655 lines
20 KiB
HTML
655 lines
20 KiB
HTML
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<title>Simulation of Scientific Experiments</title>
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<meta name="author" content="Dehaeze Thomas" />
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<a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="./index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Simulation of Scientific Experiments</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org03b2a76">1. Simscape Model</a></li>
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<li><a href="#org6ed78a0">2. Tomography Experiment with no disturbances</a>
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<ul>
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<li><a href="#orge3f0741">2.1. Simulation Setup</a></li>
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<li><a href="#org1836f98">2.2. Analysis</a></li>
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<li><a href="#org8cf54cb">2.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org16d8e58">3. Tomography Experiment with included perturbations</a>
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<ul>
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<li><a href="#org9d04c8b">3.1. Simulation Setup</a></li>
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<li><a href="#org746ee08">3.2. Analysis</a></li>
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<li><a href="#org42ba456">3.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org7202245">4. Tomography Experiment with Ty raster scans</a>
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<ul>
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<li><a href="#org0b606be">4.1. Simulation Setup</a></li>
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<li><a href="#org2e0557a">4.2. Analysis</a></li>
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<li><a href="#org6c8cc28">4.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org72f01ab">5. Tomography when the micro-hexapod is not centered</a>
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<ul>
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<li><a href="#org98d14be">5.1. Simulation Setup</a></li>
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<li><a href="#org6dc8ae4">5.2. Analysis</a></li>
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<li><a href="#orgb632268">5.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org8fa1632">6. Raster Scans with the translation stage</a>
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<ul>
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<li><a href="#orgdd9a5de">6.1. Simulation Setup</a></li>
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<li><a href="#orgad49d2c">6.2. Analysis</a></li>
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<li><a href="#org57c774f">6.3. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<p>
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The goal here is to simulate some scientific experiments with the Simscape model when no control is applied to the nano-hexapod.
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</p>
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<p>
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This has several goals:
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</p>
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<ul class="org-ul">
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<li>Validate the model</li>
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<li>Estimate the expected error motion for the experiments</li>
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<li>Estimate the stroke that we may need for the nano-hexapod</li>
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<li>Compare with experiments when control is applied</li>
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</ul>
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<p>
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The document in organized as follow:
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</p>
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<ul class="org-ul">
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<li>In section <a href="#orgfc7d050">1</a> the Simscape model is initialized</li>
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<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>
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<li>In section <a href="#org4e7f626">3</a>, the same is done but with disturbance included</li>
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<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>
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<li>In section <a href="#org6aaeb53">6</a>, scans with the translation stage are simulated with no perturbation included</li>
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</ul>
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<div id="outline-container-org03b2a76" class="outline-2">
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<h2 id="org03b2a76"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orgfc7d050"></a>
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</p>
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<p>
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We load the shared simulink configuration and we set the <code>StopTime</code>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load('mat/conf_simulink.mat');
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set_param(conf_simulink, 'StopTime', '2');
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</pre>
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</div>
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<p>
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We first initialize all the stages.
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The nano-hexapod is considered to be a rigid body.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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initializeNanoHexapod('type', 'rigid');
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initializeSample('mass', 1);
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</pre>
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</div>
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<p>
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No controller is used (Open Loop).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeController('type', 'open-loop');
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</pre>
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</div>
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<p>
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We don’t gravity.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeSimscapeConfiguration('gravity', false);
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</pre>
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</div>
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<p>
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We log the signals for further analysis.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeLoggingConfiguration('log', 'all');
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org6ed78a0" class="outline-2">
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<h2 id="org6ed78a0"><span class="section-number-2">2</span> Tomography Experiment with no disturbances</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org3effbb8"></a>
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</p>
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<p>
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In this section, a tomography experiment is performed with the sample aligned with the rotation axis.
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No disturbance is included.
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</p>
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</div>
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<div id="outline-container-orge3f0741" class="outline-3">
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<h3 id="orge3f0741"><span class="section-number-3">2.1</span> Simulation Setup</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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And we initialize the disturbances to be equal to zero.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeDisturbances(...
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'Dwx', false, ... % Ground Motion - X direction
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'Dwy', false, ... % Ground Motion - Y direction
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'Dwz', false, ... % Ground Motion - Z direction
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'Fty_x', false, ... % Translation Stage - X direction
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'Fty_z', false, ... % Translation Stage - Z direction
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'Frz_z', false ... % Spindle - Z direction
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);
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</pre>
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</div>
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<p>
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We initialize the reference path for all the stages.
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All stage is set to its zero position except the Spindle which is rotating at 60rpm.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
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</pre>
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</div>
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<p>
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We simulate the model.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">sim('nass_model');
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</pre>
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</div>
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<p>
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And we save the obtained data.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">tomo_align_no_dist = simout;
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save('./mat/experiment_tomography.mat', 'tomo_align_no_dist', '-append');
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org1836f98" class="outline-3">
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<h3 id="org1836f98"><span class="section-number-3">2.2</span> Analysis</h3>
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<div class="outline-text-3" id="text-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_align_no_dist');
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</pre>
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</div>
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<div id="orgfcc6055" class="figure">
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<p><img src="figs/exp_tomo_without_dist.png" alt="exp_tomo_without_dist.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_without_dist.png">png</a>, <a href="./figs/exp_tomo_without_dist.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org8cf54cb" class="outline-3">
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<h3 id="org8cf54cb"><span class="section-number-3">2.3</span> Conclusion</h3>
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<div class="outline-text-3" id="text-2-3">
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<div class="important">
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<p>
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When everything is aligned, the resulting error motion is very small (nm range) and is quite negligible with respect to the error when disturbances are included.
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This residual error motion probably comes from a small misalignment somewhere.
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</p>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org16d8e58" class="outline-2">
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<h2 id="org16d8e58"><span class="section-number-2">3</span> Tomography Experiment with included perturbations</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="org4e7f626"></a>
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</p>
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<p>
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In this section, we also perform a tomography experiment with the sample’s center of mass aligned with the rotation axis.
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However this time, we include perturbations such as ground motion and stage vibrations.
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</p>
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</div>
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<div id="outline-container-org9d04c8b" class="outline-3">
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<h3 id="org9d04c8b"><span class="section-number-3">3.1</span> Simulation Setup</h3>
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<div class="outline-text-3" id="text-3-1">
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<p>
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We now activate the disturbances.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeDisturbances(...
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'Dwx', true, ... % Ground Motion - X direction
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'Dwy', true, ... % Ground Motion - Y direction
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'Dwz', true, ... % Ground Motion - Z direction
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'Fty_x', false, ... % Translation Stage - X direction
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'Fty_z', false, ... % Translation Stage - Z direction
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'Frz_z', true ... % Spindle - Z direction
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);
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</pre>
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</div>
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<p>
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We initialize the reference path for all the stages.
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All stage is set to its zero position except the Spindle which is rotating at 60rpm.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
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</pre>
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</div>
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<p>
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We simulate the model.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">sim('nass_model');
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</pre>
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</div>
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<p>
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And we save the obtained data.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">tomo_align_dist = simout;
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save('./mat/experiment_tomography.mat', 'tomo_align_dist', '-append');
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org746ee08" class="outline-3">
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<h3 id="org746ee08"><span class="section-number-3">3.2</span> Analysis</h3>
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<div class="outline-text-3" id="text-3-2">
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<div class="org-src-container">
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<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_align_dist', 'tomo_align_no_dist');
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</pre>
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</div>
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<div id="org8030dba" class="figure">
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<p><img src="figs/exp_tomo_dist.png" alt="exp_tomo_dist.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>X-Y-Z translations and rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist.png">png</a>, <a href="./figs/exp_tomo_dist.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org42ba456" class="outline-3">
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<h3 id="org42ba456"><span class="section-number-3">3.3</span> Conclusion</h3>
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<div class="outline-text-3" id="text-3-3">
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<div class="important">
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<p>
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Here, no vibration is included in the X and Y directions.
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</p>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org7202245" class="outline-2">
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<h2 id="org7202245"><span class="section-number-2">4</span> Tomography Experiment with Ty raster scans</h2>
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<div class="outline-text-2" id="text-4">
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<p>
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<a id="orgd4f0240"></a>
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</p>
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<p>
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In this section, we also perform a tomography experiment with scans of the Translation stage.
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All the perturbations are included.
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</p>
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</div>
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<div id="outline-container-org0b606be" class="outline-3">
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<h3 id="org0b606be"><span class="section-number-3">4.1</span> Simulation Setup</h3>
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<div class="outline-text-3" id="text-4-1">
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<p>
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We now activate the disturbances.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeDisturbances(...
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'Dwx', true, ... % Ground Motion - X direction
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'Dwy', true, ... % Ground Motion - Y direction
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'Dwz', true, ... % Ground Motion - Z direction
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'Fty_x', true, ... % Translation Stage - X direction
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'Fty_z', true, ... % Translation Stage - Z direction
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'Frz_z', true ... % Spindle - Z direction
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);
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</pre>
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</div>
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<p>
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We initialize the reference path for all the stages.
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The Spindle which is rotating at 60rpm and the translation stage not moving as it would take a long time to simulate.
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However, vibrations of the Ty stage are included.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
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</pre>
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</div>
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<p>
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We simulate the model.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">sim('nass_model');
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</pre>
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</div>
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<p>
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And we save the obtained data.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">scans_rz_align_dist = simout;
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save('./mat/experiment_tomography.mat', 'scans_rz_align_dist', '-append');
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org2e0557a" class="outline-3">
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<h3 id="org2e0557a"><span class="section-number-3">4.2</span> Analysis</h3>
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<div class="outline-text-3" id="text-4-2">
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<div class="org-src-container">
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<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'scans_rz_align_dist');
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</pre>
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</div>
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<div id="org38e229c" class="figure">
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<p><img src="figs/exp_scans_rz_dist.png" alt="exp_scans_rz_dist.png" />
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</p>
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<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>
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</div>
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</div>
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</div>
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<div id="outline-container-org6c8cc28" class="outline-3">
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<h3 id="org6c8cc28"><span class="section-number-3">4.3</span> Conclusion</h3>
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</div>
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</div>
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<div id="outline-container-org72f01ab" class="outline-2">
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<h2 id="org72f01ab"><span class="section-number-2">5</span> Tomography when the micro-hexapod is not centered</h2>
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<div class="outline-text-2" id="text-5">
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<p>
|
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<a id="orgb31e3fb"></a>
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</p>
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<p>
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In this section, the sample’s center of mass is not aligned with the rotation axis anymore.
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This is due to the fact that the micro-hexapod has performed some displacement.
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</p>
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<p>
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No disturbances are included.
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</p>
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</div>
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<div id="outline-container-org98d14be" class="outline-3">
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<h3 id="org98d14be"><span class="section-number-3">5.1</span> Simulation Setup</h3>
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<div class="outline-text-3" id="text-5-1">
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<p>
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We first set the wanted translation of the Micro Hexapod.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">P_micro_hexapod = [0.01; 0; 0]; % [m]
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</pre>
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</div>
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<p>
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We initialize the reference path.
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</p>
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<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We initialize the stages.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeMicroHexapod('AP', P_micro_hexapod);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we initialize the disturbances to zero.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeDisturbances(...
|
|
'Dwx', false, ... % Ground Motion - X direction
|
|
'Dwy', false, ... % Ground Motion - Y direction
|
|
'Dwz', false, ... % Ground Motion - Z direction
|
|
'Fty_x', false, ... % Translation Stage - X direction
|
|
'Fty_z', false, ... % Translation Stage - Z direction
|
|
'Frz_z', false ... % Spindle - Z direction
|
|
);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We simulate the model.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sim('nass_model');
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save the obtained data.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">tomo_not_align = simout;
|
|
save('./mat/experiment_tomography.mat', 'tomo_not_align', '-append');
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6dc8ae4" class="outline-3">
|
|
<h3 id="org6dc8ae4"><span class="section-number-3">5.2</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-5-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'tomo_not_align', 'tomo_align_no_dist');
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgb824a01" class="figure">
|
|
<p><img src="figs/exp_tomo_offset.png" alt="exp_tomo_offset.png" />
|
|
</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 id="outline-container-orgb632268" class="outline-3">
|
|
<h3 id="orgb632268"><span class="section-number-3">5.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
<div class="important">
|
|
<p>
|
|
The main motion error are 1Hz X-Y translations and constant Ry error.
|
|
This is mainly due to finite stiffness of the elements.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8fa1632" class="outline-2">
|
|
<h2 id="org8fa1632"><span class="section-number-2">6</span> Raster Scans with the translation stage</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="org6aaeb53"></a>
|
|
</p>
|
|
<p>
|
|
In this section, scans with the translation stage are performed.
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-orgdd9a5de" class="outline-3">
|
|
<h3 id="orgdd9a5de"><span class="section-number-3">6.1</span> Simulation Setup</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<p>
|
|
We initialize the stages.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod('type', 'rigid');
|
|
initializeSample('mass', 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we initialize the disturbances to zero.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeDisturbances(...
|
|
'Dwx', false, ... % Ground Motion - X direction
|
|
'Dwy', false, ... % Ground Motion - Y direction
|
|
'Dwz', false, ... % Ground Motion - Z direction
|
|
'Fty_x', false, ... % Translation Stage - X direction
|
|
'Fty_z', false, ... % Translation Stage - Z direction
|
|
'Frz_z', false ... % Spindle - Z direction
|
|
);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We set the reference path to be a triangular signal for the Translation Stage.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We simulate the model.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sim('nass_model');
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save the obtained data.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ty_scan_triangle = simout;
|
|
save('./mat/experiment_tomography.mat', 'ty_scan_triangle', '-append');
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We now set the reference path to be a sinusoidal signal for the Translation Stage.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences('Dy_type', 'sinusoidal', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We simulate the model.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">sim('nass_model');
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we save the obtained data.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ty_scan_sinus = simout;
|
|
save('./mat/experiment_tomography.mat', 'ty_scan_sinus', '-append');
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgad49d2c" class="outline-3">
|
|
<h3 id="orgad49d2c"><span class="section-number-3">6.2</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-6-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load('./mat/experiment_tomography.mat', 'ty_scan_triangle', 'ty_scan_sinus');
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org888f0bf" class="figure">
|
|
<p><img src="figs/exp_ty_scan.png" alt="exp_ty_scan.png" />
|
|
</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 id="outline-container-org57c774f" class="outline-3">
|
|
<h3 id="org57c774f"><span class="section-number-3">6.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-6-3">
|
|
<div class="important">
|
|
<p>
|
|
Scans with the translation stage induces some errors in the Y direction and Rx translations.
|
|
</p>
|
|
|
|
<p>
|
|
Also, scanning with a sinusoidal wave induces less position errors and at lower frequencies.
|
|
Thus, this should be preferred.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-05-05 mar. 10:34</p>
|
|
</div>
|
|
</body>
|
|
</html>
|