
plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 1)); plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 1));
@ -1310,7 +1285,7 @@ exportFig('figs/opt_stiff_hac_dvf_L_cas_disp_error.pdf', 'width', 'full', 'heigh
ax2 = subplot(2, 3, 2); ax2 = subplot(2, 3, 2);
hold on; hold on;
plot(tomo_align_dist.Em.En.Time, tomo_align_dist.Em.En.Data(:, 2), 'k-') plot(scans_rz_align_dist.Em.En.Time, scans_rz_align_dist.Em.En.Data(:, 2), 'k-')
for i = 1:length(Ms) for i = 1:length(Ms)
set(gca,'ColorOrderIndex',i); set(gca,'ColorOrderIndex',i);
plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 2)); plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 2));
@ -1321,7 +1296,7 @@ exportFig('figs/opt_stiff_hac_dvf_L_cas_disp_error.pdf', 'width', 'full', 'heigh
ax3 = subplot(2, 3, 3); ax3 = subplot(2, 3, 3);
hold on; hold on;
plot(tomo_align_dist.Em.En.Time, tomo_align_dist.Em.En.Data(:, 3), 'k-') plot(scans_rz_align_dist.Em.En.Time, scans_rz_align_dist.Em.En.Data(:, 3), 'k-')
for i = 1:length(Ms) for i = 1:length(Ms)
set(gca,'ColorOrderIndex',i); set(gca,'ColorOrderIndex',i);
plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 3)); plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 3));
@ -1332,7 +1307,7 @@ exportFig('figs/opt_stiff_hac_dvf_L_cas_disp_error.pdf', 'width', 'full', 'heigh
ax4 = subplot(2, 3, 4); ax4 = subplot(2, 3, 4);
hold on; hold on;
plot(tomo_align_dist.Em.En.Time, tomo_align_dist.Em.En.Data(:, 4), 'k-') plot(scans_rz_align_dist.Em.En.Time, scans_rz_align_dist.Em.En.Data(:, 4), 'k-')
for i = 1:length(Ms) for i = 1:length(Ms)
set(gca,'ColorOrderIndex',i); set(gca,'ColorOrderIndex',i);
plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 4)); plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 4));
@ -1343,7 +1318,7 @@ exportFig('figs/opt_stiff_hac_dvf_L_cas_disp_error.pdf', 'width', 'full', 'heigh
ax5 = subplot(2, 3, 5); ax5 = subplot(2, 3, 5);
hold on; hold on;
plot(tomo_align_dist.Em.En.Time, tomo_align_dist.Em.En.Data(:, 5), 'k-') plot(scans_rz_align_dist.Em.En.Time, scans_rz_align_dist.Em.En.Data(:, 5), 'k-')
for i = 1:length(Ms) for i = 1:length(Ms)
set(gca,'ColorOrderIndex',i); set(gca,'ColorOrderIndex',i);
plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 5)); plot(hac_dvf_L{i}.Em.En.Time, hac_dvf_L{i}.Em.En.Data(:, 5));
@ -1354,7 +1329,7 @@ exportFig('figs/opt_stiff_hac_dvf_L_cas_disp_error.pdf', 'width', 'full', 'heigh
ax6 = subplot(2, 3, 6); ax6 = subplot(2, 3, 6);
hold on; hold on;
plot(tomo_align_dist.Em.En.Time, tomo_align_dist.Em.En.Data(:, 6), 'k-', ... plot(scans_rz_align_dist.Em.En.Time, scans_rz_align_dist.Em.En.Data(:, 6), 'k-', ...
'DisplayName', '$\mu$-Station'); 'DisplayName', '$\mu$-Station');
for i = 1:length(Ms) for i = 1:length(Ms)
set(gca,'ColorOrderIndex',i); set(gca,'ColorOrderIndex',i);

27
org/optimal_stiffness_disturbances.org
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@ -1,30 +1,5 @@
#+TITLE: Determination of the optimal nano-hexapod's stiffness for reducing the effect of disturbances #+TITLE: Determination of the optimal nano-hexapod's stiffness for reducing the effect of disturbances
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :tangle ../matlab/optimal_stiffness.m
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
* Introduction :ignore: * Introduction :ignore:
In this document is studied how the stiffness of the nano-hexapod will impact the effect of disturbances on the position error of the sample. In this document is studied how the stiffness of the nano-hexapod will impact the effect of disturbances on the position error of the sample.

25
org/positioning_error.org
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@ -1,28 +1,5 @@
#+TITLE: Computation of the Positioning Error with respect to the nano-hexapod #+TITLE: Computation of the Positioning Error with respect to the nano-hexapod
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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:END:
* Introduction :ignore: * Introduction :ignore:
The global measurement and control schematic is shown in figure [[fig:control-schematic-nass]]. The global measurement and control schematic is shown in figure [[fig:control-schematic-nass]].

36
org/setup/org-setup-file.org Normal file
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@ -0,0 +1,36 @@
#+STARTUP: overview
#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ./index.html
#+HTML_LINK_UP: ./index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:latex+ :output-dir figs

25
org/simscape.org
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@ -1,28 +1,5 @@
#+TITLE: Simscape Model #+TITLE: Simscape Model
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :output-dir figs
:END:
* Introduction :ignore: * Introduction :ignore:
A [[https://.mathworks.com/products/simscape.html][simscape]] model permits to model multi-physics systems. A [[https://.mathworks.com/products/simscape.html][simscape]] model permits to model multi-physics systems.

25
org/simscape_subsystems.org
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@ -1,28 +1,5 @@
#+TITLE: Subsystems used for the Simscape Models #+TITLE: Subsystems used for the Simscape Models
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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:END:
* Introduction :ignore: * Introduction :ignore:
The full Simscape Model is represented in Figure [[fig:simscape_picture]]. The full Simscape Model is represented in Figure [[fig:simscape_picture]].

25
org/simulink_project.org
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@ -1,28 +1,5 @@
#+TITLE: Simulink Project for the NASS #+TITLE: Simulink Project for the NASS
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#+STARTUP: overview
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:END:
Simulink Project is used for the study of the NASS using Simscape. Simulink Project is used for the study of the NASS using Simscape.

11
org/stewart_platform.org
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@ -1,14 +1,5 @@
#+TITLE: Stewart Platform - Simscape Model #+TITLE: Stewart Platform - Simscape Model
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :output-dir figs
:END:
* Introduction :ignore: * Introduction :ignore:
Stewart platforms are generated in multiple steps. Stewart platforms are generated in multiple steps.

25
org/uncertainty_experiment.org
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@ -1,28 +1,5 @@
#+TITLE: Evaluating the Plant Uncertainty in various experimental conditions #+TITLE: Evaluating the Plant Uncertainty in various experimental conditions
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
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:END:
* Introduction :ignore: * Introduction :ignore:
The goal of this document is to study how the dynamics of the system is changing with the experimental conditions. The goal of this document is to study how the dynamics of the system is changing with the experimental conditions.

25
org/uncertainty_optimal_stiffness.org
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@ -1,28 +1,5 @@
#+TITLE: Determination of the optimal nano-hexapod's stiffness #+TITLE: Determination of the optimal nano-hexapod's stiffness
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :tangle ../matlab/optimal_stiffness.m
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#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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:END:
* Introduction :ignore: * Introduction :ignore:
As shown before, many parameters other than the nano-hexapod itself do influence the plant dynamics: As shown before, many parameters other than the nano-hexapod itself do influence the plant dynamics:

27
org/uncertainty_payload.org
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@ -1,30 +1,5 @@
#+TITLE: Effect of Uncertainty on the payload's dynamics on the isolation platform dynamics #+TITLE: Effect of Uncertainty on the payload's dynamics on the isolation platform dynamics
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
* Introduction :ignore: * Introduction :ignore:
In this document we will consider an *isolation platform* (e.g. the nano-hexapod) with a *payload* on top (e.g. the the sample to be positioned). In this document we will consider an *isolation platform* (e.g. the nano-hexapod) with a *payload* on top (e.g. the the sample to be positioned).

27
org/uncertainty_support.org
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@ -1,30 +1,5 @@
#+TITLE: Effect of Uncertainty on the support's dynamics on the isolation platform dynamics #+TITLE: Effect of Uncertainty on the support's dynamics on the isolation platform dynamics
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
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#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END:
* Introduction :ignore: * Introduction :ignore:
In this document we will consider an *isolation platform* (e.g. the nano-hexapod) on top of a *flexible support* (e.g. the micro-station). In this document we will consider an *isolation platform* (e.g. the nano-hexapod) on top of a *flexible support* (e.g. the micro-station).

25
org/uniaxial.org
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@ -1,28 +1,5 @@
#+TITLE: Simscape Uniaxial Model #+TITLE: Simscape Uniaxial Model
:DRAWER: #+SETUPFILE: ./setup/org-setup-file.org
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
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#+PROPERTY: header-args:latex+ :output-dir figs
:END:
* Introduction :ignore: * Introduction :ignore:
The idea is to use the same model as the full Simscape Model but to restrict the motion only in the vertical direction. The idea is to use the same model as the full Simscape Model but to restrict the motion only in the vertical direction.

18
readme.org
View File

@ -4,3 +4,21 @@
#+OPTIONS: num:nil toc:nil todo:nil #+OPTIONS: num:nil toc:nil todo:nil
The goal of this project is to study the Nano-Active-Stabilization-System concept using Matlab/Simscape. The goal of this project is to study the Nano-Active-Stabilization-System concept using Matlab/Simscape.
#+begin_src emacs-lisp :tangle no
(setq org-publish-project-alist
'(("nass-simscape"
:base-directory "~/Cloud/thesis/matlab/nass-simscape/org/"
:base-extension "org"
:publishing-directory "~/Cloud/thesis/matlab/nass-simscape/docs/"
:author "Dehaeze Thomas"
:email "dehaeze.thomas@gmail.com/"
:recursive nil
:publishing-function org-html-publish-to-html
:auto-preamble t
:auto-sitemap nil
:with-todo-keywords nil
:html-wrap-src-lines nil
:table-of-contents nil)
))
#+end_src