Update - New Simscape Model
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<title>Identification of the Stewart Platform using Simscape</title>
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<title>Identification of the Stewart Platform using Simscape</title>
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<h2>Table of Contents</h2>
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<div id="text-table-of-contents">
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<ul>
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<ul>
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<li><a href="#org36eeb29">1. Identification</a>
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<li><a href="#orgcb2f4c2">1. Modal Analysis of the Stewart Platform</a>
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<ul>
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<ul>
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<li><a href="#orgb4842a1">1.1. Simscape Model</a></li>
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<li><a href="#org66d09e9">1.1. Initialize the Stewart Platform</a></li>
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<li><a href="#org4240dd7">1.2. Initialize the Stewart Platform</a></li>
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<li><a href="#org8b1c587">1.2. Identification</a></li>
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<li><a href="#org5695094">1.3. Identification</a></li>
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<li><a href="#orge68adea">1.3. Coordinate transformation</a></li>
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<li><a href="#org4973ae1">1.4. Analysis</a></li>
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<li><a href="#orge7b97c8">1.5. Visualizing the modes</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#orge464de2">2. States as the motion of the mobile platform</a>
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<ul>
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<li><a href="#org8d12d8c">2.1. Initialize the Stewart Platform</a></li>
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<li><a href="#orgef8d225">2.2. Identification</a></li>
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<li><a href="#orge68adea">2.3. Coordinate transformation</a></li>
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<li><a href="#org4973ae1">2.4. Analysis</a></li>
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<li><a href="#orge7b97c8">2.5. Visualizing the modes</a></li>
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<li><a href="#org009b696">2.6. Identification</a></li>
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<li><a href="#orgf7a52cb">2.7. Change of states</a></li>
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</ul>
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</li>
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<li><a href="#org23d7e7b">3. Simple Model without any sensor</a>
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<ul>
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<li><a href="#org2ad9d50">3.1. Simscape Model</a></li>
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<li><a href="#orgbc1f736">3.2. Initialize the Stewart Platform</a></li>
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<li><a href="#org43f8fc6">3.3. Identification</a></li>
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</ul>
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</li>
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<li><a href="#org0502cd2">4. Cartesian Plot</a></li>
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<li><a href="#org32e2eb3">5. From a force to force sensor</a></li>
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<li><a href="#org8ddfd2c">6. From a force applied in the leg to the displacement of the leg</a></li>
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<li><a href="#org5685537">7. Transmissibility</a></li>
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<li><a href="#org3335d1e">8. Compliance</a></li>
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<li><a href="#org5ca7af8">9. Inertial</a></li>
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</ul>
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</ul>
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</div>
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</div>
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</div>
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</div>
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<p>
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<div id="outline-container-orgcb2f4c2" class="outline-2">
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We would like to extract a state space model of the Stewart Platform from the Simscape model.
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<h2 id="orgcb2f4c2"><span class="section-number-2">1</span> Modal Analysis of the Stewart Platform</h2>
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</p>
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<p>
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The inputs are:
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</p>
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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-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">Symbol</th>
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<th scope="col" class="org-left">Meaning</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">\(\bm{\mathcal{F}}_{d}\)</td>
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<td class="org-left">External forces applied in {B}</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{\tau}\)</td>
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<td class="org-left">Joint forces</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{\mathcal{F}}\)</td>
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<td class="org-left">Cartesian forces applied by the Joints</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{D}_{w}\)</td>
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<td class="org-left">Fixed Based translation and rotations around {A}</td>
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</tr>
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</tbody>
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</table>
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<p>
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The outputs are:
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</p>
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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-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">Symbol</th>
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<th scope="col" class="org-left">Meaning</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">\(\bm{\mathcal{X}}\)</td>
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<td class="org-left">Relative Motion of {B} with respect to {A}</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{\mathcal{L}}\)</td>
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<td class="org-left">Joint Displacement</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{F}_{m}\)</td>
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<td class="org-left">Force Sensors in each strut</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{v}_{m}\)</td>
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<td class="org-left">Inertial Sensors located at \(b_i\) measuring in the direction of the strut</td>
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</tr>
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</tbody>
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</table>
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<blockquote>
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<p>
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An important difference from basic Simulink models is that the states in a physical network are not independent in general, because some states have dependencies on other states through constraints.
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</p>
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</blockquote>
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<div id="outline-container-org36eeb29" class="outline-2">
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<h2 id="org36eeb29"><span class="section-number-2">1</span> Identification</h2>
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<div class="outline-text-2" id="text-1">
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<div class="outline-text-2" id="text-1">
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</div>
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</div>
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<div id="outline-container-orgb4842a1" class="outline-3">
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<div id="outline-container-org66d09e9" class="outline-3">
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<h3 id="orgb4842a1"><span class="section-number-3">1.1</span> Simscape Model</h3>
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<h3 id="org66d09e9"><span class="section-number-3">1.1</span> Initialize the Stewart Platform</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">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);
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stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeInertialSensor(stewart);
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</pre>
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</div>
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</div>
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<div id="outline-container-org4240dd7" class="outline-3">
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<div class="org-src-container">
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<h3 id="org4240dd7"><span class="section-number-3">1.2</span> Initialize the Stewart Platform</h3>
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<pre class="src src-matlab">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</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-org8b1c587" class="outline-3">
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<h3 id="org8b1c587"><span class="section-number-3">1.2</span> Identification</h3>
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<div class="outline-text-3" id="text-1-2">
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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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<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);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(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-org5695094" class="outline-3">
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<h3 id="org5695094"><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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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options = linearizeOptions;
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options.SampleTime = 0;
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options.SampleTime = 0;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'stewart_platform_identification'</span>;
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mdl = <span class="org-string">'stewart_platform_model'</span>;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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clear io; io_i = 1;
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clear io; io_i = 1;
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io(io_i) = linio([mdl, <span class="org-string">'/tau'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Fext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Position/Orientation of {B} w.r.t. {A}</span>
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io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Relative Motion Sensor'</span>], 2, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Velocity of {B} w.r.t. {A}</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Vm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Taum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Lm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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G = linearize(mdl, io, options);
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G.InputName = {<span class="org-string">'tau1'</span>, <span class="org-string">'tau2'</span>, <span class="org-string">'tau3'</span>, <span class="org-string">'tau4'</span>, <span class="org-string">'tau5'</span>, <span class="org-string">'tau6'</span>, ...
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<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
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G.OutputName = {<span class="org-string">'Xdx'</span>, <span class="org-string">'Xdy'</span>, <span class="org-string">'Xdz'</span>, <span class="org-string">'Xrx'</span>, <span class="org-string">'Xry'</span>, <span class="org-string">'Xrz'</span>, ...
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<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>, ...
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<span class="org-string">'taum1'</span>, <span class="org-string">'taum2'</span>, <span class="org-string">'taum3'</span>, <span class="org-string">'taum4'</span>, <span class="org-string">'taum5'</span>, <span class="org-string">'taum6'</span>, ...
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<span class="org-string">'Lm1'</span>, <span class="org-string">'Lm2'</span>, <span class="org-string">'Lm3'</span>, <span class="org-string">'Lm4'</span>, <span class="org-string">'Lm5'</span>, <span class="org-string">'Lm6'</span>};
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</pre>
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</div>
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<div id="outline-container-orge464de2" class="outline-2">
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<h2 id="orge464de2"><span class="section-number-2">2</span> States as the motion of the mobile platform</h2>
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<div class="outline-text-2" id="text-2">
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</div>
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<div id="outline-container-org8d12d8c" class="outline-3">
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<h3 id="org8d12d8c"><span class="section-number-3">2.1</span> Initialize the Stewart Platform</h3>
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<div class="outline-text-3" id="text-2-1">
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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);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(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-orgef8d225" class="outline-3">
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<h3 id="orgef8d225"><span class="section-number-3">2.2</span> Identification</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"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options.SampleTime = 0;
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||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
||||||
mdl = <span class="org-string">'stewart_platform_identification_simple'</span>;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
||||||
clear io; io_i = 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/tau'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Xdot'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
@ -541,8 +373,8 @@ And indeed, we obtain 12 states.
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge68adea" class="outline-3">
|
<div id="outline-container-orge68adea" class="outline-3">
|
||||||
<h3 id="orge68adea"><span class="section-number-3">2.3</span> Coordinate transformation</h3>
|
<h3 id="orge68adea"><span class="section-number-3">1.3</span> Coordinate transformation</h3>
|
||||||
<div class="outline-text-3" id="text-2-3">
|
<div class="outline-text-3" id="text-1-3">
|
||||||
<p>
|
<p>
|
||||||
We can perform the following transformation using the <code>ss2ss</code> command.
|
We can perform the following transformation using the <code>ss2ss</code> command.
|
||||||
</p>
|
</p>
|
||||||
@ -577,8 +409,8 @@ Gt = ss(At, Bt, Ct, Dt);
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org4973ae1" class="outline-3">
|
<div id="outline-container-org4973ae1" class="outline-3">
|
||||||
<h3 id="org4973ae1"><span class="section-number-3">2.4</span> Analysis</h3>
|
<h3 id="org4973ae1"><span class="section-number-3">1.4</span> Analysis</h3>
|
||||||
<div class="outline-text-3" id="text-2-4">
|
<div class="outline-text-3" id="text-1-4">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">[V,D] = eig(Gt.A);
|
<pre class="src src-matlab">[V,D] = eig(Gt.A);
|
||||||
</pre>
|
</pre>
|
||||||
@ -604,38 +436,38 @@ Gt = ss(At, Bt, Ct, Dt);
|
|||||||
<tbody>
|
<tbody>
|
||||||
<tr>
|
<tr>
|
||||||
<td class="org-right">1.0</td>
|
<td class="org-right">1.0</td>
|
||||||
<td class="org-right">174.5</td>
|
<td class="org-right">780.6</td>
|
||||||
<td class="org-right">0.9</td>
|
<td class="org-right">0.4</td>
|
||||||
</tr>
|
</tr>
|
||||||
|
|
||||||
<tr>
|
<tr>
|
||||||
<td class="org-right">2.0</td>
|
<td class="org-right">2.0</td>
|
||||||
<td class="org-right">174.5</td>
|
<td class="org-right">780.6</td>
|
||||||
<td class="org-right">0.7</td>
|
<td class="org-right">0.3</td>
|
||||||
</tr>
|
</tr>
|
||||||
|
|
||||||
<tr>
|
<tr>
|
||||||
<td class="org-right">3.0</td>
|
<td class="org-right">3.0</td>
|
||||||
<td class="org-right">202.1</td>
|
<td class="org-right">903.9</td>
|
||||||
<td class="org-right">0.7</td>
|
<td class="org-right">0.3</td>
|
||||||
</tr>
|
</tr>
|
||||||
|
|
||||||
<tr>
|
<tr>
|
||||||
<td class="org-right">4.0</td>
|
<td class="org-right">4.0</td>
|
||||||
<td class="org-right">237.3</td>
|
<td class="org-right">1061.4</td>
|
||||||
<td class="org-right">0.6</td>
|
<td class="org-right">0.3</td>
|
||||||
</tr>
|
</tr>
|
||||||
|
|
||||||
<tr>
|
<tr>
|
||||||
<td class="org-right">5.0</td>
|
<td class="org-right">5.0</td>
|
||||||
<td class="org-right">237.3</td>
|
<td class="org-right">1061.4</td>
|
||||||
<td class="org-right">0.5</td>
|
<td class="org-right">0.2</td>
|
||||||
</tr>
|
</tr>
|
||||||
|
|
||||||
<tr>
|
<tr>
|
||||||
<td class="org-right">6.0</td>
|
<td class="org-right">6.0</td>
|
||||||
<td class="org-right">283.8</td>
|
<td class="org-right">1269.6</td>
|
||||||
<td class="org-right">0.5</td>
|
<td class="org-right">0.2</td>
|
||||||
</tr>
|
</tr>
|
||||||
</tbody>
|
</tbody>
|
||||||
</table>
|
</table>
|
||||||
@ -643,8 +475,8 @@ Gt = ss(At, Bt, Ct, Dt);
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge7b97c8" class="outline-3">
|
<div id="outline-container-orge7b97c8" class="outline-3">
|
||||||
<h3 id="orge7b97c8"><span class="section-number-3">2.5</span> Visualizing the modes</h3>
|
<h3 id="orge7b97c8"><span class="section-number-3">1.5</span> Visualizing the modes</h3>
|
||||||
<div class="outline-text-3" id="text-2-5">
|
<div class="outline-text-3" id="text-1-5">
|
||||||
<p>
|
<p>
|
||||||
To visualize the i’th mode, we may excite the system using the inputs \(U_i\) such that \(B U_i\) is co-linear to \(\xi_i\) (the mode we want to excite).
|
To visualize the i’th mode, we may excite the system using the inputs \(U_i\) such that \(B U_i\) is co-linear to \(\xi_i\) (the mode we want to excite).
|
||||||
</p>
|
</p>
|
||||||
@ -744,359 +576,11 @@ Save the movie of the mode shape.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org009b696" class="outline-3">
|
|
||||||
<h3 id="org009b696"><span class="section-number-3">2.6</span> Identification</h3>
|
|
||||||
<div class="outline-text-3" id="text-2-6">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
||||||
options = linearizeOptions;
|
|
||||||
options.SampleTime = 0;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
||||||
mdl = <span class="org-string">'stewart_platform_identification'</span>;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
||||||
clear io; io_i = 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/tau'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Lm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
||||||
G = linearize(mdl, io, options);
|
|
||||||
<span class="org-comment">% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};</span>
|
|
||||||
<span class="org-comment">% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};</span>
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">size(G)
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-orgf7a52cb" class="outline-3">
|
|
||||||
<h3 id="orgf7a52cb"><span class="section-number-3">2.7</span> Change of states</h3>
|
|
||||||
<div class="outline-text-3" id="text-2-7">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">At = G.C<span class="org-type">*</span>G.A<span class="org-type">*</span>pinv(G.C);
|
|
||||||
|
|
||||||
Bt = G.C<span class="org-type">*</span>G.B;
|
|
||||||
|
|
||||||
Ct = eye(12);
|
|
||||||
Dt = zeros(12, 6);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">Gt = ss(At, Bt, Ct, Dt);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">size(Gt)
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org23d7e7b" class="outline-2">
|
|
||||||
<h2 id="org23d7e7b"><span class="section-number-2">3</span> Simple Model without any sensor</h2>
|
|
||||||
<div class="outline-text-2" id="text-3">
|
|
||||||
</div>
|
|
||||||
<div id="outline-container-org2ad9d50" class="outline-3">
|
|
||||||
<h3 id="org2ad9d50"><span class="section-number-3">3.1</span> Simscape Model</h3>
|
|
||||||
<div class="outline-text-3" id="text-3-1">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">open <span class="org-string">'stewart_identification_simple.slx'</span>
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
|
|
||||||
<div id="outline-container-orgbc1f736" class="outline-3">
|
|
||||||
<h3 id="orgbc1f736"><span class="section-number-3">3.2</span> Initialize the Stewart Platform</h3>
|
|
||||||
<div class="outline-text-3" id="text-3-2">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
|
||||||
stewart = initializeFramesPositions(stewart);
|
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
|
||||||
stewart = computeJointsPose(stewart);
|
|
||||||
stewart = initializeStrutDynamics(stewart);
|
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
|
||||||
stewart = computeJacobian(stewart);
|
|
||||||
stewart = initializeStewartPose(stewart);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org43f8fc6" class="outline-3">
|
|
||||||
<h3 id="org43f8fc6"><span class="section-number-3">3.3</span> Identification</h3>
|
|
||||||
<div class="outline-text-3" id="text-3-3">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">stateorder = {...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_1_1_1'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_2_1_1'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_3_1_1'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_4_1_1'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_5_1_1'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_6_1_1'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.Q'</span>,...
|
|
||||||
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.w'</span>};
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
||||||
options = linearizeOptions;
|
|
||||||
options.SampleTime = 0;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
||||||
mdl = <span class="org-string">'stewart_platform_identification_simple'</span>;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
||||||
clear io; io_i = 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/tau'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
io(io_i) = linio([mdl, <span class="org-string">'/Xdot'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
||||||
|
|
||||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
||||||
G = linearize(mdl, io, options);
|
|
||||||
G.InputName = {<span class="org-string">'tau1'</span>, <span class="org-string">'tau2'</span>, <span class="org-string">'tau3'</span>, <span class="org-string">'tau4'</span>, <span class="org-string">'tau5'</span>, <span class="org-string">'tau6'</span>};
|
|
||||||
|
|
||||||
G.OutputName = {<span class="org-string">'Xdx'</span>, <span class="org-string">'Xdy'</span>, <span class="org-string">'Xdz'</span>, <span class="org-string">'Xrx'</span>, <span class="org-string">'Xry'</span>, <span class="org-string">'Xrz'</span>, <span class="org-string">'Vdx'</span>, <span class="org-string">'Vdy'</span>, <span class="org-string">'Vdz'</span>, <span class="org-string">'Vrx'</span>, <span class="org-string">'Vry'</span>, <span class="org-string">'Vrz'</span>};
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">size(G)
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">G.StateName
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org0502cd2" class="outline-2">
|
|
||||||
<h2 id="org0502cd2"><span class="section-number-2">4</span> Cartesian Plot</h2>
|
|
||||||
<div class="outline-text-2" id="text-4">
|
|
||||||
<p>
|
|
||||||
From a force applied in the Cartesian frame to a displacement in the Cartesian frame.
|
|
||||||
</p>
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_cart(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_cart(2, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_cart(3, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
bode(G.G_cart, freqs);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org32e2eb3" class="outline-2">
|
|
||||||
<h2 id="org32e2eb3"><span class="section-number-2">5</span> From a force to force sensor</h2>
|
|
||||||
<div class="outline-text-2" id="text-5">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$F_{m_i}/F_{i}$'</span>);
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [N/N]'</span>);
|
|
||||||
legend(<span class="org-string">'location'</span>, <span class="org-string">'southeast'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$F_{m_i}/F_{i}$'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(2, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$F_{m_j}/F_{i}$'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(3, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(4, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(5, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(6, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [N/N]'</span>);
|
|
||||||
legend(<span class="org-string">'location'</span>, <span class="org-string">'southeast'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org8ddfd2c" class="outline-2">
|
|
||||||
<h2 id="org8ddfd2c"><span class="section-number-2">6</span> From a force applied in the leg to the displacement of the leg</h2>
|
|
||||||
<div class="outline-text-2" id="text-6">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$D_{i}/F_{i}$'</span>);
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$D_{i}/F_{i}$'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(2, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$D_{j}/F_{i}$'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(3, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(4, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(5, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(6, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
||||||
legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org5685537" class="outline-2">
|
|
||||||
<h2 id="org5685537"><span class="section-number-2">7</span> Transmissibility</h2>
|
|
||||||
<div class="outline-text-2" id="text-7">
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(2, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(3, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/m]'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(4, 4), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(5, 5), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(6, 6), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [$\frac{rad/s}{rad/s}$]'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/m]'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org3335d1e" class="outline-2">
|
|
||||||
<h2 id="org3335d1e"><span class="section-number-2">8</span> Compliance</h2>
|
|
||||||
<div class="outline-text-2" id="text-8">
|
|
||||||
<p>
|
|
||||||
From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base.
|
|
||||||
</p>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_comp(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_comp(2, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_comp(3, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org5ca7af8" class="outline-2">
|
|
||||||
<h2 id="org5ca7af8"><span class="section-number-2">9</span> Inertial</h2>
|
|
||||||
<div class="outline-text-2" id="text-9">
|
|
||||||
<p>
|
|
||||||
From a force applied on the Cartesian frame to the absolute displacement of the mobile platform.
|
|
||||||
</p>
|
|
||||||
|
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_iner(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_iner(2, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_iner(3, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
||||||
hold off;
|
|
||||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
||||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2020-02-11 mar. 17:51</p>
|
<p class="date">Created: 2020-02-13 jeu. 15:44</p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
@ -39,32 +39,9 @@
|
|||||||
:END:
|
:END:
|
||||||
|
|
||||||
* Introduction :ignore:
|
* Introduction :ignore:
|
||||||
We would like to extract a state space model of the Stewart Platform from the Simscape model.
|
|
||||||
|
|
||||||
The inputs are:
|
* Modal Analysis of the Stewart Platform
|
||||||
| Symbol | Meaning |
|
** Introduction :ignore:
|
||||||
|------------------------+--------------------------------------------------|
|
|
||||||
| $\bm{\mathcal{F}}_{d}$ | External forces applied in {B} |
|
|
||||||
| $\bm{\tau}$ | Joint forces |
|
|
||||||
| $\bm{\mathcal{F}}$ | Cartesian forces applied by the Joints |
|
|
||||||
| $\bm{D}_{w}$ | Fixed Based translation and rotations around {A} |
|
|
||||||
|
|
||||||
The outputs are:
|
|
||||||
| Symbol | Meaning |
|
|
||||||
|--------------------+---------------------------------------------------------------------------|
|
|
||||||
| $\bm{\mathcal{X}}$ | Relative Motion of {B} with respect to {A} |
|
|
||||||
| $\bm{\mathcal{L}}$ | Joint Displacement |
|
|
||||||
| $\bm{F}_{m}$ | Force Sensors in each strut |
|
|
||||||
| $\bm{v}_{m}$ | Inertial Sensors located at $b_i$ measuring in the direction of the strut |
|
|
||||||
|
|
||||||
|
|
||||||
#+begin_quote
|
|
||||||
An important difference from basic Simulink models is that the states in a physical network are not independent in general, because some states have dependencies on other states through constraints.
|
|
||||||
#+end_quote
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
* Identification
|
|
||||||
** Matlab Init :noexport:ignore:
|
** Matlab Init :noexport:ignore:
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||||
<<matlab-dir>>
|
<<matlab-dir>>
|
||||||
@ -78,62 +55,8 @@ An important difference from basic Simulink models is that the states in a physi
|
|||||||
simulinkproject('../');
|
simulinkproject('../');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Simscape Model
|
|
||||||
|
|
||||||
** Initialize the Stewart Platform
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
stewart = initializeStewartPlatform();
|
open('stewart_platform_model.slx')
|
||||||
stewart = initializeFramesPositions(stewart);
|
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
|
||||||
stewart = computeJointsPose(stewart);
|
|
||||||
stewart = initializeStrutDynamics(stewart);
|
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
|
||||||
stewart = computeJacobian(stewart);
|
|
||||||
stewart = initializeStewartPose(stewart);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** Identification
|
|
||||||
#+begin_src matlab
|
|
||||||
%% Options for Linearized
|
|
||||||
options = linearizeOptions;
|
|
||||||
options.SampleTime = 0;
|
|
||||||
|
|
||||||
%% Name of the Simulink File
|
|
||||||
mdl = 'stewart_platform_identification';
|
|
||||||
|
|
||||||
%% Input/Output definition
|
|
||||||
clear io; io_i = 1;
|
|
||||||
io(io_i) = linio([mdl, '/tau'], 1, 'openinput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/Fext'], 1, 'openinput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/Vm'], 1, 'openoutput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/Taum'], 1, 'openoutput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/Lm'], 1, 'openoutput'); io_i = io_i + 1;
|
|
||||||
|
|
||||||
%% Run the linearization
|
|
||||||
G = linearize(mdl, io, options);
|
|
||||||
G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6', ...
|
|
||||||
'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
|
|
||||||
|
|
||||||
G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', ...
|
|
||||||
'Vm1', 'Vm2', 'Vm3', 'Vm4', 'Vm5', 'Vm6', ...
|
|
||||||
'taum1', 'taum2', 'taum3', 'taum4', 'taum5', 'taum6', ...
|
|
||||||
'Lm1', 'Lm2', 'Lm3', 'Lm4', 'Lm5', 'Lm6'};
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* States as the motion of the mobile platform
|
|
||||||
** Matlab Init :noexport:ignore:
|
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
|
||||||
<<matlab-dir>>
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
|
||||||
<<matlab-init>>
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :results none :exports none
|
|
||||||
simulinkproject('../');
|
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Initialize the Stewart Platform
|
** Initialize the Stewart Platform
|
||||||
@ -143,10 +66,17 @@ An important difference from basic Simulink models is that the states in a physi
|
|||||||
stewart = generateGeneralConfiguration(stewart);
|
stewart = generateGeneralConfiguration(stewart);
|
||||||
stewart = computeJointsPose(stewart);
|
stewart = computeJointsPose(stewart);
|
||||||
stewart = initializeStrutDynamics(stewart);
|
stewart = initializeStrutDynamics(stewart);
|
||||||
|
stewart = initializeJointDynamics(stewart, 'type_F', 'universal_p', 'type_M', 'spherical_p');
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
stewart = initializeCylindricalPlatforms(stewart);
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
stewart = initializeCylindricalStruts(stewart);
|
||||||
stewart = computeJacobian(stewart);
|
stewart = computeJacobian(stewart);
|
||||||
stewart = initializeStewartPose(stewart);
|
stewart = initializeStewartPose(stewart);
|
||||||
|
stewart = initializeInertialSensor(stewart);
|
||||||
|
#+end_src
|
||||||
|
|
||||||
|
#+begin_src matlab
|
||||||
|
ground = initializeGround('type', 'none');
|
||||||
|
payload = initializePayload('type', 'none');
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
** Identification
|
** Identification
|
||||||
@ -156,13 +86,13 @@ An important difference from basic Simulink models is that the states in a physi
|
|||||||
options.SampleTime = 0;
|
options.SampleTime = 0;
|
||||||
|
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'stewart_platform_identification_simple';
|
mdl = 'stewart_platform_model';
|
||||||
|
|
||||||
%% Input/Output definition
|
%% Input/Output definition
|
||||||
clear io; io_i = 1;
|
clear io; io_i = 1;
|
||||||
io(io_i) = linio([mdl, '/tau'], 1, 'openinput'); io_i = io_i + 1;
|
io(io_i) = linio([mdl, '/Controller'], 1, 'openinput'); io_i = io_i + 1; % Actuator Force Inputs [N]
|
||||||
io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1;
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Position/Orientation of {B} w.r.t. {A}
|
||||||
io(io_i) = linio([mdl, '/Xdot'], 1, 'openoutput'); io_i = io_i + 1;
|
io(io_i) = linio([mdl, '/Relative Motion Sensor'], 2, 'openoutput'); io_i = io_i + 1; % Velocity of {B} w.r.t. {A}
|
||||||
|
|
||||||
%% Run the linearization
|
%% Run the linearization
|
||||||
G = linearize(mdl, io);
|
G = linearize(mdl, io);
|
||||||
@ -233,12 +163,12 @@ We could perform the transformation by hand:
|
|||||||
#+RESULTS:
|
#+RESULTS:
|
||||||
| Mode Number | Resonance Frequency [Hz] | Damping Ratio [%] |
|
| Mode Number | Resonance Frequency [Hz] | Damping Ratio [%] |
|
||||||
|-------------+--------------------------+-------------------|
|
|-------------+--------------------------+-------------------|
|
||||||
| 1.0 | 174.5 | 0.9 |
|
| 1.0 | 780.6 | 0.4 |
|
||||||
| 2.0 | 174.5 | 0.7 |
|
| 2.0 | 780.6 | 0.3 |
|
||||||
| 3.0 | 202.1 | 0.7 |
|
| 3.0 | 903.9 | 0.3 |
|
||||||
| 4.0 | 237.3 | 0.6 |
|
| 4.0 | 1061.4 | 0.3 |
|
||||||
| 5.0 | 237.3 | 0.5 |
|
| 5.0 | 1061.4 | 0.2 |
|
||||||
| 6.0 | 283.8 | 0.5 |
|
| 6.0 | 1269.6 | 0.2 |
|
||||||
|
|
||||||
** Visualizing the modes
|
** Visualizing the modes
|
||||||
To visualize the i'th mode, we may excite the system using the inputs $U_i$ such that $B U_i$ is co-linear to $\xi_i$ (the mode we want to excite).
|
To visualize the i'th mode, we may excite the system using the inputs $U_i$ such that $B U_i$ is co-linear to $\xi_i$ (the mode we want to excite).
|
||||||
@ -309,288 +239,3 @@ Save the movie of the mode shape.
|
|||||||
#+caption: Identified mode - 5
|
#+caption: Identified mode - 5
|
||||||
[[file:figs/mode5.gif]]
|
[[file:figs/mode5.gif]]
|
||||||
|
|
||||||
** Identification
|
|
||||||
#+begin_src matlab
|
|
||||||
%% Options for Linearized
|
|
||||||
options = linearizeOptions;
|
|
||||||
options.SampleTime = 0;
|
|
||||||
|
|
||||||
%% Name of the Simulink File
|
|
||||||
mdl = 'stewart_platform_identification';
|
|
||||||
|
|
||||||
%% Input/Output definition
|
|
||||||
clear io; io_i = 1;
|
|
||||||
io(io_i) = linio([mdl, '/tau'], 1, 'openinput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/Lm'], 1, 'openoutput'); io_i = io_i + 1;
|
|
||||||
|
|
||||||
%% Run the linearization
|
|
||||||
G = linearize(mdl, io, options);
|
|
||||||
% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};
|
|
||||||
% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
size(G)
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** Change of states
|
|
||||||
#+begin_src matlab
|
|
||||||
At = G.C*G.A*pinv(G.C);
|
|
||||||
|
|
||||||
Bt = G.C*G.B;
|
|
||||||
|
|
||||||
Ct = eye(12);
|
|
||||||
Dt = zeros(12, 6);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
Gt = ss(At, Bt, Ct, Dt);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
size(Gt)
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* Simple Model without any sensor
|
|
||||||
** Matlab Init :noexport:ignore:
|
|
||||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
|
||||||
<<matlab-dir>>
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :exports none :results silent :noweb yes
|
|
||||||
<<matlab-init>>
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :results none :exports none
|
|
||||||
simulinkproject('../');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** Simscape Model
|
|
||||||
#+begin_src matlab
|
|
||||||
open 'stewart_identification_simple.slx'
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
|
|
||||||
** Initialize the Stewart Platform
|
|
||||||
#+begin_src matlab
|
|
||||||
stewart = initializeStewartPlatform();
|
|
||||||
stewart = initializeFramesPositions(stewart);
|
|
||||||
stewart = generateGeneralConfiguration(stewart);
|
|
||||||
stewart = computeJointsPose(stewart);
|
|
||||||
stewart = initializeStrutDynamics(stewart);
|
|
||||||
stewart = initializeCylindricalPlatforms(stewart);
|
|
||||||
stewart = initializeCylindricalStruts(stewart);
|
|
||||||
stewart = computeJacobian(stewart);
|
|
||||||
stewart = initializeStewartPose(stewart);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
** Identification
|
|
||||||
#+begin_src matlab
|
|
||||||
stateorder = {...
|
|
||||||
'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_1_1_1',...
|
|
||||||
'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_2_1_1',...
|
|
||||||
'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_3_1_1',...
|
|
||||||
'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_4_1_1',...
|
|
||||||
'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_5_1_1',...
|
|
||||||
'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_6_1_1',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.p',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.p',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.p',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.p',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.p',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.p',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.v',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.v',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.v',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.v',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.v',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.v',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.Q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.Q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.Q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.Q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.Q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.Q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.w',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.Q',...
|
|
||||||
'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.w'};
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
%% Options for Linearized
|
|
||||||
options = linearizeOptions;
|
|
||||||
options.SampleTime = 0;
|
|
||||||
|
|
||||||
%% Name of the Simulink File
|
|
||||||
mdl = 'stewart_platform_identification_simple';
|
|
||||||
|
|
||||||
%% Input/Output definition
|
|
||||||
clear io; io_i = 1;
|
|
||||||
io(io_i) = linio([mdl, '/tau'], 1, 'openinput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/X'], 1, 'openoutput'); io_i = io_i + 1;
|
|
||||||
io(io_i) = linio([mdl, '/Xdot'], 1, 'openoutput'); io_i = io_i + 1;
|
|
||||||
|
|
||||||
%% Run the linearization
|
|
||||||
G = linearize(mdl, io, options);
|
|
||||||
G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};
|
|
||||||
|
|
||||||
G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
size(G)
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab
|
|
||||||
G.StateName
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* Cartesian Plot
|
|
||||||
From a force applied in the Cartesian frame to a displacement in the Cartesian frame.
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_cart(1, 1), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_cart(2, 1), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_cart(3, 1), freqs, 'Hz'))));
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
bode(G.G_cart, freqs);
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* From a force to force sensor
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$F_{m_i}/F_{i}$');
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [N/N]');
|
|
||||||
legend('location', 'southeast');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$F_{m_i}/F_{i}$');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(2, 1), freqs, 'Hz'))), 'k--', 'DisplayName', '$F_{m_j}/F_{i}$');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(3, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(4, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(5, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_forc(6, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [N/N]');
|
|
||||||
legend('location', 'southeast');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* From a force applied in the leg to the displacement of the leg
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$D_{i}/F_{i}$');
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, 'Hz'))), 'k-', 'DisplayName', '$D_{i}/F_{i}$');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(2, 1), freqs, 'Hz'))), 'k--', 'DisplayName', '$D_{j}/F_{i}$');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(3, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(4, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(5, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_legs(6, 1), freqs, 'Hz'))), 'k--', 'HandleVisibility', 'off');
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
|
||||||
legend('location', 'northeast');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* Transmissibility
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(2, 2), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(3, 3), freqs, 'Hz'))));
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/m]');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(4, 4), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(5, 5), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(6, 6), freqs, 'Hz'))));
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [$\frac{rad/s}{rad/s}$]');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 2), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 3), freqs, 'Hz'))));
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/m]');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* Compliance
|
|
||||||
From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base.
|
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_comp(1, 1), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_comp(2, 2), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_comp(3, 3), freqs, 'Hz'))));
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
* Inertial
|
|
||||||
From a force applied on the Cartesian frame to the absolute displacement of the mobile platform.
|
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
|
||||||
figure;
|
|
||||||
hold on;
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_iner(1, 1), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_iner(2, 2), freqs, 'Hz'))));
|
|
||||||
plot(freqs, abs(squeeze(freqresp(G.G_iner(3, 3), freqs, 'Hz'))));
|
|
||||||
hold off;
|
|
||||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
|
||||||
xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
|
|
||||||
#+end_src
|
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user