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@ -3,7 +3,7 @@
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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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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<head>
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<!-- 2019-10-24 jeu. 17:44 -->
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<!-- 2019-10-25 ven. 12:32 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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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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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Simscape Uniaxial Model</title>
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<title>Simscape Uniaxial Model</title>
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@ -246,6 +246,28 @@ for the JavaScript code in this tag.
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<script type="text/javascript"
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</head>
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</head>
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||||||
<body>
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<body>
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||||||
<div id="org-div-home-and-up">
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<div id="org-div-home-and-up">
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||||||
@ -258,51 +280,48 @@ for the JavaScript code in this tag.
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<h2>Table of Contents</h2>
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<h2>Table of Contents</h2>
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||||||
<div id="text-table-of-contents">
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<div id="text-table-of-contents">
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||||||
<ul>
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<ul>
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||||||
<li><a href="#orge60b193">1. Undamped System</a>
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<li><a href="#orgd9a890c">1. Simscape Model</a></li>
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<li><a href="#orgeafc497">2. Undamped System</a>
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<ul>
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<ul>
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<li><a href="#org46cb925">1.1. Init</a></li>
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<li><a href="#org631c716">2.1. Init</a></li>
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||||||
<li><a href="#orgbaff26c">1.2. Identification</a></li>
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<li><a href="#orgbbef650">2.2. Identification</a></li>
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||||||
<li><a href="#orgf051d6b">1.3. Sensitivity to Disturbances</a></li>
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<li><a href="#orgb5102fd">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org809a04d">1.4. Plant</a></li>
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<li><a href="#orgafe8970">2.4. Plant</a></li>
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<li><a href="#orge7de64d">1.5. Save</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#org0e4b7a2">2. Integral Force Feedback</a>
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<li><a href="#orgeab4870">3. Integral Force Feedback</a>
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<ul>
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<ul>
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<li><a href="#orge7eac97">2.1. Control Design</a></li>
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<li><a href="#org6cf62a2">3.1. Control Design</a></li>
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||||||
<li><a href="#org1da475f">2.2. Identification</a></li>
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<li><a href="#orgf9a5f33">3.2. Identification</a></li>
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||||||
<li><a href="#orgba751b8">2.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org7a80859">3.3. Sensitivity to Disturbance</a></li>
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||||||
<li><a href="#org215411f">2.4. Damped Plant</a></li>
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<li><a href="#org7bab9e9">3.4. Damped Plant</a></li>
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||||||
<li><a href="#org14fe313">2.5. Save</a></li>
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<li><a href="#orgaac01c0">3.5. Conclusion</a></li>
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||||||
<li><a href="#org00d3320">2.6. Conclusion</a></li>
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</ul>
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</ul>
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</li>
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</li>
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<li><a href="#org6ef0786">3. Relative Motion Control</a>
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<li><a href="#org8d9b463">4. Relative Motion Control</a>
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<ul>
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<ul>
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<li><a href="#orgdcdfe4c">3.1. Control Design</a></li>
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<li><a href="#orgbf2540a">4.1. Control Design</a></li>
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||||||
<li><a href="#orgc768160">3.2. Identification</a></li>
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<li><a href="#org1d106d7">4.2. Identification</a></li>
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||||||
<li><a href="#org340b3bb">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orgeb7d680">4.3. Sensitivity to Disturbance</a></li>
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||||||
<li><a href="#org67127eb">3.4. Damped Plant</a></li>
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<li><a href="#org573eda0">4.4. Damped Plant</a></li>
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||||||
<li><a href="#org21a13ba">3.5. Save</a></li>
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<li><a href="#org02ca488">4.5. Conclusion</a></li>
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||||||
<li><a href="#org6394f36">3.6. Conclusion</a></li>
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</ul>
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</ul>
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||||||
</li>
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</li>
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||||||
<li><a href="#org273e223">4. Direct Velocity Feedback</a>
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<li><a href="#org57948ea">5. Direct Velocity Feedback</a>
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||||||
<ul>
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<ul>
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||||||
<li><a href="#org254f765">4.1. Control Design</a></li>
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<li><a href="#org4b4d061">5.1. Control Design</a></li>
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||||||
<li><a href="#org3f4f45f">4.2. Identification</a></li>
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<li><a href="#orgd4f4973">5.2. Identification</a></li>
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||||||
<li><a href="#org580de8a">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org6cfeae5">5.3. Sensitivity to Disturbance</a></li>
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||||||
<li><a href="#org5e7c1c3">4.4. Damped Plant</a></li>
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<li><a href="#org89e0408">5.4. Damped Plant</a></li>
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||||||
<li><a href="#org0c0adf6">4.5. Save</a></li>
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<li><a href="#orgc27bce5">5.5. Conclusion</a></li>
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||||||
<li><a href="#orgbbb2968">4.6. Conclusion</a></li>
|
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||||||
</ul>
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</ul>
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||||||
</li>
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</li>
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||||||
<li><a href="#org9720eac">5. Comparison of Active Damping Techniques</a>
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<li><a href="#org6dd07d9">6. Comparison of Active Damping Techniques</a>
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<ul>
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<ul>
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<li><a href="#org04bc1e0">5.1. Load the plants</a></li>
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<li><a href="#orgd62929a">6.1. Load the plants</a></li>
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||||||
<li><a href="#orga979580">5.2. Sensitivity to Disturbance</a></li>
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<li><a href="#orgbd35b93">6.2. Sensitivity to Disturbance</a></li>
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||||||
<li><a href="#orgc4c2c73">5.3. Damped Plant</a></li>
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<li><a href="#org72ab5fd">6.3. Damped Plant</a></li>
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||||||
<li><a href="#org1c2b3da">5.4. Conclusion</a></li>
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<li><a href="#org2c43078">6.4. Conclusion</a></li>
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||||||
</ul>
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</ul>
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||||||
</li>
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</li>
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||||||
</ul>
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</ul>
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||||||
@ -317,52 +336,102 @@ 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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This is done in order to more easily study the system and evaluate control techniques.
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</p>
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</p>
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<div id="outline-container-orge60b193" class="outline-2">
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<div id="outline-container-orgd9a890c" class="outline-2">
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<h2 id="orge60b193"><span class="section-number-2">1</span> Undamped System</h2>
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<h2 id="orgd9a890c"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
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<div class="outline-text-2" id="text-1">
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<p>
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||||||
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#org9234e2b">1</a>.
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</p>
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<p>
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The perturbations \(w\) are:
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</p>
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<ul class="org-ul">
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<li>\(F_s\): direct forces applied to the sample such as inertia forces and cable forces</li>
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<li>\(F_{rz}\): parasitic forces due to the rotation of the spindle</li>
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<li>\(F_{ty}\): parasitic forces due to scans with the translation stage</li>
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<li>\(D_w\): ground motion</li>
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</ul>
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<p>
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The quantity to \(z\) to control is:
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</p>
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<ul class="org-ul">
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<li>\(D\): the position of the sample with respect to the granite</li>
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</ul>
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<p>
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The measured quantities \(v\) are:
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</p>
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<ul class="org-ul">
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<li>\(D\): the position of the sample with respect to the granite</li>
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</ul>
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<p>
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We study the use of an additional sensor:
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</p>
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<ul class="org-ul">
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<li>\(F_n\): a force sensor located in the nano-hexapod</li>
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<li>\(v_n\): an absolute velocity sensor located on the top platform of the nano-hexapod</li>
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<li>\(d_r\): a relative motion sensor located in the nano-hexapod</li>
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</ul>
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<p>
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The control signal \(u\) is:
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</p>
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<ul class="org-ul">
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<li>\(F\) the force applied by the nano-hexapod actuator</li>
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</ul>
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<div id="org9234e2b" 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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</div>
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</div>
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<div id="outline-container-org46cb925" class="outline-3">
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<h3 id="org46cb925"><span class="section-number-3">1.1</span> Init</h3>
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<div class="outline-text-3" id="text-1-1">
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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="#org49f5486">2</a>.
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</p>
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<div id="org49f5486" 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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</div>
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</div>
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</div>
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<div id="outline-container-orgeafc497" class="outline-2">
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<h2 id="orgeafc497"><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-org631c716" class="outline-3">
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<h3 id="org631c716"><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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<p>
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We initialize all the stages with the default parameters.
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We initialize all the stages with the default parameters.
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The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
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The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg.
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</p>
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">initializeGround<span class="org-rainbow-delimiters-depth-1">()</span>;
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||||||
initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
||||||
initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
||||||
initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
||||||
initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
||||||
initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
||||||
initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
||||||
initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
||||||
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
</pre>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
All the controllers are set to 0.
|
All the controllers are set to 0 (Open Loop).
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
|
||||||
<pre class="src src-matlab">K = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
K_iff = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
K_rmc = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
K_dvf = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
||||||
</pre>
|
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
<div id="outline-container-orgbbef650" class="outline-3">
|
||||||
|
<h3 id="orgbbef650"><span class="section-number-3">2.2</span> Identification</h3>
|
||||||
<div id="outline-container-orgbaff26c" class="outline-3">
|
<div class="outline-text-3" id="text-2-2">
|
||||||
<h3 id="orgbaff26c"><span class="section-number-3">1.2</span> Identification</h3>
|
<p>
|
||||||
<div class="outline-text-3" id="text-1-2">
|
We identify the dynamics of the system.
|
||||||
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||||
options = linearizeOptions;
|
options = linearizeOptions;
|
||||||
@ -373,6 +442,9 @@ mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
|
|||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
The inputs and outputs are defined below and corresponds to the name of simulink blocks.
|
||||||
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
|
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
|
||||||
@ -389,6 +461,9 @@ io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highligh
|
|||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
<p>
|
||||||
|
Finally, we use the <code>linearize</code> Matlab function to extract a state space model from the simscape model.
|
||||||
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||||
G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
|
G = linearize<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
@ -404,62 +479,79 @@ G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class=
|
|||||||
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-orgf051d6b" class="outline-3">
|
<p>
|
||||||
<h3 id="orgf051d6b"><span class="section-number-3">1.3</span> Sensitivity to Disturbances</h3>
|
Finally, we save the identified system dynamics for further analysis.
|
||||||
<div class="outline-text-3" id="text-1-3">
|
|
||||||
|
|
||||||
<div id="org4bc7134" class="figure">
|
|
||||||
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
|
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 1: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-disturbances.pdf">pdf</a>)</p>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
<div id="orga192bc9" class="figure">
|
|
||||||
<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 2: </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>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org809a04d" class="outline-3">
|
|
||||||
<h3 id="org809a04d"><span class="section-number-3">1.4</span> Plant</h3>
|
|
||||||
<div class="outline-text-3" id="text-1-4">
|
|
||||||
|
|
||||||
<div id="org1f07ded" class="figure">
|
|
||||||
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 3: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-orge7de64d" class="outline-3">
|
|
||||||
<h3 id="orge7de64d"><span class="section-number-3">1.5</span> Save</h3>
|
|
||||||
<div class="outline-text-3" id="text-1-5">
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">save<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>;
|
<pre class="src src-matlab">save<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>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgb5102fd" class="outline-3">
|
||||||
|
<h3 id="orgb5102fd"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-3">
|
||||||
|
<p>
|
||||||
|
We show several plots representing the sensitivity to disturbances:
|
||||||
|
</p>
|
||||||
|
<ul class="org-ul">
|
||||||
|
<li>in figure <a href="#orge3abf0f">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>
|
||||||
|
<li>in figure <a href="#org25d95cb">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>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orge3abf0f" class="figure">
|
||||||
|
<p><img src="figs/uniaxial-sensitivity-disturbances.png" alt="uniaxial-sensitivity-disturbances.png" />
|
||||||
|
</p>
|
||||||
|
<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>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org0e4b7a2" class="outline-2">
|
|
||||||
<h2 id="org0e4b7a2"><span class="section-number-2">2</span> Integral Force Feedback</h2>
|
|
||||||
<div class="outline-text-2" id="text-2">
|
<div id="org25d95cb" class="figure">
|
||||||
<p>
|
<p><img src="figs/uniaxial-sensitivity-force-dist.png" alt="uniaxial-sensitivity-force-dist.png" />
|
||||||
<a id="org8efbd63"></a>
|
|
||||||
</p>
|
</p>
|
||||||
|
<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>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orge7eac97" class="outline-3">
|
</div>
|
||||||
<h3 id="orge7eac97"><span class="section-number-3">2.1</span> Control Design</h3>
|
</div>
|
||||||
<div class="outline-text-3" id="text-2-1">
|
|
||||||
|
<div id="outline-container-orgafe8970" class="outline-3">
|
||||||
|
<h3 id="orgafe8970"><span class="section-number-3">2.4</span> Plant</h3>
|
||||||
|
<div class="outline-text-3" id="text-2-4">
|
||||||
|
<p>
|
||||||
|
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="#org62d1d12">5</a>.
|
||||||
|
It corresponds to the plant to control.
|
||||||
|
</p>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org62d1d12" class="figure">
|
||||||
|
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
|
||||||
|
</p>
|
||||||
|
<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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgeab4870" class="outline-2">
|
||||||
|
<h2 id="orgeab4870"><span class="section-number-2">3</span> Integral Force Feedback</h2>
|
||||||
|
<div class="outline-text-2" id="text-3">
|
||||||
|
<p>
|
||||||
|
<a id="org04c8f6e"></a>
|
||||||
|
</p>
|
||||||
|
|
||||||
|
<div id="orge50f87e" 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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div id="outline-container-org6cf62a2" class="outline-3">
|
||||||
|
<h3 id="org6cf62a2"><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">
|
<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>;
|
<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>;
|
||||||
</pre>
|
</pre>
|
||||||
@ -470,10 +562,10 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org07202e9" class="figure">
|
<div id="org26ea3c1" class="figure">
|
||||||
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 4: </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 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>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -485,17 +577,17 @@ The controller for each pair of actuator/sensor is:
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org4918c15" class="figure">
|
<div id="org27d1bb0" class="figure">
|
||||||
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 5: </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 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>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org1da475f" class="outline-3">
|
<div id="outline-container-orgf9a5f33" class="outline-3">
|
||||||
<h3 id="org1da475f"><span class="section-number-3">2.2</span> Identification</h3>
|
<h3 id="orgf9a5f33"><span class="section-number-3">3.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-2-2">
|
<div class="outline-text-3" id="text-3-2">
|
||||||
<p>
|
<p>
|
||||||
Let's initialize the system prior to identification.
|
Let's initialize the system prior to identification.
|
||||||
</p>
|
</p>
|
||||||
@ -569,43 +661,7 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-orgba751b8" class="outline-3">
|
|
||||||
<h3 id="orgba751b8"><span class="section-number-3">2.3</span> Sensitivity to Disturbance</h3>
|
|
||||||
<div class="outline-text-3" id="text-2-3">
|
|
||||||
|
|
||||||
<div id="org433ca31" class="figure">
|
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 6: </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="org129b2c0" 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 7: </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-org215411f" class="outline-3">
|
|
||||||
<h3 id="org215411f"><span class="section-number-3">2.4</span> Damped Plant</h3>
|
|
||||||
<div class="outline-text-3" id="text-2-4">
|
|
||||||
|
|
||||||
<div id="org9cbc1b3" class="figure">
|
|
||||||
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 8: </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-org14fe313" class="outline-3">
|
|
||||||
<h3 id="org14fe313"><span class="section-number-3">2.5</span> Save</h3>
|
|
||||||
<div class="outline-text-3" id="text-2-5">
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
@ -613,9 +669,40 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org00d3320" class="outline-3">
|
<div id="outline-container-org7a80859" class="outline-3">
|
||||||
<h3 id="org00d3320"><span class="section-number-3">2.6</span> Conclusion</h3>
|
<h3 id="org7a80859"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||||
<div class="outline-text-3" id="text-2-6">
|
<div class="outline-text-3" id="text-3-3">
|
||||||
|
|
||||||
|
<div id="orgca12220" 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>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org19c25c8" 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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org7bab9e9" class="outline-3">
|
||||||
|
<h3 id="org7bab9e9"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-4">
|
||||||
|
|
||||||
|
<div id="org60ea1f1" 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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgaac01c0" class="outline-3">
|
||||||
|
<h3 id="orgaac01c0"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-3-5">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
Integral Force Feedback:
|
Integral Force Feedback:
|
||||||
@ -626,19 +713,26 @@ Integral Force Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org6ef0786" class="outline-2">
|
<div id="outline-container-org8d9b463" class="outline-2">
|
||||||
<h2 id="org6ef0786"><span class="section-number-2">3</span> Relative Motion Control</h2>
|
<h2 id="org8d9b463"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||||
<div class="outline-text-2" id="text-3">
|
<div class="outline-text-2" id="text-4">
|
||||||
<p>
|
<p>
|
||||||
<a id="orgd075f22"></a>
|
<a id="orgdc4ae31"></a>
|
||||||
</p>
|
</p>
|
||||||
<p>
|
<p>
|
||||||
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
|
In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org46f85ef" 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>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orgdcdfe4c" class="outline-3">
|
</div>
|
||||||
<h3 id="orgdcdfe4c"><span class="section-number-3">3.1</span> Control Design</h3>
|
<div id="outline-container-orgbf2540a" class="outline-3">
|
||||||
<div class="outline-text-3" id="text-3-1">
|
<h3 id="orgbf2540a"><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">
|
<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>;
|
<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>;
|
||||||
</pre>
|
</pre>
|
||||||
@ -649,10 +743,10 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgd4c9455" class="figure">
|
<div id="orgc47e343" class="figure">
|
||||||
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 9: </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 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>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -665,17 +759,17 @@ A Low pass Filter is added to make the controller transfer function proper.
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgde55454" class="figure">
|
<div id="org9c157b6" class="figure">
|
||||||
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 10: </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 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>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgc768160" class="outline-3">
|
<div id="outline-container-org1d106d7" class="outline-3">
|
||||||
<h3 id="orgc768160"><span class="section-number-3">3.2</span> Identification</h3>
|
<h3 id="org1d106d7"><span class="section-number-3">4.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-3-2">
|
<div class="outline-text-3" id="text-4-2">
|
||||||
<p>
|
<p>
|
||||||
Let's initialize the system prior to identification.
|
Let's initialize the system prior to identification.
|
||||||
</p>
|
</p>
|
||||||
@ -749,44 +843,7 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
|
|
||||||
<div id="outline-container-org340b3bb" class="outline-3">
|
|
||||||
<h3 id="org340b3bb"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
|
||||||
<div class="outline-text-3" id="text-3-3">
|
|
||||||
|
|
||||||
<div id="orgc8a11d1" class="figure">
|
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 11: </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="org919dd9d" 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 12: </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-org67127eb" class="outline-3">
|
|
||||||
<h3 id="org67127eb"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
|
||||||
<div class="outline-text-3" id="text-3-4">
|
|
||||||
|
|
||||||
<div id="org8490305" class="figure">
|
|
||||||
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 13: </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-org21a13ba" class="outline-3">
|
|
||||||
<h3 id="org21a13ba"><span class="section-number-3">3.5</span> Save</h3>
|
|
||||||
<div class="outline-text-3" id="text-3-5">
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
@ -794,9 +851,41 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org6394f36" class="outline-3">
|
|
||||||
<h3 id="org6394f36"><span class="section-number-3">3.6</span> Conclusion</h3>
|
<div id="outline-container-orgeb7d680" class="outline-3">
|
||||||
<div class="outline-text-3" id="text-3-6">
|
<h3 id="orgeb7d680"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-3">
|
||||||
|
|
||||||
|
<div id="org7a8bd68" 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>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="orgb8fed93" 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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org573eda0" class="outline-3">
|
||||||
|
<h3 id="org573eda0"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-4">
|
||||||
|
|
||||||
|
<div id="org1f8e935" 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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org02ca488" class="outline-3">
|
||||||
|
<h3 id="org02ca488"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-4-5">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
Relative Motion Control:
|
Relative Motion Control:
|
||||||
@ -807,29 +896,36 @@ Relative Motion Control:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org273e223" class="outline-2">
|
<div id="outline-container-org57948ea" class="outline-2">
|
||||||
<h2 id="org273e223"><span class="section-number-2">4</span> Direct Velocity Feedback</h2>
|
<h2 id="org57948ea"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||||
<div class="outline-text-2" id="text-4">
|
<div class="outline-text-2" id="text-5">
|
||||||
<p>
|
<p>
|
||||||
<a id="org5a18f77"></a>
|
<a id="orgdd11541"></a>
|
||||||
</p>
|
</p>
|
||||||
<p>
|
<p>
|
||||||
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
|
In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org0fcd7e7" 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>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org254f765" class="outline-3">
|
</div>
|
||||||
<h3 id="org254f765"><span class="section-number-3">4.1</span> Control Design</h3>
|
<div id="outline-container-org4b4d061" class="outline-3">
|
||||||
<div class="outline-text-3" id="text-4-1">
|
<h3 id="org4b4d061"><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">
|
<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>;
|
<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>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org505b157" class="figure">
|
<div id="orgbf7145f" class="figure">
|
||||||
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 14: </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 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>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -838,17 +934,17 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org3ef68bd" class="figure">
|
<div id="org1b6adf4" class="figure">
|
||||||
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 15: </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 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>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org3f4f45f" class="outline-3">
|
<div id="outline-container-orgd4f4973" class="outline-3">
|
||||||
<h3 id="org3f4f45f"><span class="section-number-3">4.2</span> Identification</h3>
|
<h3 id="orgd4f4973"><span class="section-number-3">5.2</span> Identification</h3>
|
||||||
<div class="outline-text-3" id="text-4-2">
|
<div class="outline-text-3" id="text-5-2">
|
||||||
<p>
|
<p>
|
||||||
Let's initialize the system prior to identification.
|
Let's initialize the system prior to identification.
|
||||||
</p>
|
</p>
|
||||||
@ -922,43 +1018,7 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
<span class="org-string">'Vlm'</span><span class="org-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
|
||||||
</div>
|
|
||||||
|
|
||||||
<div id="outline-container-org580de8a" class="outline-3">
|
|
||||||
<h3 id="org580de8a"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
|
||||||
<div class="outline-text-3" id="text-4-3">
|
|
||||||
|
|
||||||
<div id="orged4b1f3" class="figure">
|
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 16: </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="org151dc83" 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 17: </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-org5e7c1c3" class="outline-3">
|
|
||||||
<h3 id="org5e7c1c3"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
|
||||||
<div class="outline-text-3" id="text-4-4">
|
|
||||||
|
|
||||||
<div id="orgfb4eb8b" class="figure">
|
|
||||||
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
|
|
||||||
</p>
|
|
||||||
<p><span class="figure-number">Figure 18: </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-org0c0adf6" class="outline-3">
|
|
||||||
<h3 id="org0c0adf6"><span class="section-number-3">4.5</span> Save</h3>
|
|
||||||
<div class="outline-text-3" id="text-4-5">
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
@ -966,9 +1026,40 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgbbb2968" class="outline-3">
|
<div id="outline-container-org6cfeae5" class="outline-3">
|
||||||
<h3 id="orgbbb2968"><span class="section-number-3">4.6</span> Conclusion</h3>
|
<h3 id="org6cfeae5"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||||
<div class="outline-text-3" id="text-4-6">
|
<div class="outline-text-3" id="text-5-3">
|
||||||
|
|
||||||
|
<div id="org6fb6e94" 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>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
<div id="org6f13385" 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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-org89e0408" class="outline-3">
|
||||||
|
<h3 id="org89e0408"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||||
|
<div class="outline-text-3" id="text-5-4">
|
||||||
|
|
||||||
|
<div id="org7051238" 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>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
<div id="outline-container-orgc27bce5" class="outline-3">
|
||||||
|
<h3 id="orgc27bce5"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-5-5">
|
||||||
<div class="important">
|
<div class="important">
|
||||||
<p>
|
<p>
|
||||||
Direct Velocity Feedback:
|
Direct Velocity Feedback:
|
||||||
@ -978,16 +1069,16 @@ Direct Velocity Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org9720eac" class="outline-2">
|
<div id="outline-container-org6dd07d9" class="outline-2">
|
||||||
<h2 id="org9720eac"><span class="section-number-2">5</span> Comparison of Active Damping Techniques</h2>
|
<h2 id="org6dd07d9"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
|
||||||
<div class="outline-text-2" id="text-5">
|
<div class="outline-text-2" id="text-6">
|
||||||
<p>
|
<p>
|
||||||
<a id="org7404a5b"></a>
|
<a id="org5272a4c"></a>
|
||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org04bc1e0" class="outline-3">
|
<div id="outline-container-orgd62929a" class="outline-3">
|
||||||
<h3 id="org04bc1e0"><span class="section-number-3">5.1</span> Load the plants</h3>
|
<h3 id="orgd62929a"><span class="section-number-3">6.1</span> Load the plants</h3>
|
||||||
<div class="outline-text-3" id="text-5-1">
|
<div class="outline-text-3" id="text-6-1">
|
||||||
<div class="org-src-container">
|
<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>;
|
<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>;
|
||||||
</pre>
|
</pre>
|
||||||
@ -995,44 +1086,126 @@ Direct Velocity Feedback:
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga979580" class="outline-3">
|
<div id="outline-container-orgbd35b93" class="outline-3">
|
||||||
<h3 id="orga979580"><span class="section-number-3">5.2</span> Sensitivity to Disturbance</h3>
|
<h3 id="orgbd35b93"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
|
||||||
<div class="outline-text-3" id="text-5-2">
|
<div class="outline-text-3" id="text-6-2">
|
||||||
|
|
||||||
<div id="org076a7e7" class="figure">
|
<div id="org5eda09f" class="figure">
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_comp.png" alt="uniaxial_sensitivity_dist_comp.png" />
|
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 19: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_dist_comp.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_comp.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 24: </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>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgd0777da" class="figure">
|
|
||||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_comp.png" alt="uniaxial_sensitivity_dist_stages_comp.png" />
|
<div id="org1fae0e7" class="figure">
|
||||||
|
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 20: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_dist_stages_comp.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_comp.pdf">pdf</a>)</p>
|
<p><span class="figure-number">Figure 25: </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="orgb2bd39c" class="figure">
|
||||||
|
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 26: </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="org1f00826" class="figure">
|
||||||
|
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
|
||||||
|
</p>
|
||||||
|
<p><span class="figure-number">Figure 27: </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>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgc4c2c73" class="outline-3">
|
<div id="outline-container-org72ab5fd" class="outline-3">
|
||||||
<h3 id="orgc4c2c73"><span class="section-number-3">5.3</span> Damped Plant</h3>
|
<h3 id="org72ab5fd"><span class="section-number-3">6.3</span> Damped Plant</h3>
|
||||||
<div class="outline-text-3" id="text-5-3">
|
<div class="outline-text-3" id="text-6-3">
|
||||||
|
|
||||||
<div id="orge2efd1a" class="figure">
|
<div id="org0296cfa" class="figure">
|
||||||
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 21: </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 28: </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>
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-org1c2b3da" class="outline-3">
|
|
||||||
<h3 id="org1c2b3da"><span class="section-number-3">5.4</span> Conclusion</h3>
|
<div id="outline-container-org2c43078" class="outline-3">
|
||||||
|
<h3 id="org2c43078"><span class="section-number-3">6.4</span> Conclusion</h3>
|
||||||
|
<div class="outline-text-3" id="text-6-4">
|
||||||
|
<table id="orga82a170" 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>
|
||||||
|
|
||||||
|
<colgroup>
|
||||||
|
<col class="org-left" />
|
||||||
|
|
||||||
|
<col class="org-left" />
|
||||||
|
|
||||||
|
<col class="org-left" />
|
||||||
|
|
||||||
|
<col class="org-left" />
|
||||||
|
</colgroup>
|
||||||
|
<thead>
|
||||||
|
<tr>
|
||||||
|
<th scope="col" class="org-left"> </th>
|
||||||
|
<th scope="col" class="org-left">IFF</th>
|
||||||
|
<th scope="col" class="org-left">RMC</th>
|
||||||
|
<th scope="col" class="org-left">DVF</th>
|
||||||
|
</tr>
|
||||||
|
</thead>
|
||||||
|
<tbody>
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Sensor Type</td>
|
||||||
|
<td class="org-left">Force sensor</td>
|
||||||
|
<td class="org-left">Relative Motion</td>
|
||||||
|
<td class="org-left">Inertial</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Guaranteed Stability</td>
|
||||||
|
<td class="org-left">+</td>
|
||||||
|
<td class="org-left">+</td>
|
||||||
|
<td class="org-left">-</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Sensitivity (\(D_w\))</td>
|
||||||
|
<td class="org-left">-</td>
|
||||||
|
<td class="org-left">+</td>
|
||||||
|
<td class="org-left">-</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Sensitivity (\(F_s\))</td>
|
||||||
|
<td class="org-left">- (at low freq)</td>
|
||||||
|
<td class="org-left">+</td>
|
||||||
|
<td class="org-left">+</td>
|
||||||
|
</tr>
|
||||||
|
|
||||||
|
<tr>
|
||||||
|
<td class="org-left">Sensitivity (\(F_{ty,rz}\))</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>
|
||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<p class="author">Author: Dehaeze Thomas</p>
|
||||||
<p class="date">Created: 2019-10-24 jeu. 17:44</p>
|
<p class="date">Created: 2019-10-25 ven. 12:32</p>
|
||||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
|
|||||||
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Reference in New Issue
Block a user