779 lines
33 KiB
HTML
779 lines
33 KiB
HTML
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<body>
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<div id="org-div-home-and-up">
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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">Tomography Experiment</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="#orgab2c05f">2.1. Simulation Setup</a></li>
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<li><a href="#org7d6c417">2.2. Analysis</a></li>
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<li><a href="#orgc8896a6">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="#org89b64b9">3.1. Simulation Setup</a></li>
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<li><a href="#orgd3d5cc3">3.2. Analysis</a></li>
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<li><a href="#org744b6a3">3.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org72f01ab">4. Tomography when the micro-hexapod is not centered</a>
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<ul>
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<li><a href="#org3c7fe25">4.1. Simulation Setup</a></li>
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<li><a href="#orgbf003b8">4.2. Analysis</a></li>
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<li><a href="#org0577a39">4.3. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org8fa1632">5. Raster Scans with the translation stage</a>
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<ul>
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<li><a href="#org06c656a">5.1. Simulation Setup</a></li>
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<li><a href="#orgc5cbe68">5.2. Analysis</a></li>
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<li><a href="#org6c038f1">5.3. 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 tuned 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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</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">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>
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<li>In section <a href="#org6aaeb53">5</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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<div class="org-src-container">
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<pre class="src src-matlab">open(<span class="org-string">'nass_model.slx'</span>);
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</pre>
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</div>
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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(<span class="org-string">'mat/conf_simulink.mat'</span>);
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<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">'5'</span>);
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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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</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(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
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initializeSample(<span class="org-string">'mass'</span>, 1);
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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(<span class="org-string">'Rz_type'</span>, <span class="org-string">'rotating'</span>, <span class="org-string">'Rz_period'</span>, 1);
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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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</div>
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<div id="outline-container-orgab2c05f" class="outline-3">
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<h3 id="orgab2c05f"><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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<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
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<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
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<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z direction</span>
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<span class="org-string">'Fty_x'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - X direction</span>
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<span class="org-string">'Fty_z'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
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<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
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);
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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"><span class="org-matlab-simulink-keyword">sim</span>(<span class="org-string">'nass_model'</span>);
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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 = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
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save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>, <span class="org-string">'-append'</span>);
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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-org7d6c417" class="outline-3">
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<h3 id="org7d6c417"><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">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_no_dist'</span>);
|
|
t = tomo_align_no_dist.t;
|
|
MTr = tomo_align_no_dist.MTr;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
|
|
Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
|
|
Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
|
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
|
Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
|
|
Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
|
Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org47272c3" class="figure">
|
|
<p><img src="figs/exp_tomo_without_dist_trans.png" alt="exp_tomo_without_dist_trans.png" />
|
|
</p>
|
|
<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_trans.png">png</a>, <a href="./figs/exp_tomo_without_dist_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org72f4825" class="figure">
|
|
<p><img src="figs/exp_tomo_without_dist_rot.png" alt="exp_tomo_without_dist_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_without_dist_rot.png">png</a>, <a href="./figs/exp_tomo_without_dist_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc8896a6" class="outline-3">
|
|
<h3 id="orgc8896a6"><span class="section-number-3">2.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<div class="important">
|
|
<p>
|
|
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.
|
|
This residual error motion probably comes from a small misalignment somewhere.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org16d8e58" class="outline-2">
|
|
<h2 id="org16d8e58"><span class="section-number-2">3</span> Tomography Experiment with included perturbations</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="org4e7f626"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org89b64b9" class="outline-3">
|
|
<h3 id="org89b64b9"><span class="section-number-3">3.1</span> Simulation Setup</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<p>
|
|
We now activate the disturbances.
|
|
</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 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">tomo_align_dist = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
|
|
save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd3d5cc3" class="outline-3">
|
|
<h3 id="orgd3d5cc3"><span class="section-number-3">3.2</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_align_dist'</span>);
|
|
t = tomo_align_dist.t;
|
|
MTr = tomo_align_dist.MTr;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
|
|
Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
|
|
Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
|
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
|
Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
|
|
Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
|
Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org5b3411f" class="figure">
|
|
<p><img src="figs/exp_tomo_dist_trans.png" alt="exp_tomo_dist_trans.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>X-Y-Z translation of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist_trans.png">png</a>, <a href="./figs/exp_tomo_dist_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org7934376" class="figure">
|
|
<p><img src="figs/exp_tomo_dist_rot.png" alt="exp_tomo_dist_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>X-Y-Z rotations of the sample w.r.t. the granite when performing tomography experiment with disturbances (<a href="./figs/exp_tomo_dist_rot.png">png</a>, <a href="./figs/exp_tomo_dist_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org744b6a3" class="outline-3">
|
|
<h3 id="org744b6a3"><span class="section-number-3">3.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<div class="important">
|
|
<p>
|
|
Error motion is what expected from the disturbance measurements.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org72f01ab" class="outline-2">
|
|
<h2 id="org72f01ab"><span class="section-number-2">4</span> Tomography when the micro-hexapod is not centered</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="orgb31e3fb"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org3c7fe25" class="outline-3">
|
|
<h3 id="org3c7fe25"><span class="section-number-3">4.1</span> Simulation Setup</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<p>
|
|
We first set the wanted translation of the Micro Hexapod.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">P_micro_hexapod = [0.01; 0; 0]; <span class="org-comment">% [m]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We initialize the reference path.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Dh_pos'</span>, [P_micro_hexapod; 0; 0; 0], <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 initialize the stages.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeMicroHexapod(<span class="org-string">'AP'</span>, 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(...
|
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z 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">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
|
);
|
|
</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">tomo_not_align = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
|
|
save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'tomo_not_align'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgbf003b8" class="outline-3">
|
|
<h3 id="orgbf003b8"><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">'tomo_not_align'</span>);
|
|
t = tomo_not_align.t;
|
|
MTr = tomo_not_align.MTr;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
|
|
Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
|
|
Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
|
|
<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
|
|
Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
|
|
Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
|
Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org40355c3" class="figure">
|
|
<p><img src="figs/exp_tomo_offset_trans.png" alt="exp_tomo_offset_trans.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_tomo_offset_trans.png">png</a>, <a href="./figs/exp_tomo_offset_trans.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org3f64362" class="figure">
|
|
<p><img src="figs/exp_tomo_offset_rot.png" alt="exp_tomo_offset_rot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_tomo_offset_rot.png">png</a>, <a href="./figs/exp_tomo_offset_rot.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0577a39" class="outline-3">
|
|
<h3 id="org0577a39"><span class="section-number-3">4.3</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<div class="important">
|
|
<p>
|
|
The main motions are translations in the X direction of the mobile platform (corresponds to the eccentricity of the micro-hexapod) and rotations along the rotating Y axis.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<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>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="org6aaeb53"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org06c656a" class="outline-3">
|
|
<h3 id="org06c656a"><span class="section-number-3">5.1</span> Simulation Setup</h3>
|
|
<div class="outline-text-3" id="text-5-1">
|
|
<p>
|
|
We set the reference path.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeReferences(<span class="org-string">'Dy_type'</span>, <span class="org-string">'triangular'</span>, <span class="org-string">'Dy_amplitude'</span>, 10e<span class="org-type">-</span>3, <span class="org-string">'Dy_period'</span>, 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<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(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
|
initializeSample(<span class="org-string">'mass'</span>, 1);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we initialize the disturbances to zero.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeDisturbances(...
|
|
<span class="org-string">'Dwx'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - X direction</span>
|
|
<span class="org-string">'Dwy'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Y direction</span>
|
|
<span class="org-string">'Dwz'</span>, <span class="org-constant">false</span>, ...<span class="org-comment"> % Ground Motion - Z 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">false</span>, ...<span class="org-comment"> % Translation Stage - Z direction</span>
|
|
<span class="org-string">'Frz_z'</span>, <span class="org-constant">false</span> ...<span class="org-comment"> % Spindle - Z direction</span>
|
|
);
|
|
</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">ty_scan = struct(<span class="org-string">'t'</span>, t, <span class="org-string">'MTr'</span>, MTr);
|
|
save(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'ty_scan'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
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<div id="outline-container-orgc5cbe68" class="outline-3">
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<h3 id="orgc5cbe68"><span class="section-number-3">5.2</span> Analysis</h3>
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<div class="outline-text-3" id="text-5-2">
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'./mat/experiment_tomography.mat'</span>, <span class="org-string">'ty_scan'</span>);
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t = ty_scan.t;
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MTr = ty_scan.MTr;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">Edx = squeeze(MTr(1, 4, <span class="org-type">:</span>));
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Edy = squeeze(MTr(2, 4, <span class="org-type">:</span>));
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Edz = squeeze(MTr(3, 4, <span class="org-type">:</span>));
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<span class="org-comment">% The angles obtained are u-v-w Euler angles (rotations in the moving frame)</span>
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Ery = atan2( squeeze(MTr(1, 3, <span class="org-type">:</span>)), squeeze(sqrt(MTr(1, 1, <span class="org-type">:</span>)<span class="org-type">.^</span>2 <span class="org-type">+</span> MTr(1, 2, <span class="org-type">:</span>)<span class="org-type">.^</span>2)));
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Erx = atan2(<span class="org-type">-</span>squeeze(MTr(2, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(3, 3, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
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Erz = atan2(<span class="org-type">-</span>squeeze(MTr(1, 2, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery), squeeze(MTr(1, 1, <span class="org-type">:</span>))<span class="org-type">./</span>cos(Ery));
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</pre>
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</div>
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<div id="org042610c" class="figure">
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<p><img src="figs/exp_ty_scan_trans.png" alt="exp_ty_scan_trans.png" />
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</p>
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<p><span class="figure-number">Figure 7: </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_trans.png">png</a>, <a href="./figs/exp_ty_scan_trans.pdf">pdf</a>)</p>
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</div>
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<div id="org26a730c" class="figure">
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<p><img src="figs/exp_ty_scan_rot.png" alt="exp_ty_scan_rot.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>X-Y-Z rotations of the sample w.r.t. granite when performing tomography experiment with no disturbances (<a href="./figs/exp_ty_scan_rot.png">png</a>, <a href="./figs/exp_ty_scan_rot.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-org6c038f1" class="outline-3">
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<h3 id="org6c038f1"><span class="section-number-3">5.3</span> Conclusion</h3>
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<div class="outline-text-3" id="text-5-3">
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<div class="important">
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<p>
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This is logic that the main error moving is translation along the Y axis and rotation along the X axis.
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In order to reduce the errors, we can make a smoother reference path for the translation stage.
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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>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-03-13 ven. 17:39</p>
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</div>
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</body>
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</html>
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