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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2019-11-05 mar. 11:27 -->
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<!-- 2019-11-11 lun. 14:50 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Simscape Uniaxial Model</title>
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@ -280,72 +280,72 @@ for the JavaScript code in this tag.
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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="#org5379e01">1. Simscape Model</a></li>
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<li><a href="#org985bb58">2. Undamped System</a>
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<li><a href="#orgb71e7ae">1. Simscape Model</a></li>
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<li><a href="#orga5d5945">2. Undamped System</a>
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<ul>
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<li><a href="#org282af69">2.1. Init</a></li>
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<li><a href="#orgc86b374">2.2. Identification</a></li>
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<li><a href="#org3f8d2fb">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org364e9bb">2.4. Noise Budget</a></li>
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<li><a href="#orgb4daaef">2.5. Plant</a></li>
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<li><a href="#org2fbbd0e">2.1. Init</a></li>
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<li><a href="#org33d8ecc">2.2. Identification</a></li>
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<li><a href="#org8c5d7f8">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org97a5979">2.4. Noise Budget</a></li>
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<li><a href="#org7525f32">2.5. Plant</a></li>
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</ul>
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</li>
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<li><a href="#orga653f73">3. Integral Force Feedback</a>
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<li><a href="#orgc6b843b">3. Integral Force Feedback</a>
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<ul>
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<li><a href="#org0151f36">3.1. Control Design</a></li>
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<li><a href="#org98318db">3.2. Identification</a></li>
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<li><a href="#orgff50004">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org466c9e5">3.4. Damped Plant</a></li>
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<li><a href="#org2c6af48">3.5. Conclusion</a></li>
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<li><a href="#org78be696">3.1. Control Design</a></li>
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<li><a href="#orgef1c965">3.2. Identification</a></li>
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<li><a href="#orgca3bd8a">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orgb7e6096">3.4. Damped Plant</a></li>
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<li><a href="#org4f0a2b9">3.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgd931aba">4. Relative Motion Control</a>
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<li><a href="#orgcc4cdcc">4. Relative Motion Control</a>
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<ul>
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<li><a href="#org4c925ca">4.1. Control Design</a></li>
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<li><a href="#org64a2751">4.2. Identification</a></li>
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<li><a href="#org03b5726">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orgcf70df5">4.4. Damped Plant</a></li>
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<li><a href="#orga259511">4.5. Conclusion</a></li>
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<li><a href="#orgd198cd8">4.1. Control Design</a></li>
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<li><a href="#orgcf5bb38">4.2. Identification</a></li>
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<li><a href="#orgb8479f2">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org9e3dd36">4.4. Damped Plant</a></li>
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<li><a href="#org3cd3d80">4.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgb0f2fac">5. Direct Velocity Feedback</a>
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<li><a href="#org9fd5335">5. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#org83437ab">5.1. Control Design</a></li>
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<li><a href="#orgd6906f3">5.2. Identification</a></li>
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<li><a href="#org2f6bd60">5.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org0c90e43">5.4. Damped Plant</a></li>
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<li><a href="#orgb63901b">5.5. Conclusion</a></li>
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<li><a href="#org80df2a6">5.1. Control Design</a></li>
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<li><a href="#orgf585eca">5.2. Identification</a></li>
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<li><a href="#org8b0401b">5.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org5f335db">5.4. Damped Plant</a></li>
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<li><a href="#orged3cacf">5.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org7970e47">6. With Cedrat Piezo-electric Actuators</a>
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<li><a href="#org54f600e">6. With Cedrat Piezo-electric Actuators</a>
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<ul>
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<li><a href="#org575c09c">6.1. Identification</a></li>
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<li><a href="#org2d4d30c">6.2. Control Design</a></li>
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<li><a href="#org1101905">6.3. Identification</a></li>
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<li><a href="#orgafc6298">6.4. Sensitivity to Disturbance</a></li>
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<li><a href="#orgebe455d">6.5. Damped Plant</a></li>
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<li><a href="#org33843ee">6.6. Conclusion</a></li>
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<li><a href="#org9619137">6.1. Identification</a></li>
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<li><a href="#org0702041">6.2. Control Design</a></li>
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<li><a href="#org432c3b9">6.3. Identification</a></li>
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<li><a href="#org92524a2">6.4. Sensitivity to Disturbance</a></li>
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<li><a href="#org36995c4">6.5. Damped Plant</a></li>
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<li><a href="#org293c60a">6.6. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org43dd103">7. Comparison of Active Damping Techniques</a>
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<li><a href="#org3679584">7. Comparison of Active Damping Techniques</a>
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<ul>
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<li><a href="#orgbd3fe7b">7.1. Load the plants</a></li>
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<li><a href="#org82a27fa">7.2. Sensitivity to Disturbance</a></li>
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<li><a href="#org0dc21b7">7.3. Noise Budget</a></li>
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<li><a href="#orgf592486">7.4. Damped Plant</a></li>
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<li><a href="#orgfc2e28b">7.5. Conclusion</a></li>
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<li><a href="#org7ead2f2">7.1. Load the plants</a></li>
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<li><a href="#org7b3030d">7.2. Sensitivity to Disturbance</a></li>
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<li><a href="#org4f38837">7.3. Noise Budget</a></li>
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<li><a href="#org1cab4a1">7.4. Damped Plant</a></li>
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<li><a href="#org89243de">7.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgded5bc7">8. Voice Coil</a>
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<li><a href="#orgf7fa09b">8. Voice Coil</a>
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<ul>
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<li><a href="#orgbba145f">8.1. Init</a></li>
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<li><a href="#org465be28">8.2. Identification</a></li>
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<li><a href="#orgda14068">8.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org49bb7e7">8.4. Noise Budget</a></li>
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<li><a href="#org04357b8">8.5. Integral Force Feedback</a></li>
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<li><a href="#org83d9caa">8.6. Identification of the Damped Plant</a></li>
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<li><a href="#orge278186">8.7. Noise Budget</a></li>
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<li><a href="#org152df36">8.8. Conclusion</a></li>
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<li><a href="#org5bfd692">8.1. Init</a></li>
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<li><a href="#org145a9df">8.2. Identification</a></li>
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<li><a href="#org3b53ae6">8.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org33c2392">8.4. Noise Budget</a></li>
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<li><a href="#org332ecb6">8.5. Integral Force Feedback</a></li>
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<li><a href="#orgd420efb">8.6. Identification of the Damped Plant</a></li>
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<li><a href="#org99ecd1f">8.7. Noise Budget</a></li>
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<li><a href="#orgffe5e36">8.8. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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@ -360,15 +360,15 @@ The idea is to use the same model as the full Simscape Model but to restrict the
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This is done in order to more easily study the system and evaluate control techniques.
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</p>
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<div id="outline-container-org5379e01" class="outline-2">
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<h2 id="org5379e01"><span class="section-number-2">1</span> Simscape Model</h2>
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<div id="outline-container-orgb71e7ae" class="outline-2">
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<h2 id="orgb71e7ae"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="org233f30c"></a>
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<a id="org4affa13"></a>
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</p>
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<p>
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#orgb72b23c">1</a>.
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#orge3c5fac">1</a>.
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</p>
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<p>
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@ -412,7 +412,7 @@ The control signal \(u\) is:
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</ul>
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<div id="orgb72b23c" class="figure">
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<div id="orge3c5fac" class="figure">
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<p><img src="figs/uniaxial-model-nass-flexible.png" alt="uniaxial-model-nass-flexible.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Schematic of the uniaxial model used</p>
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@ -421,11 +421,11 @@ The control signal \(u\) is:
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<p>
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Few active damping techniques will be compared in order to decide which sensor is to be included in the system.
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Schematics of the active damping techniques are displayed in figure <a href="#orgf6769a3">2</a>.
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Schematics of the active damping techniques are displayed in figure <a href="#org4593626">2</a>.
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</p>
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<div id="orgf6769a3" class="figure">
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<div id="org4593626" class="figure">
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<p><img src="figs/uniaxial-model-nass-flexible-active-damping.png" alt="uniaxial-model-nass-flexible-active-damping.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Comparison of used active damping techniques</p>
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@ -433,18 +433,18 @@ Schematics of the active damping techniques are displayed in figure <a href="#or
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</div>
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</div>
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<div id="outline-container-org985bb58" class="outline-2">
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<h2 id="org985bb58"><span class="section-number-2">2</span> Undamped System</h2>
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<div id="outline-container-orga5d5945" class="outline-2">
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<h2 id="orga5d5945"><span class="section-number-2">2</span> Undamped System</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org99f2016"></a>
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<a id="orge23ab54"></a>
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</p>
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<p>
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Let's start by study the undamped system.
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</p>
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</div>
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<div id="outline-container-org282af69" class="outline-3">
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<h3 id="org282af69"><span class="section-number-3">2.1</span> Init</h3>
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<div id="outline-container-org2fbbd0e" class="outline-3">
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<h3 id="org2fbbd0e"><span class="section-number-3">2.1</span> Init</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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We initialize all the stages with the default parameters.
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@ -456,8 +456,8 @@ All the controllers are set to 0 (Open Loop).
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</p>
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</div>
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</div>
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<div id="outline-container-orgc86b374" class="outline-3">
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<h3 id="orgc86b374"><span class="section-number-3">2.2</span> Identification</h3>
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<div id="outline-container-org33d8ecc" class="outline-3">
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<h3 id="org33d8ecc"><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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<p>
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We identify the dynamics of the system.
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@ -520,19 +520,19 @@ Finally, we save the identified system dynamics for further analysis.
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</div>
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</div>
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<div id="outline-container-org3f8d2fb" class="outline-3">
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<h3 id="org3f8d2fb"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
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<div id="outline-container-org8c5d7f8" class="outline-3">
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<h3 id="org8c5d7f8"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
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<div class="outline-text-3" id="text-2-3">
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<p>
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We show several plots representing the sensitivity to disturbances:
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</p>
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<ul class="org-ul">
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<li>in figure <a href="#org65e5bc4">3</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
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<li>in figure <a href="#org01c7629">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
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<li>in figure <a href="#org811b66a">3</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
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<li>in figure <a href="#org5df06c0">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
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</ul>
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<div id="org65e5bc4" class="figure">
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<div id="org811b66a" class="figure">
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<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-disturbances.pdf">pdf</a>)</p>
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@ -540,7 +540,7 @@ We show several plots representing the sensitivity to disturbances:
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<div id="org01c7629" class="figure">
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<div id="org5df06c0" class="figure">
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<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-force-dist.pdf">pdf</a>)</p>
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@ -548,8 +548,8 @@ We show several plots representing the sensitivity to disturbances:
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</div>
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</div>
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<div id="outline-container-org364e9bb" class="outline-3">
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<h3 id="org364e9bb"><span class="section-number-3">2.4</span> Noise Budget</h3>
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<div id="outline-container-org97a5979" class="outline-3">
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<h3 id="org97a5979"><span class="section-number-3">2.4</span> Noise Budget</h3>
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<div class="outline-text-3" id="text-2-4">
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<p>
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We first load the measured PSD of the disturbance.
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@ -561,12 +561,12 @@ We first load the measured PSD of the disturbance.
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<p>
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The effect of these disturbances on the distance \(D\) is computed below.
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The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#org062cf88">5</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#orgf07d38b">6</a>.
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The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#org415c8fd">5</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org52ed86e">6</a>.
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</p>
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||||
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<p>
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The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#orgf07d38b">6</a>.
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The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#org52ed86e">6</a>.
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</p>
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||||
<pre class="example">
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||||
3.3793e-06
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@ -574,32 +574,32 @@ The Root Mean Square value of the obtained displacement \(D\) is computed below
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||||
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<div id="org062cf88" class="figure">
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||||
<div id="org415c8fd" class="figure">
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||||
<p><img src="figs/uniaxial-psd-dist.png" alt="uniaxial-psd-dist.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>caption (<a href="./figs/uniaxial-psd-dist.png">png</a>, <a href="./figs/uniaxial-psd-dist.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 5: </span>PSD of the effect of disturbances on \(D\) (<a href="./figs/uniaxial-psd-dist.png">png</a>, <a href="./figs/uniaxial-psd-dist.pdf">pdf</a>)</p>
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</div>
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<div id="orgf07d38b" class="figure">
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<div id="org52ed86e" class="figure">
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<p><img src="figs/uniaxial-cas-dist.png" alt="uniaxial-cas-dist.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>caption (<a href="./figs/uniaxial-cas-dist.png">png</a>, <a href="./figs/uniaxial-cas-dist.pdf">pdf</a>)</p>
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<p><span class="figure-number">Figure 6: </span>CAS of the effect of disturbances on \(D\) (<a href="./figs/uniaxial-cas-dist.png">png</a>, <a href="./figs/uniaxial-cas-dist.pdf">pdf</a>)</p>
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</div>
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||||
</div>
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</div>
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<div id="outline-container-orgb4daaef" class="outline-3">
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<h3 id="orgb4daaef"><span class="section-number-3">2.5</span> Plant</h3>
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<div id="outline-container-org7525f32" class="outline-3">
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||||
<h3 id="org7525f32"><span class="section-number-3">2.5</span> Plant</h3>
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<div class="outline-text-3" id="text-2-5">
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<p>
|
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The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#orgcb273be">7</a>.
|
||||
The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#org209e53c">7</a>.
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It corresponds to the plant to control.
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||||
</p>
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<div id="orgcb273be" class="figure">
|
||||
<div id="org209e53c" class="figure">
|
||||
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
|
||||
@ -608,21 +608,21 @@ It corresponds to the plant to control.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga653f73" class="outline-2">
|
||||
<h2 id="orga653f73"><span class="section-number-2">3</span> Integral Force Feedback</h2>
|
||||
<div id="outline-container-orgc6b843b" class="outline-2">
|
||||
<h2 id="orgc6b843b"><span class="section-number-2">3</span> Integral Force Feedback</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="org0f88f24"></a>
|
||||
<a id="org5d395a2"></a>
|
||||
</p>
|
||||
|
||||
<div id="orga00e5a6" class="figure">
|
||||
<div id="orgea17388" class="figure">
|
||||
<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Uniaxial IFF Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org0151f36" class="outline-3">
|
||||
<h3 id="org0151f36"><span class="section-number-3">3.1</span> Control Design</h3>
|
||||
<div id="outline-container-org78be696" class="outline-3">
|
||||
<h3 id="org78be696"><span class="section-number-3">3.1</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
@ -634,7 +634,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgf741d44" class="figure">
|
||||
<div id="org952556f" class="figure">
|
||||
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p>
|
||||
@ -649,7 +649,7 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org331d87b" class="figure">
|
||||
<div id="orgf9d4fb1" class="figure">
|
||||
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p>
|
||||
@ -657,8 +657,8 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org98318db" class="outline-3">
|
||||
<h3 id="org98318db"><span class="section-number-3">3.2</span> Identification</h3>
|
||||
<div id="outline-container-orgef1c965" class="outline-3">
|
||||
<h3 id="orgef1c965"><span class="section-number-3">3.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
Let's initialize the system prior to identification.
|
||||
@ -741,18 +741,18 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgff50004" class="outline-3">
|
||||
<h3 id="orgff50004"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-orgca3bd8a" class="outline-3">
|
||||
<h3 id="orgca3bd8a"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
|
||||
<div id="orgbc9fdaa" class="figure">
|
||||
<div id="org0740db4" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0f6056d" class="figure">
|
||||
<div id="org02782a2" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
|
||||
@ -760,11 +760,11 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org466c9e5" class="outline-3">
|
||||
<h3 id="org466c9e5"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-orgb7e6096" class="outline-3">
|
||||
<h3 id="orgb7e6096"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
|
||||
<div id="orge4f80dd" class="figure">
|
||||
<div id="orge1b1f09" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
|
||||
@ -772,8 +772,8 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2c6af48" class="outline-3">
|
||||
<h3 id="org2c6af48"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org4f0a2b9" class="outline-3">
|
||||
<h3 id="org4f0a2b9"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -785,25 +785,25 @@ Integral Force Feedback:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd931aba" class="outline-2">
|
||||
<h2 id="orgd931aba"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||
<div id="outline-container-orgcc4cdcc" class="outline-2">
|
||||
<h2 id="orgcc4cdcc"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="orgd4bc59d"></a>
|
||||
<a id="org30fd654"></a>
|
||||
</p>
|
||||
<p>
|
||||
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org38e55a9" class="figure">
|
||||
<div id="orge8dc6c5" class="figure">
|
||||
<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Uniaxial RMC Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org4c925ca" class="outline-3">
|
||||
<h3 id="org4c925ca"><span class="section-number-3">4.1</span> Control Design</h3>
|
||||
<div id="outline-container-orgd198cd8" class="outline-3">
|
||||
<h3 id="orgd198cd8"><span class="section-number-3">4.1</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
@ -815,7 +815,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org8d77310" class="figure">
|
||||
<div id="org34aa38e" class="figure">
|
||||
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p>
|
||||
@ -831,7 +831,7 @@ A Low pass Filter is added to make the controller transfer function proper.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org5ac4f8e" class="figure">
|
||||
<div id="orgaf673bf" class="figure">
|
||||
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p>
|
||||
@ -839,8 +839,8 @@ A Low pass Filter is added to make the controller transfer function proper.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org64a2751" class="outline-3">
|
||||
<h3 id="org64a2751"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div id="outline-container-orgcf5bb38" class="outline-3">
|
||||
<h3 id="orgcf5bb38"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
Let's initialize the system prior to identification.
|
||||
@ -924,18 +924,18 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org03b5726" class="outline-3">
|
||||
<h3 id="org03b5726"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-orgb8479f2" class="outline-3">
|
||||
<h3 id="orgb8479f2"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
|
||||
<div id="org9d3c40d" class="figure">
|
||||
<div id="orga612d6b" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org97c0227" class="figure">
|
||||
<div id="org525bbf8" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 18: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
|
||||
@ -943,11 +943,11 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcf70df5" class="outline-3">
|
||||
<h3 id="orgcf70df5"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-org9e3dd36" class="outline-3">
|
||||
<h3 id="org9e3dd36"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
|
||||
<div id="org73b1d75" class="figure">
|
||||
<div id="org1f3d1fb" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
|
||||
@ -955,8 +955,8 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga259511" class="outline-3">
|
||||
<h3 id="orga259511"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org3cd3d80" class="outline-3">
|
||||
<h3 id="org3cd3d80"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-4-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -968,25 +968,25 @@ Relative Motion Control:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb0f2fac" class="outline-2">
|
||||
<h2 id="orgb0f2fac"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||
<div id="outline-container-org9fd5335" class="outline-2">
|
||||
<h2 id="org9fd5335"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<p>
|
||||
<a id="org1655ed1"></a>
|
||||
<a id="org6af5294"></a>
|
||||
</p>
|
||||
<p>
|
||||
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org9c6dfe4" class="figure">
|
||||
<div id="orgb69aba0" class="figure">
|
||||
<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Uniaxial DVF Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org83437ab" class="outline-3">
|
||||
<h3 id="org83437ab"><span class="section-number-3">5.1</span> Control Design</h3>
|
||||
<div id="outline-container-org80df2a6" class="outline-3">
|
||||
<h3 id="org80df2a6"><span class="section-number-3">5.1</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
@ -994,7 +994,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org28bd4a3" class="figure">
|
||||
<div id="org8ef9378" class="figure">
|
||||
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 21: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p>
|
||||
@ -1006,7 +1006,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org3b9273f" class="figure">
|
||||
<div id="orgd6cd975" class="figure">
|
||||
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 22: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p>
|
||||
@ -1014,8 +1014,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd6906f3" class="outline-3">
|
||||
<h3 id="orgd6906f3"><span class="section-number-3">5.2</span> Identification</h3>
|
||||
<div id="outline-container-orgf585eca" class="outline-3">
|
||||
<h3 id="orgf585eca"><span class="section-number-3">5.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-5-2">
|
||||
<p>
|
||||
Let's initialize the system prior to identification.
|
||||
@ -1098,18 +1098,18 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2f6bd60" class="outline-3">
|
||||
<h3 id="org2f6bd60"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org8b0401b" class="outline-3">
|
||||
<h3 id="org8b0401b"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
|
||||
<div id="orged28a54" class="figure">
|
||||
<div id="orgf96e285" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 23: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org76a4395" class="figure">
|
||||
<div id="org10e4399" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 24: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
|
||||
@ -1117,11 +1117,11 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0c90e43" class="outline-3">
|
||||
<h3 id="org0c90e43"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-org5f335db" class="outline-3">
|
||||
<h3 id="org5f335db"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-5-4">
|
||||
|
||||
<div id="orgfbee72a" class="figure">
|
||||
<div id="org5432972" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 25: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
|
||||
@ -1129,8 +1129,8 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb63901b" class="outline-3">
|
||||
<h3 id="orgb63901b"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||
<div id="outline-container-orged3cacf" class="outline-3">
|
||||
<h3 id="orged3cacf"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-5-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -1141,25 +1141,25 @@ Direct Velocity Feedback:
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org7970e47" class="outline-2">
|
||||
<h2 id="org7970e47"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2>
|
||||
<div id="outline-container-org54f600e" class="outline-2">
|
||||
<h2 id="org54f600e"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
<p>
|
||||
<a id="org86ab0ae"></a>
|
||||
<a id="org64ee63d"></a>
|
||||
</p>
|
||||
<p>
|
||||
The model used for the Cedrat actuator is shown in figure <a href="#orgd05de0b">26</a>.
|
||||
The model used for the Cedrat actuator is shown in figure <a href="#orgc9104bb">26</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgd05de0b" class="figure">
|
||||
<div id="orgc9104bb" class="figure">
|
||||
<p><img src="figs/cedrat-uniaxial-actuator.png" alt="cedrat-uniaxial-actuator.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 26: </span>Schematic of the model used for the Cedrat Actuator</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org575c09c" class="outline-3">
|
||||
<h3 id="org575c09c"><span class="section-number-3">6.1</span> Identification</h3>
|
||||
<div id="outline-container-org9619137" class="outline-3">
|
||||
<h3 id="org9619137"><span class="section-number-3">6.1</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<p>
|
||||
Let's initialize the system prior to identification.
|
||||
@ -1247,15 +1247,15 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2d4d30c" class="outline-3">
|
||||
<h3 id="org2d4d30c"><span class="section-number-3">6.2</span> Control Design</h3>
|
||||
<div id="outline-container-org0702041" class="outline-3">
|
||||
<h3 id="org0702041"><span class="section-number-3">6.2</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-6-2">
|
||||
<p>
|
||||
Let's look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org3651b4e" class="figure">
|
||||
<div id="org2f4f9cc" class="figure">
|
||||
<p><img src="figs/uniaxial_cedrat_plant.png" alt="uniaxial_cedrat_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 27: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_cedrat_plant.png">png</a>, <a href="./figs/uniaxial_cedrat_plant.pdf">pdf</a>)</p>
|
||||
@ -1270,7 +1270,7 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6ed3ff4" class="figure">
|
||||
<div id="orgb4dfba9" class="figure">
|
||||
<p><img src="figs/uniaxial_cedrat_open_loop.png" alt="uniaxial_cedrat_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 28: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_cedrat_open_loop.png">png</a>, <a href="./figs/uniaxial_cedrat_open_loop.pdf">pdf</a>)</p>
|
||||
@ -1278,8 +1278,8 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1101905" class="outline-3">
|
||||
<h3 id="org1101905"><span class="section-number-3">6.3</span> Identification</h3>
|
||||
<div id="outline-container-org432c3b9" class="outline-3">
|
||||
<h3 id="org432c3b9"><span class="section-number-3">6.3</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-6-3">
|
||||
<p>
|
||||
Let's initialize the system prior to identification.
|
||||
@ -1363,18 +1363,18 @@ G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgafc6298" class="outline-3">
|
||||
<h3 id="orgafc6298"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org92524a2" class="outline-3">
|
||||
<h3 id="org92524a2"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-6-4">
|
||||
|
||||
<div id="org57267c2" class="figure">
|
||||
<div id="orga3eef15" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_cedrat.png" alt="uniaxial_sensitivity_dist_cedrat.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 29: </span>Sensitivity to disturbance once the CEDRAT controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_cedrat.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org89fd25b" class="figure">
|
||||
<div id="org1c759e8" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_cedrat.png" alt="uniaxial_sensitivity_dist_stages_cedrat.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 30: </span>Sensitivity to force disturbances in various stages when CEDRAT is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.pdf">pdf</a>)</p>
|
||||
@ -1382,11 +1382,11 @@ G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgebe455d" class="outline-3">
|
||||
<h3 id="orgebe455d"><span class="section-number-3">6.5</span> Damped Plant</h3>
|
||||
<div id="outline-container-org36995c4" class="outline-3">
|
||||
<h3 id="org36995c4"><span class="section-number-3">6.5</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-6-5">
|
||||
|
||||
<div id="org0979790" class="figure">
|
||||
<div id="org0a5327e" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_cedrat_damped.png" alt="uniaxial_plant_cedrat_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 31: </span>Damped Plant after CEDRAT is applied (<a href="./figs/uniaxial_plant_cedrat_damped.png">png</a>, <a href="./figs/uniaxial_plant_cedrat_damped.pdf">pdf</a>)</p>
|
||||
@ -1394,8 +1394,8 @@ G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org33843ee" class="outline-3">
|
||||
<h3 id="org33843ee"><span class="section-number-3">6.6</span> Conclusion</h3>
|
||||
<div id="outline-container-org293c60a" class="outline-3">
|
||||
<h3 id="org293c60a"><span class="section-number-3">6.6</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-6-6">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -1407,15 +1407,15 @@ This gives similar results than with a classical force sensor.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org43dd103" class="outline-2">
|
||||
<h2 id="org43dd103"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2>
|
||||
<div id="outline-container-org3679584" class="outline-2">
|
||||
<h2 id="org3679584"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2>
|
||||
<div class="outline-text-2" id="text-7">
|
||||
<p>
|
||||
<a id="org59d45b8"></a>
|
||||
<a id="org43accf4"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgbd3fe7b" class="outline-3">
|
||||
<h3 id="orgbd3fe7b"><span class="section-number-3">7.1</span> Load the plants</h3>
|
||||
<div id="outline-container-org7ead2f2" class="outline-3">
|
||||
<h3 id="org7ead2f2"><span class="section-number-3">7.1</span> Load the plants</h3>
|
||||
<div class="outline-text-3" id="text-7-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'G_dvf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
@ -1424,11 +1424,11 @@ This gives similar results than with a classical force sensor.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org82a27fa" class="outline-3">
|
||||
<h3 id="org82a27fa"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org7b3030d" class="outline-3">
|
||||
<h3 id="org7b3030d"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-7-2">
|
||||
|
||||
<div id="org53c3b19" class="figure">
|
||||
<div id="org6a0735b" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 32: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
|
||||
@ -1436,21 +1436,21 @@ This gives similar results than with a classical force sensor.
|
||||
|
||||
|
||||
|
||||
<div id="org9fcda32" class="figure">
|
||||
<div id="orgecd4e90" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 33: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgb63ab99" class="figure">
|
||||
<div id="orgdaf4675" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 34: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd60bc47" class="figure">
|
||||
<div id="org08001e9" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 35: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
|
||||
@ -1458,8 +1458,8 @@ This gives similar results than with a classical force sensor.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0dc21b7" class="outline-3">
|
||||
<h3 id="org0dc21b7"><span class="section-number-3">7.3</span> Noise Budget</h3>
|
||||
<div id="outline-container-org4f38837" class="outline-3">
|
||||
<h3 id="org4f38837"><span class="section-number-3">7.3</span> Noise Budget</h3>
|
||||
<div class="outline-text-3" id="text-7-3">
|
||||
<p>
|
||||
We first load the measured PSD of the disturbance.
|
||||
@ -1471,10 +1471,10 @@ We first load the measured PSD of the disturbance.
|
||||
|
||||
<p>
|
||||
The effect of these disturbances on the distance \(D\) is computed for all active damping techniques.
|
||||
We then compute the Cumulative Amplitude Spectrum (figure <a href="#org7065c50">36</a>).
|
||||
We then compute the Cumulative Amplitude Spectrum (figure <a href="#orgea4a3e5">36</a>).
|
||||
</p>
|
||||
|
||||
<div id="org7065c50" class="figure">
|
||||
<div id="orgea4a3e5" class="figure">
|
||||
<p><img src="figs/uniaxial-comp-cas-dist.png" alt="uniaxial-comp-cas-dist.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 36: </span>Comparison of the Cumulative Amplitude Spectrum of \(D\) for different active damping techniques (<a href="./figs/uniaxial-comp-cas-dist.png">png</a>, <a href="./figs/uniaxial-comp-cas-dist.pdf">pdf</a>)</p>
|
||||
@ -1483,7 +1483,7 @@ We then compute the Cumulative Amplitude Spectrum (figure <a href="#org7065c50">
|
||||
<p>
|
||||
The obtained Root Mean Square Value for each active damping technique is shown below.
|
||||
</p>
|
||||
<table id="orgb85f411" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org4d742c7" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 1:</span> Obtain Root Mean Square value of \(D\) for each Active Damping Technique applied</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -1526,11 +1526,11 @@ It is important to note that the effect of direct forces applied to the sample a
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf592486" class="outline-3">
|
||||
<h3 id="orgf592486"><span class="section-number-3">7.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-org1cab4a1" class="outline-3">
|
||||
<h3 id="org1cab4a1"><span class="section-number-3">7.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-7-4">
|
||||
|
||||
<div id="org8d5fcfc" class="figure">
|
||||
<div id="orgd715679" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 37: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
|
||||
@ -1538,10 +1538,10 @@ It is important to note that the effect of direct forces applied to the sample a
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfc2e28b" class="outline-3">
|
||||
<h3 id="orgfc2e28b"><span class="section-number-3">7.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org89243de" class="outline-3">
|
||||
<h3 id="org89243de"><span class="section-number-3">7.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-7-5">
|
||||
<table id="org56bbb29" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<table id="org25a4511" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 2:</span> Comparison of proposed active damping techniques</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -1608,15 +1608,15 @@ It is important to note that the effect of direct forces applied to the sample a
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgded5bc7" class="outline-2">
|
||||
<h2 id="orgded5bc7"><span class="section-number-2">8</span> Voice Coil</h2>
|
||||
<div id="outline-container-orgf7fa09b" class="outline-2">
|
||||
<h2 id="orgf7fa09b"><span class="section-number-2">8</span> Voice Coil</h2>
|
||||
<div class="outline-text-2" id="text-8">
|
||||
<p>
|
||||
<a id="orga8a45b8"></a>
|
||||
<a id="org42314a9"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-orgbba145f" class="outline-3">
|
||||
<h3 id="orgbba145f"><span class="section-number-3">8.1</span> Init</h3>
|
||||
<div id="outline-container-org5bfd692" class="outline-3">
|
||||
<h3 id="org5bfd692"><span class="section-number-3">8.1</span> Init</h3>
|
||||
<div class="outline-text-3" id="text-8-1">
|
||||
<p>
|
||||
We initialize all the stages with the default parameters.
|
||||
@ -1628,8 +1628,8 @@ All the controllers are set to 0 (Open Loop).
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org465be28" class="outline-3">
|
||||
<h3 id="org465be28"><span class="section-number-3">8.2</span> Identification</h3>
|
||||
<div id="outline-container-org145a9df" class="outline-3">
|
||||
<h3 id="org145a9df"><span class="section-number-3">8.2</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-8-2">
|
||||
<p>
|
||||
We identify the dynamics of the system.
|
||||
@ -1692,8 +1692,8 @@ Finally, we save the identified system dynamics for further analysis.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgda14068" class="outline-3">
|
||||
<h3 id="orgda14068"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3>
|
||||
<div id="outline-container-org3b53ae6" class="outline-3">
|
||||
<h3 id="org3b53ae6"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3>
|
||||
<div class="outline-text-3" id="text-8-3">
|
||||
<p>
|
||||
We load the dynamics when using a piezo-electric nano hexapod to compare the results.
|
||||
@ -1707,19 +1707,19 @@ We load the dynamics when using a piezo-electric nano hexapod to compare the res
|
||||
We show several plots representing the sensitivity to disturbances:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>in figure <a href="#org164997f">38</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
|
||||
<li>in figure <a href="#org6542b94">39</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
|
||||
<li>in figure <a href="#org34141f6">38</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
|
||||
<li>in figure <a href="#orgbbc6e41">39</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<div id="org164997f" class="figure">
|
||||
<div id="org34141f6" class="figure">
|
||||
<p><img src="figs/uniaxial-sensitivity-vc-disturbances.png" alt="uniaxial-sensitivity-vc-disturbances.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 38: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-disturbances.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6542b94" class="figure">
|
||||
<div id="orgbbc6e41" class="figure">
|
||||
<p><img src="figs/uniaxial-sensitivity-vc-force-dist.png" alt="uniaxial-sensitivity-vc-force-dist.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 39: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-force-dist.pdf">pdf</a>)</p>
|
||||
@ -1727,8 +1727,8 @@ We show several plots representing the sensitivity to disturbances:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org49bb7e7" class="outline-3">
|
||||
<h3 id="org49bb7e7"><span class="section-number-3">8.4</span> Noise Budget</h3>
|
||||
<div id="outline-container-org33c2392" class="outline-3">
|
||||
<h3 id="org33c2392"><span class="section-number-3">8.4</span> Noise Budget</h3>
|
||||
<div class="outline-text-3" id="text-8-4">
|
||||
<p>
|
||||
We first load the measured PSD of the disturbance.
|
||||
@ -1740,11 +1740,11 @@ We first load the measured PSD of the disturbance.
|
||||
|
||||
<p>
|
||||
The effect of these disturbances on the distance \(D\) is computed below.
|
||||
The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#orgecf9cc7">40</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org91093e7">41</a>.
|
||||
The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#orgf38f860">40</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org661a0fa">41</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#org91093e7">41</a>.
|
||||
The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#org661a0fa">41</a>.
|
||||
</p>
|
||||
<pre class="example">
|
||||
4.8793e-06
|
||||
@ -1752,14 +1752,14 @@ The Root Mean Square value of the obtained displacement \(D\) is computed below
|
||||
|
||||
|
||||
|
||||
<div id="orgecf9cc7" class="figure">
|
||||
<div id="orgf38f860" class="figure">
|
||||
<p><img src="figs/uniaxial-vc-psd-dist.png" alt="uniaxial-vc-psd-dist.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 40: </span>PSD of the displacement \(D\) due to disturbances (<a href="./figs/uniaxial-vc-psd-dist.png">png</a>, <a href="./figs/uniaxial-vc-psd-dist.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org91093e7" class="figure">
|
||||
<div id="org661a0fa" class="figure">
|
||||
<p><img src="figs/uniaxial-vc-cas-dist.png" alt="uniaxial-vc-cas-dist.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 41: </span>CAS of the displacement \(D\) due the disturbances (<a href="./figs/uniaxial-vc-cas-dist.png">png</a>, <a href="./figs/uniaxial-vc-cas-dist.pdf">pdf</a>)</p>
|
||||
@ -1777,8 +1777,8 @@ Thus, it may be desirable to use voice coil actuators.
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org04357b8" class="outline-3">
|
||||
<h3 id="org04357b8"><span class="section-number-3">8.5</span> Integral Force Feedback</h3>
|
||||
<div id="outline-container-org332ecb6" class="outline-3">
|
||||
<h3 id="org332ecb6"><span class="section-number-3">8.5</span> Integral Force Feedback</h3>
|
||||
<div class="outline-text-3" id="text-8-5">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">K_iff = <span class="org-type">-</span><span class="org-highlight-numbers-number">20</span><span class="org-type">/</span>s;
|
||||
@ -1786,7 +1786,7 @@ Thus, it may be desirable to use voice coil actuators.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgb31c44e" class="figure">
|
||||
<div id="orgd31f0b8" class="figure">
|
||||
<p><img src="figs/uniaxial_iff_vc_open_loop.png" alt="uniaxial_iff_vc_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 42: </span>Open Loop Transfer Function for IFF control when using a voice coil actuator (<a href="./figs/uniaxial_iff_vc_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_vc_open_loop.pdf">pdf</a>)</p>
|
||||
@ -1794,8 +1794,8 @@ Thus, it may be desirable to use voice coil actuators.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org83d9caa" class="outline-3">
|
||||
<h3 id="org83d9caa"><span class="section-number-3">8.6</span> Identification of the Damped Plant</h3>
|
||||
<div id="outline-container-orgd420efb" class="outline-3">
|
||||
<h3 id="orgd420efb"><span class="section-number-3">8.6</span> Identification of the Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-8-6">
|
||||
<p>
|
||||
Let's initialize the system prior to identification.
|
||||
@ -1873,14 +1873,14 @@ G_vc_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge278186" class="outline-3">
|
||||
<h3 id="orge278186"><span class="section-number-3">8.7</span> Noise Budget</h3>
|
||||
<div id="outline-container-org99ecd1f" class="outline-3">
|
||||
<h3 id="org99ecd1f"><span class="section-number-3">8.7</span> Noise Budget</h3>
|
||||
<div class="outline-text-3" id="text-8-7">
|
||||
<p>
|
||||
We compute the obtain PSD of the displacement \(D\) when using IFF.
|
||||
</p>
|
||||
|
||||
<div id="orgd1d775f" class="figure">
|
||||
<div id="orgda5106f" class="figure">
|
||||
<p><img src="figs/uniaxial-cas-iff-vc.png" alt="uniaxial-cas-iff-vc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 43: </span>CAS of the displacement \(D\) (<a href="./figs/uniaxial-cas-iff-vc.png">png</a>, <a href="./figs/uniaxial-cas-iff-vc.pdf">pdf</a>)</p>
|
||||
@ -1888,8 +1888,8 @@ We compute the obtain PSD of the displacement \(D\) when using IFF.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org152df36" class="outline-3">
|
||||
<h3 id="org152df36"><span class="section-number-3">8.8</span> Conclusion</h3>
|
||||
<div id="outline-container-orgffe5e36" class="outline-3">
|
||||
<h3 id="orgffe5e36"><span class="section-number-3">8.8</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-8-8">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -1907,7 +1907,7 @@ Similarly, it would require much lower bandwidth to attain the same level of dis
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-11-05 mar. 11:27</p>
|
||||
<p class="date">Created: 2019-11-11 lun. 14:50</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
@ -825,7 +825,7 @@ The Root Mean Square value of the obtained displacement $D$ is computed below an
|
||||
plot(dist_f.f, psd_rz_d, 'DisplayName', '$R_z$');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('CAS of the effect of disturbances on $D$ $\left[\frac{m^2}{Hz}\right]$'); xlabel('Frequency [Hz]');
|
||||
ylabel('PSD of the effect of disturbances on $D$ $\left[\frac{m^2}{Hz}\right]$'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast')
|
||||
xlim([0.5, 500]);
|
||||
#+end_src
|
||||
@ -836,7 +836,7 @@ The Root Mean Square value of the obtained displacement $D$ is computed below an
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial-psd-dist
|
||||
#+CAPTION: caption ([[./figs/uniaxial-psd-dist.png][png]], [[./figs/uniaxial-psd-dist.pdf][pdf]])
|
||||
#+CAPTION: PSD of the effect of disturbances on $D$ ([[./figs/uniaxial-psd-dist.png][png]], [[./figs/uniaxial-psd-dist.pdf][pdf]])
|
||||
[[file:figs/uniaxial-psd-dist.png]]
|
||||
|
||||
|
||||
@ -862,7 +862,7 @@ The Root Mean Square value of the obtained displacement $D$ is computed below an
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial-cas-dist
|
||||
#+CAPTION: caption ([[./figs/uniaxial-cas-dist.png][png]], [[./figs/uniaxial-cas-dist.pdf][pdf]])
|
||||
#+CAPTION: CAS of the effect of disturbances on $D$ ([[./figs/uniaxial-cas-dist.png][png]], [[./figs/uniaxial-cas-dist.pdf][pdf]])
|
||||
[[file:figs/uniaxial-cas-dist.png]]
|
||||
|
||||
** Plant
|
||||
|
||||
Loading…
Reference in New Issue
Block a user