Add noise budget to compare active damping techniques
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@ -3,7 +3,7 @@
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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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<!-- 2019-10-28 lun. 17:34 -->
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<!-- 2019-11-04 lun. 17:33 -->
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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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@ -280,58 +280,60 @@ 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="#orgfc3044a">1. Simscape Model</a></li>
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<li><a href="#org8da4eb0">2. Undamped System</a>
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<li><a href="#orgac9343f">1. Simscape Model</a></li>
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<li><a href="#org3890417">2. Undamped System</a>
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<ul>
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<li><a href="#orgcb2b0a1">2.1. Init</a></li>
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<li><a href="#org7f40bf7">2.2. Identification</a></li>
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<li><a href="#org7908bab">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org5a57afd">2.4. Plant</a></li>
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<li><a href="#orgbc01ced">2.1. Init</a></li>
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<li><a href="#org699bc2c">2.2. Identification</a></li>
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<li><a href="#org0c59d84">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#orgb191841">2.4. Noise Budget</a></li>
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<li><a href="#org1b2f77b">2.5. Plant</a></li>
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</ul>
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</li>
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<li><a href="#org68d1bb0">3. Integral Force Feedback</a>
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<li><a href="#org27aabe3">3. Integral Force Feedback</a>
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<ul>
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<li><a href="#orga5e22eb">3.1. Control Design</a></li>
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<li><a href="#org0fdf2fd">3.2. Identification</a></li>
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<li><a href="#org8b81fd6">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org80d5d2d">3.4. Damped Plant</a></li>
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<li><a href="#orga9ed49c">3.5. Conclusion</a></li>
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<li><a href="#org04b5ef2">3.1. Control Design</a></li>
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<li><a href="#orgd976043">3.2. Identification</a></li>
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<li><a href="#orgb785fd5">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org7f2e353">3.4. Damped Plant</a></li>
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<li><a href="#org46695ba">3.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org5d0bc94">4. Relative Motion Control</a>
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<li><a href="#org8f75c3f">4. Relative Motion Control</a>
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<ul>
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<li><a href="#org4ffacc7">4.1. Control Design</a></li>
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<li><a href="#orgf86862c">4.2. Identification</a></li>
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<li><a href="#org0211838">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orgefb061f">4.4. Damped Plant</a></li>
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<li><a href="#org467a5d6">4.5. Conclusion</a></li>
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<li><a href="#org7291ab1">4.1. Control Design</a></li>
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<li><a href="#org72b4f0a">4.2. Identification</a></li>
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<li><a href="#org7669eee">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orgab2a3d1">4.4. Damped Plant</a></li>
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<li><a href="#orgbc19b27">4.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org408eed0">5. Direct Velocity Feedback</a>
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<li><a href="#org264e55c">5. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#org64e7b3f">5.1. Control Design</a></li>
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<li><a href="#orga75fa6d">5.2. Identification</a></li>
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<li><a href="#org0d535fa">5.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org9643807">5.4. Damped Plant</a></li>
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<li><a href="#org6e6fd47">5.5. Conclusion</a></li>
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<li><a href="#orge1aa5cd">5.1. Control Design</a></li>
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<li><a href="#org2a880b1">5.2. Identification</a></li>
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<li><a href="#orgd7e4638">5.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org9524bf4">5.4. Damped Plant</a></li>
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<li><a href="#org329f7b9">5.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgd792cab">6. With Cedrat Piezo-electric Actuators</a>
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<li><a href="#org8ffadeb">6. With Cedrat Piezo-electric Actuators</a>
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<ul>
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<li><a href="#org7707a0a">6.1. Identification</a></li>
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<li><a href="#orgd921ae7">6.2. Control Design</a></li>
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<li><a href="#org1d5a39c">6.3. Identification</a></li>
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<li><a href="#orgb163c6c">6.4. Sensitivity to Disturbance</a></li>
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<li><a href="#org552dcab">6.5. Damped Plant</a></li>
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<li><a href="#org5065aae">6.6. Conclusion</a></li>
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<li><a href="#org8f92e1b">6.1. Identification</a></li>
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<li><a href="#org9183f23">6.2. Control Design</a></li>
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<li><a href="#orge8484c9">6.3. Identification</a></li>
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<li><a href="#org35ee201">6.4. Sensitivity to Disturbance</a></li>
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<li><a href="#orgfdfe26c">6.5. Damped Plant</a></li>
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<li><a href="#org7b0ae1d">6.6. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org60dfb12">7. Comparison of Active Damping Techniques</a>
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<li><a href="#org51051c1">7. Comparison of Active Damping Techniques</a>
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<ul>
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<li><a href="#org249a650">7.1. Load the plants</a></li>
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<li><a href="#org0c1cccb">7.2. Sensitivity to Disturbance</a></li>
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<li><a href="#orgb54c9e3">7.3. Damped Plant</a></li>
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<li><a href="#org1c67523">7.4. Conclusion</a></li>
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<li><a href="#orga925887">7.1. Load the plants</a></li>
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<li><a href="#orga01b1a9">7.2. Sensitivity to Disturbance</a></li>
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<li><a href="#orga4fdd66">7.3. Noise Budget</a></li>
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<li><a href="#orgbb2291d">7.4. Damped Plant</a></li>
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<li><a href="#org40f7a4d">7.5. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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@ -346,11 +348,11 @@ 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-orgfc3044a" class="outline-2">
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<h2 id="orgfc3044a"><span class="section-number-2">1</span> Simscape Model</h2>
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<div id="outline-container-orgac9343f" class="outline-2">
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<h2 id="orgac9343f"><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 schematic of the uniaxial model used for simulations is represented in figure <a href="#orgc5e0a56">1</a>.
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#org7ac1a00">1</a>.
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</p>
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<p>
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@ -394,7 +396,7 @@ The control signal \(u\) is:
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</ul>
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<div id="orgc5e0a56" class="figure">
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<div id="org7ac1a00" 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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@ -403,11 +405,11 @@ 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="#orgdb9985c">2</a>.
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Schematics of the active damping techniques are displayed in figure <a href="#orgb379a31">2</a>.
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</p>
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<div id="orgdb9985c" class="figure">
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<div id="orgb379a31" 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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@ -415,16 +417,16 @@ 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-org8da4eb0" class="outline-2">
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<h2 id="org8da4eb0"><span class="section-number-2">2</span> Undamped System</h2>
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<div id="outline-container-org3890417" class="outline-2">
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<h2 id="org3890417"><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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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-orgcb2b0a1" class="outline-3">
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<h3 id="orgcb2b0a1"><span class="section-number-3">2.1</span> Init</h3>
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<div id="outline-container-orgbc01ced" class="outline-3">
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<h3 id="orgbc01ced"><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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@ -436,8 +438,8 @@ 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-org7f40bf7" class="outline-3">
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<h3 id="org7f40bf7"><span class="section-number-3">2.2</span> Identification</h3>
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<div id="outline-container-org699bc2c" class="outline-3">
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<h3 id="org699bc2c"><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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@ -500,19 +502,19 @@ 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-org7908bab" class="outline-3">
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<h3 id="org7908bab"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
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<div id="outline-container-org0c59d84" class="outline-3">
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<h3 id="org0c59d84"><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="#orgd82c2ce">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="#org72d40e7">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="#orgc6b4646">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="#orgbcfd91e">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="orgd82c2ce" class="figure">
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<div id="orgc6b4646" 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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@ -520,7 +522,7 @@ We show several plots representing the sensitivity to disturbances:
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<div id="org72d40e7" class="figure">
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<div id="orgbcfd91e" 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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@ -528,39 +530,81 @@ 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-org5a57afd" class="outline-3">
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<h3 id="org5a57afd"><span class="section-number-3">2.4</span> Plant</h3>
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<div id="outline-container-orgb191841" class="outline-3">
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<h3 id="orgb191841"><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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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="#org5789c3f">5</a>.
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We first load the measured PSD of the disturbance.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/dist_psd.mat'</span>, <span class="org-string">'dist_f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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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="#orgb199386">5</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org3989b84">6</a>.
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</p>
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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="#org3989b84">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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</pre>
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<div id="orgb199386" 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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</div>
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<div id="org3989b84" 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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</div>
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</div>
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</div>
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<div id="outline-container-org1b2f77b" class="outline-3">
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<h3 id="org1b2f77b"><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="#org63b704d">7</a>.
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It corresponds to the plant to control.
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</p>
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<div id="org5789c3f" class="figure">
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<div id="org63b704d" class="figure">
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<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
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<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>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org68d1bb0" class="outline-2">
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<h2 id="org68d1bb0"><span class="section-number-2">3</span> Integral Force Feedback</h2>
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<div id="outline-container-org27aabe3" class="outline-2">
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<h2 id="org27aabe3"><span class="section-number-2">3</span> Integral Force Feedback</h2>
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<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="org36327e7"></a>
|
||||
<a id="orgcfb1bdd"></a>
|
||||
</p>
|
||||
|
||||
<div id="org6ca8a23" class="figure">
|
||||
<div id="org2faff5f" 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 6: </span>Uniaxial IFF Control Schematic</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Uniaxial IFF Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orga5e22eb" class="outline-3">
|
||||
<h3 id="orga5e22eb"><span class="section-number-3">3.1</span> Control Design</h3>
|
||||
<div id="outline-container-org04b5ef2" class="outline-3">
|
||||
<h3 id="org04b5ef2"><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>;
|
||||
@ -572,10 +616,10 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org5063cb4" class="figure">
|
||||
<div id="org7cefef0" class="figure">
|
||||
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </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>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@ -587,16 +631,16 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org495687f" class="figure">
|
||||
<div id="org2c6c9a0" class="figure">
|
||||
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0fdf2fd" class="outline-3">
|
||||
<h3 id="org0fdf2fd"><span class="section-number-3">3.2</span> Identification</h3>
|
||||
<div id="outline-container-orgd976043" class="outline-3">
|
||||
<h3 id="orgd976043"><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.
|
||||
@ -679,39 +723,39 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8b81fd6" class="outline-3">
|
||||
<h3 id="org8b81fd6"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-orgb785fd5" class="outline-3">
|
||||
<h3 id="orgb785fd5"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
|
||||
<div id="org307c8d8" class="figure">
|
||||
<div id="org9085a3e" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </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>
|
||||
<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="orgabd6245" class="figure">
|
||||
<div id="org087512a" 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 10: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org80d5d2d" class="outline-3">
|
||||
<h3 id="org80d5d2d"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-org7f2e353" class="outline-3">
|
||||
<h3 id="org7f2e353"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
|
||||
<div id="org35f8f43" class="figure">
|
||||
<div id="orge8dfaf6" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga9ed49c" class="outline-3">
|
||||
<h3 id="orga9ed49c"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org46695ba" class="outline-3">
|
||||
<h3 id="org46695ba"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -723,25 +767,25 @@ Integral Force Feedback:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5d0bc94" class="outline-2">
|
||||
<h2 id="org5d0bc94"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||
<div id="outline-container-org8f75c3f" class="outline-2">
|
||||
<h2 id="org8f75c3f"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="org5737634"></a>
|
||||
<a id="org14dacd3"></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="org742e0c1" class="figure">
|
||||
<div id="orgcb12d53" 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 12: </span>Uniaxial RMC Control Schematic</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Uniaxial RMC Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org4ffacc7" class="outline-3">
|
||||
<h3 id="org4ffacc7"><span class="section-number-3">4.1</span> Control Design</h3>
|
||||
<div id="outline-container-org7291ab1" class="outline-3">
|
||||
<h3 id="org7291ab1"><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>;
|
||||
@ -753,10 +797,10 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org9fd5b87" class="figure">
|
||||
<div id="org7c9427d" class="figure">
|
||||
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </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>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@ -769,16 +813,16 @@ A Low pass Filter is added to make the controller transfer function proper.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7d6a1ae" class="figure">
|
||||
<div id="org782296b" class="figure">
|
||||
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf86862c" class="outline-3">
|
||||
<h3 id="orgf86862c"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div id="outline-container-org72b4f0a" class="outline-3">
|
||||
<h3 id="org72b4f0a"><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.
|
||||
@ -862,39 +906,39 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-org0211838" class="outline-3">
|
||||
<h3 id="org0211838"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org7669eee" class="outline-3">
|
||||
<h3 id="org7669eee"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
|
||||
<div id="org00d0d6e" class="figure">
|
||||
<div id="orga53e45b" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </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>
|
||||
<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="org0006b16" class="figure">
|
||||
<div id="orgb21d169" 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 16: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgefb061f" class="outline-3">
|
||||
<h3 id="orgefb061f"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-orgab2a3d1" class="outline-3">
|
||||
<h3 id="orgab2a3d1"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
|
||||
<div id="org2092a67" class="figure">
|
||||
<div id="orgc8a382a" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org467a5d6" class="outline-3">
|
||||
<h3 id="org467a5d6"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||
<div id="outline-container-orgbc19b27" class="outline-3">
|
||||
<h3 id="orgbc19b27"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-4-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -906,25 +950,25 @@ Relative Motion Control:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org408eed0" class="outline-2">
|
||||
<h2 id="org408eed0"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||
<div id="outline-container-org264e55c" class="outline-2">
|
||||
<h2 id="org264e55c"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<p>
|
||||
<a id="orgfc1ffa1"></a>
|
||||
<a id="org96d3a12"></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="org070b73d" class="figure">
|
||||
<div id="org0856bca" 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 18: </span>Uniaxial DVF Control Schematic</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Uniaxial DVF Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org64e7b3f" class="outline-3">
|
||||
<h3 id="org64e7b3f"><span class="section-number-3">5.1</span> Control Design</h3>
|
||||
<div id="outline-container-orge1aa5cd" class="outline-3">
|
||||
<h3 id="orge1aa5cd"><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>;
|
||||
@ -932,10 +976,10 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org56e8509" class="figure">
|
||||
<div id="orga963d24" class="figure">
|
||||
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </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>
|
||||
<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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -944,16 +988,16 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgc80a1c2" class="figure">
|
||||
<div id="org84510c2" class="figure">
|
||||
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 20: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga75fa6d" class="outline-3">
|
||||
<h3 id="orga75fa6d"><span class="section-number-3">5.2</span> Identification</h3>
|
||||
<div id="outline-container-org2a880b1" class="outline-3">
|
||||
<h3 id="org2a880b1"><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.
|
||||
@ -1036,39 +1080,39 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0d535fa" class="outline-3">
|
||||
<h3 id="org0d535fa"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-orgd7e4638" class="outline-3">
|
||||
<h3 id="orgd7e4638"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
|
||||
<div id="org30e1316" class="figure">
|
||||
<div id="org5a094e1" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 21: </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>
|
||||
<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="orge40e605" class="figure">
|
||||
<div id="orga67a694" 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 22: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9643807" class="outline-3">
|
||||
<h3 id="org9643807"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-org9524bf4" class="outline-3">
|
||||
<h3 id="org9524bf4"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-5-4">
|
||||
|
||||
<div id="org48982d0" class="figure">
|
||||
<div id="org6b78506" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 23: </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>
|
||||
<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org6e6fd47" class="outline-3">
|
||||
<h3 id="org6e6fd47"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org329f7b9" class="outline-3">
|
||||
<h3 id="org329f7b9"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-5-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -1079,12 +1123,12 @@ Direct Velocity Feedback:
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgd792cab" class="outline-2">
|
||||
<h2 id="orgd792cab"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2>
|
||||
<div id="outline-container-org8ffadeb" class="outline-2">
|
||||
<h2 id="org8ffadeb"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
</div>
|
||||
<div id="outline-container-org7707a0a" class="outline-3">
|
||||
<h3 id="org7707a0a"><span class="section-number-3">6.1</span> Identification</h3>
|
||||
<div id="outline-container-org8f92e1b" class="outline-3">
|
||||
<h3 id="org8f92e1b"><span class="section-number-3">6.1</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<p>
|
||||
We identify the dynamics of the system.
|
||||
@ -1139,18 +1183,18 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd921ae7" class="outline-3">
|
||||
<h3 id="orgd921ae7"><span class="section-number-3">6.2</span> Control Design</h3>
|
||||
<div id="outline-container-org9183f23" class="outline-3">
|
||||
<h3 id="org9183f23"><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="org8bae400" class="figure">
|
||||
<div id="org8d3fc99" class="figure">
|
||||
<p><img src="figs/uniaxial_cedrat_plant.png" alt="uniaxial_cedrat_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 24: </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>
|
||||
<p><span class="figure-number">Figure 26: </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>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@ -1162,16 +1206,16 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0e53970" class="figure">
|
||||
<div id="orgc5810ab" class="figure">
|
||||
<p><img src="figs/uniaxial_cedrat_open_loop.png" alt="uniaxial_cedrat_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 25: </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>
|
||||
<p><span class="figure-number">Figure 27: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1d5a39c" class="outline-3">
|
||||
<h3 id="org1d5a39c"><span class="section-number-3">6.3</span> Identification</h3>
|
||||
<div id="outline-container-orge8484c9" class="outline-3">
|
||||
<h3 id="orge8484c9"><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.
|
||||
@ -1254,39 +1298,39 @@ G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb163c6c" class="outline-3">
|
||||
<h3 id="orgb163c6c"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org35ee201" class="outline-3">
|
||||
<h3 id="org35ee201"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-6-4">
|
||||
|
||||
<div id="org6c93b19" class="figure">
|
||||
<div id="org25c9462" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_cedrat.png" alt="uniaxial_sensitivity_dist_cedrat.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 26: </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>
|
||||
<p><span class="figure-number">Figure 28: </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="org1b2d2df" class="figure">
|
||||
<div id="org401a0e9" 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 27: </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>
|
||||
<p><span class="figure-number">Figure 29: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org552dcab" class="outline-3">
|
||||
<h3 id="org552dcab"><span class="section-number-3">6.5</span> Damped Plant</h3>
|
||||
<div id="outline-container-orgfdfe26c" class="outline-3">
|
||||
<h3 id="orgfdfe26c"><span class="section-number-3">6.5</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-6-5">
|
||||
|
||||
<div id="orge59303f" class="figure">
|
||||
<div id="org96e840c" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_cedrat_damped.png" alt="uniaxial_plant_cedrat_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 28: </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>
|
||||
<p><span class="figure-number">Figure 30: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5065aae" class="outline-3">
|
||||
<h3 id="org5065aae"><span class="section-number-3">6.6</span> Conclusion</h3>
|
||||
<div id="outline-container-org7b0ae1d" class="outline-3">
|
||||
<h3 id="org7b0ae1d"><span class="section-number-3">6.6</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-6-6">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -1298,15 +1342,15 @@ This gives similar results than with a classical force sensor.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org60dfb12" class="outline-2">
|
||||
<h2 id="org60dfb12"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2>
|
||||
<div id="outline-container-org51051c1" class="outline-2">
|
||||
<h2 id="org51051c1"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2>
|
||||
<div class="outline-text-2" id="text-7">
|
||||
<p>
|
||||
<a id="orgc7002a8"></a>
|
||||
<a id="orgf321de8"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org249a650" class="outline-3">
|
||||
<h3 id="org249a650"><span class="section-number-3">7.1</span> Load the plants</h3>
|
||||
<div id="outline-container-orga925887" class="outline-3">
|
||||
<h3 id="orga925887"><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>;
|
||||
@ -1315,60 +1359,125 @@ This gives similar results than with a classical force sensor.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0c1cccb" class="outline-3">
|
||||
<h3 id="org0c1cccb"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-orga01b1a9" class="outline-3">
|
||||
<h3 id="orga01b1a9"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-7-2">
|
||||
|
||||
<div id="org9992967" class="figure">
|
||||
<div id="orgafd9b97" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 29: </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>
|
||||
<p><span class="figure-number">Figure 31: </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>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="orgc7a133b" class="figure">
|
||||
<div id="org3efc30e" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 30: </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>
|
||||
<p><span class="figure-number">Figure 32: </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="org8eaf52e" class="figure">
|
||||
<div id="orgb329c3d" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 31: </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>
|
||||
<p><span class="figure-number">Figure 33: </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="orgb554437" class="figure">
|
||||
<div id="orgc3f8a25" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 32: </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>
|
||||
<p><span class="figure-number">Figure 34: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb54c9e3" class="outline-3">
|
||||
<h3 id="orgb54c9e3"><span class="section-number-3">7.3</span> Damped Plant</h3>
|
||||
<div id="outline-container-orga4fdd66" class="outline-3">
|
||||
<h3 id="orga4fdd66"><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.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./disturbances/mat/dist_psd.mat'</span>, <span class="org-string">'dist_f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div id="org9375b1e" class="figure">
|
||||
<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="#orge43e5e4">35</a>).
|
||||
</p>
|
||||
|
||||
<div id="orge43e5e4" class="figure">
|
||||
<p><img src="figs/uniaxial-comp-cas-dist.png" alt="uniaxial-comp-cas-dist.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 35: </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>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained Root Mean Square Value for each active damping technique is shown below.
|
||||
</p>
|
||||
<table id="org3b74f43" 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>
|
||||
<col class="org-left" />
|
||||
|
||||
<col class="org-right" />
|
||||
</colgroup>
|
||||
<thead>
|
||||
<tr>
|
||||
<th scope="col" class="org-left"> </th>
|
||||
<th scope="col" class="org-right">D [m rms]</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-left">OL</td>
|
||||
<td class="org-right">3.38e-06</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">IFF</td>
|
||||
<td class="org-right">3.40e-06</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">RMC</td>
|
||||
<td class="org-right">3.37e-06</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">DVF</td>
|
||||
<td class="org-right">3.38e-06</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<p>
|
||||
It is important to note that the effect of direct forces applied to the sample are not taken into account here.
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbb2291d" class="outline-3">
|
||||
<h3 id="orgbb2291d"><span class="section-number-3">7.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-7-4">
|
||||
|
||||
<div id="org3213591" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 33: </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>
|
||||
<p><span class="figure-number">Figure 36: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1c67523" class="outline-3">
|
||||
<h3 id="org1c67523"><span class="section-number-3">7.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-7-4">
|
||||
<p>
|
||||
#name: tab:active<sub>damping</sub><sub>comparison</sub>
|
||||
</p>
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 1:</span> Comparison of proposed active damping techniques</caption>
|
||||
<div id="outline-container-org40f7a4d" class="outline-3">
|
||||
<h3 id="org40f7a4d"><span class="section-number-3">7.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-7-5">
|
||||
<table id="org5ad7ed4" 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>
|
||||
<col class="org-left" />
|
||||
@ -1422,22 +1531,22 @@ This gives similar results than with a classical force sensor.
|
||||
<td class="org-left">-</td>
|
||||
<td class="org-left">+</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-left">Overall RMS of \(D\)</td>
|
||||
<td class="org-left">=</td>
|
||||
<td class="org-left">=</td>
|
||||
<td class="org-left">=</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<div class="important">
|
||||
<p>
|
||||
The next step is to take into account the power spectral density of each disturbance.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-10-28 lun. 17:34</p>
|
||||
<p class="date">Created: 2019-11-04 lun. 17:33</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
@ -765,12 +765,14 @@ We show several plots representing the sensitivity to disturbances:
|
||||
|
||||
subplot(2, 1, 1);
|
||||
title('$F_{ty}$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('D', 'Fty'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
|
||||
subplot(2, 1, 2);
|
||||
title('$F_{rz}$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('D', 'Frz'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
@ -785,6 +787,81 @@ We show several plots representing the sensitivity to disturbances:
|
||||
#+CAPTION: Sensitivity to disturbances ([[./figs/uniaxial-sensitivity-force-dist.png][png]], [[./figs/uniaxial-sensitivity-force-dist.pdf][pdf]])
|
||||
[[file:figs/uniaxial-sensitivity-force-dist.png]]
|
||||
|
||||
** Noise Budget
|
||||
We first load the measured PSD of the disturbance.
|
||||
#+begin_src matlab
|
||||
load('./disturbances/mat/dist_psd.mat', 'dist_f');
|
||||
#+end_src
|
||||
|
||||
The effect of these disturbances on the distance $D$ is computed below.
|
||||
#+begin_src matlab :exports none
|
||||
% Power Spectral Density of the relative Displacement [m^2/Hz]
|
||||
psd_gm_d = dist_f.psd_gm.*abs(squeeze(freqresp(G('D', 'Dw'), dist_f.f, 'Hz'))).^2;
|
||||
psd_ty_d = dist_f.psd_ty.*abs(squeeze(freqresp(G('D', 'Fty'), dist_f.f, 'Hz'))).^2;
|
||||
psd_rz_d = dist_f.psd_rz.*abs(squeeze(freqresp(G('D', 'Frz'), dist_f.f, 'Hz'))).^2;
|
||||
#+end_src
|
||||
|
||||
The PSD of the obtain distance $D$ due to each of the perturbation is shown in figure [[fig:uniaxial-psd-dist]] and the Cumulative Amplitude Spectrum is shown in figure [[fig:uniaxial-cas-dist]].
|
||||
|
||||
|
||||
The Root Mean Square value of the obtained displacement $D$ is computed below and can be determined from the figure [[fig:uniaxial-cas-dist]].
|
||||
#+begin_src matlab :results value replace :exports results
|
||||
cas_tot_d = sqrt(cumtrapz(dist_f.f, psd_rz_d+psd_ty_d+psd_gm_d)); cas_tot_d(end)
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: 3.3793e-06
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(dist_f.f, psd_gm_d, 'DisplayName', '$D_w$');
|
||||
plot(dist_f.f, psd_ty_d, 'DisplayName', '$T_y$');
|
||||
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]');
|
||||
legend('location', 'northeast')
|
||||
xlim([0.5, 500]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial-psd-dist.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial-psd-dist
|
||||
#+CAPTION: caption ([[./figs/uniaxial-psd-dist.png][png]], [[./figs/uniaxial-psd-dist.pdf][pdf]])
|
||||
[[file:figs/uniaxial-psd-dist.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_gm_d)))), 'DisplayName', '$D_w$');
|
||||
plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_ty_d)))), 'DisplayName', '$T_y$');
|
||||
plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_rz_d)))), 'DisplayName', '$R_z$');
|
||||
plot(dist_f.f, flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_gm_d+psd_ty_d+psd_rz_d)))), 'k-', 'DisplayName', 'tot');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('CAS of the effect of disturbances on $D$ [m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast')
|
||||
xlim([0.5, 500]); ylim([1e-12, 1e-6]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial-cas-dist.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial-cas-dist
|
||||
#+CAPTION: caption ([[./figs/uniaxial-cas-dist.png][png]], [[./figs/uniaxial-cas-dist.pdf][pdf]])
|
||||
[[file:figs/uniaxial-cas-dist.png]]
|
||||
|
||||
** Plant
|
||||
The transfer function from the force $F$ applied by the nano-hexapod to the position of the sample $D$ is shown in figure [[fig:uniaxial-plant]].
|
||||
It corresponds to the plant to control.
|
||||
@ -2543,6 +2620,82 @@ This gives similar results than with a classical force sensor.
|
||||
#+CAPTION: Sensitivity to force disturbances - Comparison ([[./figs/uniaxial_sensitivity_frz.png][png]], [[./figs/uniaxial_sensitivity_frz.pdf][pdf]])
|
||||
[[file:figs/uniaxial_sensitivity_frz.png]]
|
||||
|
||||
** Noise Budget
|
||||
We first load the measured PSD of the disturbance.
|
||||
#+begin_src matlab
|
||||
load('./disturbances/mat/dist_psd.mat', 'dist_f');
|
||||
#+end_src
|
||||
|
||||
The effect of these disturbances on the distance $D$ is computed for all active damping techniques.
|
||||
#+begin_src matlab :exports none
|
||||
% Power Spectral Density of the relative Displacement [m^2/Hz]
|
||||
psd_ol_gm_d = dist_f.psd_gm.*abs(squeeze(freqresp(G('D', 'Dw'), dist_f.f, 'Hz'))).^2;
|
||||
psd_ol_ty_d = dist_f.psd_ty.*abs(squeeze(freqresp(G('D', 'Fty'), dist_f.f, 'Hz'))).^2;
|
||||
psd_ol_rz_d = dist_f.psd_rz.*abs(squeeze(freqresp(G('D', 'Frz'), dist_f.f, 'Hz'))).^2;
|
||||
|
||||
psd_iff_gm_d = dist_f.psd_gm.*abs(squeeze(freqresp(G_iff('D', 'Dw'), dist_f.f, 'Hz'))).^2;
|
||||
psd_iff_ty_d = dist_f.psd_ty.*abs(squeeze(freqresp(G_iff('D', 'Fty'), dist_f.f, 'Hz'))).^2;
|
||||
psd_iff_rz_d = dist_f.psd_rz.*abs(squeeze(freqresp(G_iff('D', 'Frz'), dist_f.f, 'Hz'))).^2;
|
||||
|
||||
psd_rmc_gm_d = dist_f.psd_gm.*abs(squeeze(freqresp(G_rmc('D', 'Dw'), dist_f.f, 'Hz'))).^2;
|
||||
psd_rmc_ty_d = dist_f.psd_ty.*abs(squeeze(freqresp(G_rmc('D', 'Fty'), dist_f.f, 'Hz'))).^2;
|
||||
psd_rmc_rz_d = dist_f.psd_rz.*abs(squeeze(freqresp(G_rmc('D', 'Frz'), dist_f.f, 'Hz'))).^2;
|
||||
|
||||
psd_dvf_gm_d = dist_f.psd_gm.*abs(squeeze(freqresp(G_dvf('D', 'Dw'), dist_f.f, 'Hz'))).^2;
|
||||
psd_dvf_ty_d = dist_f.psd_ty.*abs(squeeze(freqresp(G_dvf('D', 'Fty'), dist_f.f, 'Hz'))).^2;
|
||||
psd_dvf_rz_d = dist_f.psd_rz.*abs(squeeze(freqresp(G_dvf('D', 'Frz'), dist_f.f, 'Hz'))).^2;
|
||||
#+end_src
|
||||
|
||||
We then compute the Cumulative Amplitude Spectrum (figure [[fig:uniaxial-comp-cas-dist]]).
|
||||
#+begin_src matlab :exports none
|
||||
cas_ol_tot_d = flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_ol_rz_d+psd_ol_ty_d+psd_ol_gm_d))));
|
||||
cas_iff_tot_d = flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_iff_rz_d+psd_iff_ty_d+psd_iff_gm_d))));
|
||||
cas_rmc_tot_d = flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_rmc_rz_d+psd_rmc_ty_d+psd_rmc_gm_d))));
|
||||
cas_dvf_tot_d = flip(sqrt(-cumtrapz(flip(dist_f.f), flip(psd_dvf_rz_d+psd_dvf_ty_d+psd_dvf_gm_d))));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(dist_f.f, cas_ol_tot_d, 'DisplayName', 'OL');
|
||||
plot(dist_f.f, cas_iff_tot_d, 'DisplayName', 'IFF');
|
||||
plot(dist_f.f, cas_rmc_tot_d, 'DisplayName', 'RMC');
|
||||
plot(dist_f.f, cas_dvf_tot_d, 'DisplayName', 'DVF');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('CAS of the effect of disturbances on $D$ [m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast')
|
||||
xlim([0.5, 500]); ylim([1e-11, 1e-6]);
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial-comp-cas-dist.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial-comp-cas-dist
|
||||
#+CAPTION: Comparison of the Cumulative Amplitude Spectrum of $D$ for different active damping techniques ([[./figs/uniaxial-comp-cas-dist.png][png]], [[./figs/uniaxial-comp-cas-dist.pdf][pdf]])
|
||||
[[file:figs/uniaxial-comp-cas-dist.png]]
|
||||
|
||||
The obtained Root Mean Square Value for each active damping technique is shown below.
|
||||
#+begin_src matlab :exports results :results value table replace :tangle no :post addhdr(*this*)
|
||||
data2orgtable([cas_ol_tot_d(1); cas_iff_tot_d(1); cas_rmc_tot_d(1); cas_dvf_tot_d(1)], {'OL', 'IFF', 'RMC', 'DVF'}, {'D [m rms]'}, ' %.2e ');
|
||||
#+end_src
|
||||
|
||||
#+name: tab:rms_d_comp
|
||||
#+caption: Obtain Root Mean Square value of $D$ for each Active Damping Technique applied
|
||||
#+RESULTS:
|
||||
| | D [m rms] |
|
||||
|-----+-----------|
|
||||
| OL | 3.38e-06 |
|
||||
| IFF | 3.40e-06 |
|
||||
| RMC | 3.37e-06 |
|
||||
| DVF | 3.38e-06 |
|
||||
|
||||
It is important to note that the effect of direct forces applied to the sample are not taken into account here.
|
||||
|
||||
** Damped Plant
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
@ -2586,7 +2739,7 @@ This gives similar results than with a classical force sensor.
|
||||
|
||||
** Conclusion
|
||||
|
||||
#name: tab:active_damping_comparison
|
||||
#+name: tab:active_damping_comparison
|
||||
#+caption: Comparison of proposed active damping techniques
|
||||
| | IFF | RMC | DVF |
|
||||
|---------------------------+-----------------+-----------------+----------|
|
||||
@ -2595,7 +2748,4 @@ This gives similar results than with a classical force sensor.
|
||||
| Sensitivity ($D_w$) | - | + | - |
|
||||
| Sensitivity ($F_s$) | - (at low freq) | + | + |
|
||||
| Sensitivity ($F_{ty,rz}$) | + | - | + |
|
||||
|
||||
#+begin_important
|
||||
The next step is to take into account the power spectral density of each disturbance.
|
||||
#+end_important
|
||||
| Overall RMS of $D$ | = | = | = |
|
||||
|
||||
Binary file not shown.
Loading…
Reference in New Issue
Block a user