473 lines
15 KiB
HTML
473 lines
15 KiB
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<!-- 2020-08-05 mer. 13:27 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Stewart Platform with Flexible Elements</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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<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">Stewart Platform with Flexible Elements</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="#orgbdb2a68">1. Simscape Model</a>
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<ul>
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<li><a href="#org6768ff7">1.1. Flexible APA</a></li>
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<li><a href="#org3650a90">1.2. Flexible Joint</a></li>
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<li><a href="#org75c496c">1.3. Identification</a></li>
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<li><a href="#org52d500c">1.4. No Flexible Elements</a></li>
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<li><a href="#org6800cf5">1.5. Flexible joints</a></li>
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<li><a href="#orgd80e541">1.6. Flexible APA</a></li>
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<li><a href="#org1609aa1">1.7. Flexible Joints and APA</a></li>
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<li><a href="#orge9b9e81">1.8. Direct Velocity Feedback</a></li>
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<li><a href="#org265a0a3">1.9. Integral Force Feedback</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-orgbdb2a68" class="outline-2">
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<h2 id="orgbdb2a68"><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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</div>
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<div id="outline-container-org6768ff7" class="outline-3">
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<h3 id="org6768ff7"><span class="section-number-3">1.1</span> Flexible APA</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">apa = load('./mat/APA300ML.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
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</pre>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-right" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-left">Total number of Nodes</td>
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<td class="org-right">7</td>
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</tr>
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<tr>
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<td class="org-left">Number of interface Nodes</td>
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<td class="org-right">7</td>
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</tr>
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<tr>
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<td class="org-left">Number of Modes</td>
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<td class="org-right">6</td>
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</tr>
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<tr>
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<td class="org-left">Size of M and K matrices</td>
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<td class="org-right">48</td>
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</tr>
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</tbody>
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</table>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Coordinates of the interface nodes</caption>
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<colgroup>
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<col class="org-right" />
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<col class="org-right" />
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<col class="org-right" />
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<col class="org-right" />
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<col class="org-right" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-right">Node i</th>
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<th scope="col" class="org-right">Node Number</th>
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<th scope="col" class="org-right">x [m]</th>
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<th scope="col" class="org-right">y [m]</th>
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<th scope="col" class="org-right">z [m]</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-right">1.0</td>
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<td class="org-right">53917.0</td>
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<td class="org-right">0.0</td>
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<td class="org-right">-0.015</td>
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<td class="org-right">0.0</td>
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</tr>
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<tr>
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<td class="org-right">2.0</td>
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<td class="org-right">53918.0</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.015</td>
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<td class="org-right">0.0</td>
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</tr>
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<tr>
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<td class="org-right">3.0</td>
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<td class="org-right">53919.0</td>
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<td class="org-right">-0.0325</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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</tr>
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<tr>
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<td class="org-right">4.0</td>
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<td class="org-right">53920.0</td>
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<td class="org-right">-0.0125</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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</tr>
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<tr>
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<td class="org-right">5.0</td>
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<td class="org-right">53921.0</td>
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<td class="org-right">-0.0075</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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</tr>
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<tr>
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<td class="org-right">6.0</td>
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<td class="org-right">53922.0</td>
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<td class="org-right">0.0125</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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</tr>
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<tr>
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<td class="org-right">7.0</td>
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<td class="org-right">53923.0</td>
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<td class="org-right">0.0325</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-org3650a90" class="outline-3">
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<h3 id="org3650a90"><span class="section-number-3">1.2</span> Flexible Joint</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="org-src-container">
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<pre class="src src-matlab">flex_joint = load('./mat/flexor_ID16.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K');
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</pre>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-right" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-left">Total number of Nodes</td>
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<td class="org-right">2</td>
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</tr>
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<tr>
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<td class="org-left">Number of interface Nodes</td>
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<td class="org-right">2</td>
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</tr>
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<tr>
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<td class="org-left">Number of Modes</td>
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<td class="org-right">6</td>
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</tr>
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<tr>
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<td class="org-left">Size of M and K matrices</td>
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<td class="org-right">18</td>
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</tr>
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</tbody>
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</table>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 2:</span> Coordinates of the interface nodes</caption>
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<colgroup>
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<col class="org-right" />
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<col class="org-right" />
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<col class="org-right" />
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<col class="org-right" />
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<col class="org-right" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-right">Node i</th>
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<th scope="col" class="org-right">Node Number</th>
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<th scope="col" class="org-right">x [m]</th>
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<th scope="col" class="org-right">y [m]</th>
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<th scope="col" class="org-right">z [m]</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-right">1.0</td>
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<td class="org-right">181278.0</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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</tr>
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<tr>
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<td class="org-right">2.0</td>
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<td class="org-right">181279.0</td>
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<td class="org-right">0.0</td>
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<td class="org-right">0.0</td>
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<td class="org-right">-0.0</td>
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</tr>
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</tbody>
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</table>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"><b>Caracteristic</b></th>
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<th scope="col" class="org-right"><b>Value</b></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Axial Stiffness [N/um]</td>
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<td class="org-right">119</td>
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</tr>
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<tr>
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<td class="org-left">Bending Stiffness [Nm/rad]</td>
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<td class="org-right">33</td>
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</tr>
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<tr>
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<td class="org-left">Bending Stiffness [Nm/rad]</td>
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<td class="org-right">33</td>
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</tr>
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<tr>
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<td class="org-left">Torsion Stiffness [Nm/rad]</td>
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<td class="org-right">236</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-org75c496c" class="outline-3">
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<h3 id="org75c496c"><span class="section-number-3">1.3</span> Identification</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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And we identify the dynamics from force actuators to force sensors.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'stewart_platform_model';
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%% Input/Output definition
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clear io; io_i = 1;
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io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
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io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'dLm'); io_i = io_i + 1; % Relative Displacement Outputs [m]
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io(io_i) = linio([mdl, '/Stewart Platform'], 1, 'openoutput', [], 'Taum'); io_i = io_i + 1; % Force Sensors [N]
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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">ground = initializeGround('type', 'none');
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payload = initializePayload('type', 'rigid', 'm', 50);
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controller = initializeController('type', 'open-loop');
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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">disturbances = initializeDisturbances();
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references = initializeReferences(stewart);
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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-org52d500c" class="outline-3">
|
||
|
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<h3 id="org52d500c"><span class="section-number-3">1.4</span> No Flexible Elements</h3>
|
||
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<div class="outline-text-3" id="text-1-4">
|
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<div class="org-src-container">
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<pre class="src src-matlab">stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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% stewart = initializeStrutDynamics(stewart, 'K', 1.8e6*ones(6,1));
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stewart = initializeAmplifiedStrutDynamics(stewart, 'Kr', 0.9e6*ones(6,1), 'Ka', 0.9e6*ones(6,1));
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stewart = initializeJointDynamics(stewart, 'Kf_M', 33*ones(6,1), 'Kt_M', 235*ones(6,1), 'Kf_F', 33*ones(6,1), 'Kt_F', 235*ones(6,1));
|
||
|
|
stewart = initializeCylindricalPlatforms(stewart);
|
||
|
|
stewart = initializeCylindricalStruts(stewart);
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
stewart = initializeStewartPose(stewart);
|
||
|
|
stewart = initializeInertialSensor(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">%% Run the linearization
|
||
|
|
G = linearize(mdl, io, options);
|
||
|
|
G.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||
|
|
G.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org6800cf5" class="outline-3">
|
||
|
|
<h3 id="org6800cf5"><span class="section-number-3">1.5</span> Flexible joints</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-5">
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||
|
|
stewart = initializeFramesPositions(stewart);
|
||
|
|
stewart = generateGeneralConfiguration(stewart);
|
||
|
|
stewart = computeJointsPose(stewart);
|
||
|
|
stewart = initializeAmplifiedStrutDynamics(stewart, 'Kr', 0.9e6*ones(6,1), 'Ka', 0.9e6*ones(6,1));
|
||
|
|
stewart = initializeJointDynamics(stewart, 'type_F', 'flexible', 'K_F', flex_joint.K, 'M_F', flex_joint.M, 'n_xyz_F', flex_joint.n_xyz, 'xi_F', 0.1, 'step_file_F', 'mat/flexor_ID16.STEP', 'type_M', 'flexible', 'K_M', flex_joint.K, 'M_M', flex_joint.M, 'n_xyz_M', flex_joint.n_xyz, 'xi_M', 0.1, 'step_file_M', 'mat/flexor_ID16.STEP');
|
||
|
|
stewart = initializeCylindricalPlatforms(stewart);
|
||
|
|
stewart = initializeCylindricalStruts(stewart);
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
stewart = initializeStewartPose(stewart);
|
||
|
|
stewart = initializeInertialSensor(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">%% Run the linearization
|
||
|
|
Gj = linearize(mdl, io, options);
|
||
|
|
Gj.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||
|
|
Gj.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-orgd80e541" class="outline-3">
|
||
|
|
<h3 id="orgd80e541"><span class="section-number-3">1.6</span> Flexible APA</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-6">
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||
|
|
stewart = initializeFramesPositions(stewart);
|
||
|
|
stewart = generateGeneralConfiguration(stewart);
|
||
|
|
stewart = computeJointsPose(stewart);
|
||
|
|
stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');
|
||
|
|
stewart = initializeJointDynamics(stewart, 'Kf_M', 33*ones(6,1), 'Kt_M', 235, 'Kf_F', 33*ones(6,1), 'Kt_F', 235);
|
||
|
|
stewart = initializeCylindricalPlatforms(stewart);
|
||
|
|
stewart = initializeCylindricalStruts(stewart, 'type_F', 'none', 'type_M', 'none');
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
stewart = initializeStewartPose(stewart);
|
||
|
|
stewart = initializeInertialSensor(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">%% Run the linearization
|
||
|
|
Ga = -linearize(mdl, io, options);
|
||
|
|
Ga.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||
|
|
Ga.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org1609aa1" class="outline-3">
|
||
|
|
<h3 id="org1609aa1"><span class="section-number-3">1.7</span> Flexible Joints and APA</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-7">
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
||
|
|
stewart = initializeFramesPositions(stewart);
|
||
|
|
stewart = generateGeneralConfiguration(stewart);
|
||
|
|
stewart = computeJointsPose(stewart);
|
||
|
|
stewart = initializeFlexibleStrutDynamics(stewart, 'H', 0.03, 'K', apa.K, 'M', apa.M, 'n_xyz', apa.n_xyz, 'xi', 0.1, 'step_file', 'mat/APA300ML.STEP');
|
||
|
|
stewart = initializeJointDynamics(stewart, 'type_F', 'flexible', 'K_F', flex_joint.K, 'M_F', flex_joint.M, 'n_xyz_F', flex_joint.n_xyz, 'xi_F', 0.1, 'step_file_F', 'mat/flexor_ID16.STEP', 'type_M', 'flexible', 'K_M', flex_joint.K, 'M_M', flex_joint.M, 'n_xyz_M', flex_joint.n_xyz, 'xi_M', 0.1, 'step_file_M', 'mat/flexor_ID16.STEP');
|
||
|
|
stewart = initializeCylindricalPlatforms(stewart);
|
||
|
|
stewart = initializeCylindricalStruts(stewart, 'type_F', 'none', 'type_M', 'none');
|
||
|
|
stewart = computeJacobian(stewart);
|
||
|
|
stewart = initializeStewartPose(stewart);
|
||
|
|
stewart = initializeInertialSensor(stewart);
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="org-src-container">
|
||
|
|
<pre class="src src-matlab">Gf = -linearize(mdl, io, options);
|
||
|
|
Gf.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
|
||
|
|
Gf.OutputName = {'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'};
|
||
|
|
</pre>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-orge9b9e81" class="outline-3">
|
||
|
|
<h3 id="orge9b9e81"><span class="section-number-3">1.8</span> Direct Velocity Feedback</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-8">
|
||
|
|
|
||
|
|
<div id="org2d35259" class="figure">
|
||
|
|
<p><img src="figs/flexible_elements_effect_dvf.png" alt="flexible_elements_effect_dvf.png" />
|
||
|
|
</p>
|
||
|
|
<p><span class="figure-number">Figure 1: </span>Change of the DVF plant dynamics with the added flexible elements</p>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="outline-container-org265a0a3" class="outline-3">
|
||
|
|
<h3 id="org265a0a3"><span class="section-number-3">1.9</span> Integral Force Feedback</h3>
|
||
|
|
<div class="outline-text-3" id="text-1-9">
|
||
|
|
|
||
|
|
<div id="org81cc646" class="figure">
|
||
|
|
<p><img src="figs/flexible_elements_effect_iff.png" alt="flexible_elements_effect_iff.png" />
|
||
|
|
</p>
|
||
|
|
<p><span class="figure-number">Figure 2: </span>Change of the IFF plant dynamics with the added flexible elements</p>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div id="postamble" class="status">
|
||
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
||
|
|
<p class="date">Created: 2020-08-05 mer. 13:27</p>
|
||
|
|
</div>
|
||
|
|
</body>
|
||
|
|
</html>
|