165 lines
5.9 KiB
HTML
165 lines
5.9 KiB
HTML
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<?xml version="1.0" encoding="utf-8"?>
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2020-04-17 ven. 09:35 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Study of the Metrology Frame</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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<script>MathJax = {
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tex: {
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tags: 'ams',
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macros: {bm: ["\\boldsymbol{#1}",1],}
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<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
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</head>
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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">Study of the Metrology Frame</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="#orgf049208">1. Flexibility of the reference mirror</a>
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<ul>
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<li><a href="#orgaec148c">1.1. Initialization</a></li>
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<li><a href="#orgaeca24e">1.2. Rigid fixation between the metrology frame and the nano-hexapod</a></li>
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<li><a href="#orgbe194f6">1.3. Flexible fixation between the metrology frame and the nano-hexapod</a></li>
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<li><a href="#org385c252">1.4. Comparison</a></li>
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<li><a href="#orgbe63408">1.5. 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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<div id="outline-container-orgf049208" class="outline-2">
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<h2 id="orgf049208"><span class="section-number-2">1</span> Flexibility of the reference mirror</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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In this section we wish to see how a flexibility between the nano-hexapod’s top platform and the reference mirror will change the plant dynamics and limits the performance.
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</p>
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<p>
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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.
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</p>
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<p>
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We will compare the two dynamics and conclude.
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</p>
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</div>
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<div id="outline-container-orgaec148c" class="outline-3">
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<h3 id="orgaec148c"><span class="section-number-3">1.1</span> Initialization</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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We initialize all the stages with the default parameters.
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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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initializeNanoHexapod();
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</pre>
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</div>
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<p>
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We first consider a rigid Sample to simplify the analysis.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeSample(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</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-orgaeca24e" class="outline-3">
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<h3 id="orgaeca24e"><span class="section-number-3">1.2</span> Rigid fixation between the metrology frame and the nano-hexapod</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
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Let’s first consider a rigid reference mirror and we identify the dynamics of the system.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeMirror(<span class="org-string">'type'</span>, <span class="org-string">'rigid'</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-orgbe194f6" class="outline-3">
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<h3 id="orgbe194f6"><span class="section-number-3">1.3</span> Flexible fixation between the metrology frame and the nano-hexapod</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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We now initialize a reference mirror with a main resonance frequency at \(200\ [Hz]\).
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</p>
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<div class="org-src-container">
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<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));
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</pre>
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</div>
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<p>
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And we re identify the plant dynamics.
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</p>
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</div>
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</div>
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<div id="outline-container-org385c252" class="outline-3">
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<h3 id="org385c252"><span class="section-number-3">1.4</span> Comparison</h3>
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<div class="outline-text-3" id="text-1-4">
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<p>
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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>.
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</p>
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<div id="orgfa25dbd" class="figure">
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<p><img src="figs/effect_mirror_flexibility_fz_dz.png" alt="effect_mirror_flexibility_fz_dz.png" />
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</p>
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<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>
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</div>
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</div>
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</div>
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<div id="outline-container-orgbe63408" class="outline-3">
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<h3 id="orgbe63408"><span class="section-number-3">1.5</span> Conclusion</h3>
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<div class="outline-text-3" id="text-1-5">
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<div class="important">
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<p>
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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.
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This induces 180 degrees of phase drop on the plant and will limit the attainable controller bandwidth.
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</p>
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<p>
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This phase drop appears whatever the nano-hexapod stiffness.
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Thus, care should be taken when designing the fixation of the reference mirror on top of the nano-hexapod.
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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: 2020-04-17 ven. 09:35</p>
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</div>
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</body>
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</html>
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