1669 lines
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1669 lines
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<title>Simscape Uniaxial Model</title>
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<a accesskey="h" href="./index.html"> UP </a>
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<a accesskey="H" href="./index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Simscape Uniaxial Model</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org227ba84">1. Simscape Model</a></li>
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<li><a href="#org6bfb35d">2. Undamped System</a>
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<ul>
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<li><a href="#org4609941">2.1. Init</a></li>
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<li><a href="#org294eb39">2.2. Identification</a></li>
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<li><a href="#org7a1cc07">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#orga53aea9">2.4. Noise Budget</a></li>
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<li><a href="#orgdb3535a">2.5. Plant</a></li>
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</ul>
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</li>
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<li><a href="#org1cbdf7c">3. Integral Force Feedback</a>
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<ul>
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<li><a href="#org2eefec2">3.1. Control Design</a></li>
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<li><a href="#org1a0f43f">3.2. Identification</a></li>
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<li><a href="#orgc9a5688">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org681a4b5">3.4. Damped Plant</a></li>
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<li><a href="#org7dff1b8">3.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org07ff58f">4. Relative Motion Control</a>
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<ul>
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<li><a href="#orgb8526dc">4.1. Control Design</a></li>
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<li><a href="#org08507fd">4.2. Identification</a></li>
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<li><a href="#org0f3fad3">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org652a3fa">4.4. Damped Plant</a></li>
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<li><a href="#orgae3868e">4.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#orgc9b3622">5. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#orgf39d565">5.1. Control Design</a></li>
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<li><a href="#org5546bc6">5.2. Identification</a></li>
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<li><a href="#orgd944a62">5.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org7dee42a">5.4. Damped Plant</a></li>
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<li><a href="#orgd0c02fb">5.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org5ac7dda">6. With Cedrat Piezo-electric Actuators</a>
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<ul>
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<li><a href="#orgb02fbb6">6.1. Identification</a></li>
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<li><a href="#orge2bfe04">6.2. Control Design</a></li>
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<li><a href="#org53cc9c6">6.3. Identification</a></li>
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<li><a href="#orgd6515d0">6.4. Sensitivity to Disturbance</a></li>
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<li><a href="#orgc6d991d">6.5. Damped Plant</a></li>
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<li><a href="#org8c680f2">6.6. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org77a79e6">7. Comparison of Active Damping Techniques</a>
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<ul>
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<li><a href="#orgb0afe4f">7.1. Load the plants</a></li>
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<li><a href="#orgcb13f9e">7.2. Sensitivity to Disturbance</a></li>
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<li><a href="#org5cadbe8">7.3. Noise Budget</a></li>
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<li><a href="#org8fede67">7.4. Damped Plant</a></li>
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<li><a href="#orgd8ddad5">7.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org15965e0">8. Voice Coil</a>
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<ul>
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<li><a href="#org33240ce">8.1. Init</a></li>
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<li><a href="#org1533141">8.2. Identification</a></li>
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<li><a href="#orgb814bd8">8.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org790a719">8.4. Noise Budget</a></li>
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<li><a href="#orgfa698bd">8.5. Integral Force Feedback</a></li>
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<li><a href="#org2a655f7">8.6. Identification of the Damped Plant</a></li>
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<li><a href="#org1ecc3e1">8.7. Noise Budget</a></li>
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<li><a href="#org229e708">8.8. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<p>
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The idea is to use the same model as the full Simscape Model but to restrict the motion only in the vertical direction.
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</p>
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<p>
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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-org227ba84" class="outline-2">
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<h2 id="org227ba84"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orge4f893b"></a>
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</p>
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<p>
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#org4f6d475">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="org4f6d475" 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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<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="#orgc460f0d">2</a>.
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</p>
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<div id="orgc460f0d" 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-org6bfb35d" class="outline-2">
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<h2 id="org6bfb35d"><span class="section-number-2">2</span> Undamped System</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org83e5eca"></a>
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</p>
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<p>
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Let’s start by study the undamped system.
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</p>
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</div>
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<div id="outline-container-org4609941" class="outline-3">
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<h3 id="org4609941"><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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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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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-org294eb39" class="outline-3">
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<h3 id="org294eb39"><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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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options.SampleTime = 0;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
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</pre>
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</div>
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<p>
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The inputs and outputs are defined below and corresponds to the name of simulink blocks.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
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io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
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io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
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io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
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io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
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io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
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io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
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io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
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io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
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io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
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</pre>
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</div>
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<p>
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Finally, we use the <code>linearize</code> Matlab function to extract a state space model from the simscape model.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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G = linearize(mdl, io, options);
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G.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
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<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
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<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
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<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
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<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
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G.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
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<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
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<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
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<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
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<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
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</pre>
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</div>
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<p>
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Finally, we save the identified system dynamics for further analysis.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">save(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org7a1cc07" class="outline-3">
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<h3 id="org7a1cc07"><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="#orgbfaf2d3">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="#orge6ba7ee">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="orgbfaf2d3" 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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</div>
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<div id="orge6ba7ee" 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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</div>
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</div>
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</div>
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<div id="outline-container-orga53aea9" class="outline-3">
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<h3 id="orga53aea9"><span class="section-number-3">2.4</span> Noise Budget</h3>
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<div class="outline-text-3" id="text-2-4">
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<p>
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We first load the measured PSD of the disturbance.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">load(<span class="org-string">'./mat/disturbances_dist_psd.mat'</span>, <span class="org-string">'dist_f'</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="#org1c1d9b8">5</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org2f678d5">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="#org2f678d5">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="org1c1d9b8" 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>PSD of the effect of disturbances on \(D\) (<a href="./figs/uniaxial-psd-dist.png">png</a>, <a href="./figs/uniaxial-psd-dist.pdf">pdf</a>)</p>
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</div>
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<div id="org2f678d5" 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>CAS of the effect of disturbances on \(D\) (<a href="./figs/uniaxial-cas-dist.png">png</a>, <a href="./figs/uniaxial-cas-dist.pdf">pdf</a>)</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgdb3535a" class="outline-3">
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<h3 id="orgdb3535a"><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>
|
|
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="#orgaaf3fcb">7</a>.
|
|
It corresponds to the plant to control.
|
|
</p>
|
|
|
|
|
|
<div id="orgaaf3fcb" class="figure">
|
|
<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1cbdf7c" class="outline-2">
|
|
<h2 id="org1cbdf7c"><span class="section-number-2">3</span> Integral Force Feedback</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="org37f1b7d"></a>
|
|
</p>
|
|
|
|
<div id="org884322f" class="figure">
|
|
<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Uniaxial IFF Control Schematic</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org2eefec2" class="outline-3">
|
|
<h3 id="org2eefec2"><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-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<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="orgde62a50" class="figure">
|
|
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
The controller for each pair of actuator/sensor is:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_iff = <span class="org-type">-</span>1000<span class="org-type">/</span>s;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgf0a3805" class="figure">
|
|
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1a0f43f" class="outline-3">
|
|
<h3 id="org1a0f43f"><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.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
|
initializeSample(<span class="org-string">'mass'</span>, 50);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
All the controllers are set to 0.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = <span class="org-type">-</span>K_iff;
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_rmc = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
|
|
io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
|
|
io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
|
|
io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
|
|
io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
|
|
|
|
io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
|
|
io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
|
|
io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
|
|
io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
|
|
io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
G_iff = linearize(mdl, io, options);
|
|
G_iff.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
|
|
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
|
|
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
|
|
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
|
|
<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
|
G_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
|
|
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
|
|
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
|
|
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
|
|
<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc9a5688" class="outline-3">
|
|
<h3 id="orgc9a5688"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
|
|
<div id="orge528565" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org01074d3" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org681a4b5" class="outline-3">
|
|
<h3 id="org681a4b5"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-3-4">
|
|
|
|
<div id="org57280cb" class="figure">
|
|
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7dff1b8" class="outline-3">
|
|
<h3 id="org7dff1b8"><span class="section-number-3">3.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-3-5">
|
|
<div class="important">
|
|
<p>
|
|
Integral Force Feedback:
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org07ff58f" class="outline-2">
|
|
<h2 id="org07ff58f"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
<a id="org7d87e9d"></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="orgd2f9465" class="figure">
|
|
<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Uniaxial RMC Control Schematic</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orgb8526dc" class="outline-3">
|
|
<h3 id="orgb8526dc"><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-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor.
|
|
</p>
|
|
|
|
|
|
<div id="org8260ad7" class="figure">
|
|
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
The Relative Motion Controller is defined below.
|
|
A Low pass Filter is added to make the controller transfer function proper.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_rmc = s<span class="org-type">*</span>50000<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>10000);
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orga5e2583" class="figure">
|
|
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org08507fd" class="outline-3">
|
|
<h3 id="org08507fd"><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.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
|
initializeSample(<span class="org-string">'mass'</span>, 50);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And initialize the controllers.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_rmc = <span class="org-type">-</span>K_rmc;
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
|
|
io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
|
|
io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
|
|
io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
|
|
io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
|
|
|
|
io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
|
|
io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
|
|
io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
|
|
io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
|
|
io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
G_rmc = linearize(mdl, io, options);
|
|
G_rmc.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
|
|
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
|
|
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
|
|
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
|
|
<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
|
G_rmc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
|
|
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
|
|
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
|
|
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
|
|
<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org0f3fad3" class="outline-3">
|
|
<h3 id="org0f3fad3"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
|
|
<div id="org9e0dde4" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org38d5224" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org652a3fa" class="outline-3">
|
|
<h3 id="org652a3fa"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-4-4">
|
|
|
|
<div id="org18786e8" class="figure">
|
|
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgae3868e" class="outline-3">
|
|
<h3 id="orgae3868e"><span class="section-number-3">4.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-4-5">
|
|
<div class="important">
|
|
<p>
|
|
Relative Motion Control:
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc9b3622" class="outline-2">
|
|
<h2 id="orgc9b3622"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
<a id="orgdffe2c2"></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="orgba6ec08" class="figure">
|
|
<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Uniaxial DVF Control Schematic</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orgf39d565" class="outline-3">
|
|
<h3 id="orgf39d565"><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-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org7b83a4a" class="figure">
|
|
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 21: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_dvf = tf(5e4);
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org25567d5" class="figure">
|
|
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 22: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5546bc6" class="outline-3">
|
|
<h3 id="org5546bc6"><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.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
|
initializeSample(<span class="org-string">'mass'</span>, 50);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And initialize the controllers.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_rmc = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = <span class="org-type">-</span>K_dvf;
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
|
|
io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
|
|
io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
|
|
io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
|
|
io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
|
|
|
|
io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
|
|
io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
|
|
io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
|
|
io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
|
|
io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
G_dvf = linearize(mdl, io, options);
|
|
G_dvf.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
|
|
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
|
|
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
|
|
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
|
|
<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
|
G_dvf.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
|
|
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
|
|
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
|
|
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
|
|
<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd944a62" class="outline-3">
|
|
<h3 id="orgd944a62"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-5-3">
|
|
|
|
<div id="orgf9d4052" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 23: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org98ddadb" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 24: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7dee42a" class="outline-3">
|
|
<h3 id="org7dee42a"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-5-4">
|
|
|
|
<div id="orgbc9c953" class="figure">
|
|
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 25: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd0c02fb" class="outline-3">
|
|
<h3 id="orgd0c02fb"><span class="section-number-3">5.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-5-5">
|
|
<div class="important">
|
|
<p>
|
|
Direct Velocity Feedback:
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org5ac7dda" class="outline-2">
|
|
<h2 id="org5ac7dda"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
<a id="org604af95"></a>
|
|
</p>
|
|
<p>
|
|
The model used for the Cedrat actuator is shown in figure <a href="#org83591fa">26</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org83591fa" class="figure">
|
|
<p><img src="figs/cedrat-uniaxial-actuator.png" alt="cedrat-uniaxial-actuator.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 26: </span>Schematic of the model used for the Cedrat Actuator</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orgb02fbb6" class="outline-3">
|
|
<h3 id="orgb02fbb6"><span class="section-number-3">6.1</span> Identification</h3>
|
|
<div class="outline-text-3" id="text-6-1">
|
|
<p>
|
|
Let’s initialize the system prior to identification.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
|
initializeCedratPiezo();
|
|
initializeSample(<span class="org-string">'mass'</span>, 50);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And initialize the controllers.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_rmc = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We identify the dynamics of the system.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nano_station_uniaxial_cedrat_bis'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The inputs and outputs are defined below and corresponds to the name of simulink blocks.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
|
|
io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
|
|
io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
|
|
io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
|
|
io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
|
|
|
|
io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
|
|
io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
|
|
io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
|
|
io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
|
|
io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
|
|
</pre>
|
|
</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">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
G = linearize(mdl, io, options);
|
|
G.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
|
|
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
|
|
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
|
|
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
|
|
<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
|
G.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
|
|
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
|
|
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
|
|
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
|
|
<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge2bfe04" class="outline-3">
|
|
<h3 id="orge2bfe04"><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="org2a02461" class="figure">
|
|
<p><img src="figs/uniaxial_cedrat_plant.png" alt="uniaxial_cedrat_plant.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 27: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_cedrat_plant.png">png</a>, <a href="./figs/uniaxial_cedrat_plant.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
The controller for each pair of actuator/sensor is:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_cedrat = <span class="org-type">-</span>5000<span class="org-type">/</span>s;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org7da2401" class="figure">
|
|
<p><img src="figs/uniaxial_cedrat_open_loop.png" alt="uniaxial_cedrat_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 28: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_cedrat_open_loop.png">png</a>, <a href="./figs/uniaxial_cedrat_open_loop.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org53cc9c6" class="outline-3">
|
|
<h3 id="org53cc9c6"><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.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span>);
|
|
initializeCedratPiezo();
|
|
initializeSample(<span class="org-string">'mass'</span>, 50);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
All the controllers are set to 0.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = <span class="org-type">-</span>K_cedrat;
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_rmc = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nano_station_uniaxial_cedrat_bis'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
|
|
io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
|
|
io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
|
|
io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
|
|
io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
|
|
|
|
io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
|
|
io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
|
|
io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
|
|
io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
|
|
io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
G_cedrat = linearize(mdl, io, options);
|
|
G_cedrat.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
|
|
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
|
|
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
|
|
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
|
|
<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
|
G_cedrat.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
|
|
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
|
|
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
|
|
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
|
|
<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% save('./mat/uniaxial_plants.mat', 'G_cedrat', '-append');</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd6515d0" class="outline-3">
|
|
<h3 id="orgd6515d0"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-6-4">
|
|
|
|
<div id="org90f5c2b" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_cedrat.png" alt="uniaxial_sensitivity_dist_cedrat.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 29: </span>Sensitivity to disturbance once the CEDRAT controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_cedrat.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org5acd68e" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_dist_stages_cedrat.png" alt="uniaxial_sensitivity_dist_stages_cedrat.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 30: </span>Sensitivity to force disturbances in various stages when CEDRAT is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc6d991d" class="outline-3">
|
|
<h3 id="orgc6d991d"><span class="section-number-3">6.5</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-6-5">
|
|
|
|
<div id="org0c4e61a" class="figure">
|
|
<p><img src="figs/uniaxial_plant_cedrat_damped.png" alt="uniaxial_plant_cedrat_damped.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 31: </span>Damped Plant after CEDRAT is applied (<a href="./figs/uniaxial_plant_cedrat_damped.png">png</a>, <a href="./figs/uniaxial_plant_cedrat_damped.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8c680f2" class="outline-3">
|
|
<h3 id="org8c680f2"><span class="section-number-3">6.6</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-6-6">
|
|
<div class="important">
|
|
<p>
|
|
This gives similar results than with a classical force sensor.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org77a79e6" class="outline-2">
|
|
<h2 id="org77a79e6"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<p>
|
|
<a id="orgd5640a5"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-orgb0afe4f" class="outline-3">
|
|
<h3 id="orgb0afe4f"><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-string">'./mat/uniaxial_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>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcb13f9e" class="outline-3">
|
|
<h3 id="orgcb13f9e"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
|
|
<div class="outline-text-3" id="text-7-2">
|
|
|
|
<div id="org8c59440" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 32: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgf1c26c0" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 33: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga77aca7" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 34: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="orga6c1630" class="figure">
|
|
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 35: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5cadbe8" class="outline-3">
|
|
<h3 id="org5cadbe8"><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-string">'./mat/disturbances_dist_psd.mat'</span>, <span class="org-string">'dist_f'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<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="#org68d1f1c">36</a>).
|
|
</p>
|
|
|
|
<div id="org68d1f1c" class="figure">
|
|
<p><img src="figs/uniaxial-comp-cas-dist.png" alt="uniaxial-comp-cas-dist.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 36: </span>Comparison of the Cumulative Amplitude Spectrum of \(D\) for different active damping techniques (<a href="./figs/uniaxial-comp-cas-dist.png">png</a>, <a href="./figs/uniaxial-comp-cas-dist.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
The obtained Root Mean Square Value for each active damping technique is shown below.
|
|
</p>
|
|
<table id="org63699f5" 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-org8fede67" class="outline-3">
|
|
<h3 id="org8fede67"><span class="section-number-3">7.4</span> Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-7-4">
|
|
|
|
<div id="orga0c1298" class="figure">
|
|
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 37: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd8ddad5" class="outline-3">
|
|
<h3 id="orgd8ddad5"><span class="section-number-3">7.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-7-5">
|
|
<table id="org46e95c2" 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" />
|
|
|
|
<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>
|
|
|
|
<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>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org15965e0" class="outline-2">
|
|
<h2 id="org15965e0"><span class="section-number-2">8</span> Voice Coil</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
<p>
|
|
<a id="orgf9e9d51"></a>
|
|
</p>
|
|
</div>
|
|
<div id="outline-container-org33240ce" class="outline-3">
|
|
<h3 id="org33240ce"><span class="section-number-3">8.1</span> Init</h3>
|
|
<div class="outline-text-3" id="text-8-1">
|
|
<p>
|
|
We initialize all the stages with the default parameters.
|
|
The nano-hexapod is an hexapod with voice coils and the sample has a mass of 50kg.
|
|
</p>
|
|
|
|
<p>
|
|
All the controllers are set to 0 (Open Loop).
|
|
</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org1533141" class="outline-3">
|
|
<h3 id="org1533141"><span class="section-number-3">8.2</span> Identification</h3>
|
|
<div class="outline-text-3" id="text-8-2">
|
|
<p>
|
|
We identify the dynamics of the system.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The inputs and outputs are defined below and corresponds to the name of simulink blocks.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
|
|
io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
|
|
io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
|
|
io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
|
|
io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
|
|
|
|
io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
|
|
io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
|
|
io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
|
|
io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
|
|
io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
|
|
</pre>
|
|
</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">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
|
G_vc = linearize(mdl, io, options);
|
|
G_vc.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
|
|
<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
|
|
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
|
|
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
|
|
<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
|
G_vc.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
|
|
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
|
|
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
|
|
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
|
|
<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, we save the identified system dynamics for further analysis.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G_vc'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb814bd8" class="outline-3">
|
|
<h3 id="orgb814bd8"><span class="section-number-3">8.3</span> Sensitivity to Disturbances</h3>
|
|
<div class="outline-text-3" id="text-8-3">
|
|
<p>
|
|
We load the dynamics when using a piezo-electric nano hexapod to compare the results.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./mat/uniaxial_plants.mat'</span>, <span class="org-string">'G'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We show several plots representing the sensitivity to disturbances:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>in figure <a href="#orgc80c94c">38</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
|
|
<li>in figure <a href="#org96743f2">39</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
|
|
</ul>
|
|
|
|
|
|
<div id="orgc80c94c" class="figure">
|
|
<p><img src="figs/uniaxial-sensitivity-vc-disturbances.png" alt="uniaxial-sensitivity-vc-disturbances.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 38: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-disturbances.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-disturbances.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org96743f2" class="figure">
|
|
<p><img src="figs/uniaxial-sensitivity-vc-force-dist.png" alt="uniaxial-sensitivity-vc-force-dist.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 39: </span>Sensitivity to disturbances (<a href="./figs/uniaxial-sensitivity-vc-force-dist.png">png</a>, <a href="./figs/uniaxial-sensitivity-vc-force-dist.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org790a719" class="outline-3">
|
|
<h3 id="org790a719"><span class="section-number-3">8.4</span> Noise Budget</h3>
|
|
<div class="outline-text-3" id="text-8-4">
|
|
<p>
|
|
We first load the measured PSD of the disturbance.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'./mat/disturbances_dist_psd.mat'</span>, <span class="org-string">'dist_f'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The effect of these disturbances on the distance \(D\) is computed below.
|
|
The PSD of the obtain distance \(D\) due to each of the perturbation is shown in figure <a href="#orgd3fd39b">40</a> and the Cumulative Amplitude Spectrum is shown in figure <a href="#org2ccc8a7">41</a>.
|
|
</p>
|
|
|
|
<p>
|
|
The Root Mean Square value of the obtained displacement \(D\) is computed below and can be determined from the figure <a href="#org2ccc8a7">41</a>.
|
|
</p>
|
|
<pre class="example">
|
|
4.8793e-06
|
|
</pre>
|
|
|
|
|
|
|
|
<div id="orgd3fd39b" class="figure">
|
|
<p><img src="figs/uniaxial-vc-psd-dist.png" alt="uniaxial-vc-psd-dist.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 40: </span>PSD of the displacement \(D\) due to disturbances (<a href="./figs/uniaxial-vc-psd-dist.png">png</a>, <a href="./figs/uniaxial-vc-psd-dist.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
<div id="org2ccc8a7" class="figure">
|
|
<p><img src="figs/uniaxial-vc-cas-dist.png" alt="uniaxial-vc-cas-dist.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 41: </span>CAS of the displacement \(D\) due the disturbances (<a href="./figs/uniaxial-vc-cas-dist.png">png</a>, <a href="./figs/uniaxial-vc-cas-dist.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<div class="important">
|
|
<p>
|
|
Even though the RMS value of the displacement \(D\) is lower when using a piezo-electric actuator, the motion is mainly due to high frequency disturbances which are more difficult to control (an higher control bandwidth is required).
|
|
</p>
|
|
|
|
<p>
|
|
Thus, it may be desirable to use voice coil actuators.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orgfa698bd" class="outline-3">
|
|
<h3 id="orgfa698bd"><span class="section-number-3">8.5</span> Integral Force Feedback</h3>
|
|
<div class="outline-text-3" id="text-8-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K_iff = <span class="org-type">-</span>20<span class="org-type">/</span>s;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgb6bf4fa" class="figure">
|
|
<p><img src="figs/uniaxial_iff_vc_open_loop.png" alt="uniaxial_iff_vc_open_loop.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 42: </span>Open Loop Transfer Function for IFF control when using a voice coil actuator (<a href="./figs/uniaxial_iff_vc_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_vc_open_loop.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2a655f7" class="outline-3">
|
|
<h3 id="org2a655f7"><span class="section-number-3">8.6</span> Identification of the Damped Plant</h3>
|
|
<div class="outline-text-3" id="text-8-6">
|
|
<p>
|
|
Let’s initialize the system prior to identification.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">initializeGround();
|
|
initializeGranite();
|
|
initializeTy();
|
|
initializeRy();
|
|
initializeRz();
|
|
initializeMicroHexapod();
|
|
initializeAxisc();
|
|
initializeMirror();
|
|
initializeNanoHexapod(<span class="org-string">'actuator'</span>, <span class="org-string">'lorentz'</span>);
|
|
initializeSample(<span class="org-string">'mass'</span>, 50);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
All the controllers are set to 0.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">K = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span>);
|
|
K_iff = <span class="org-type">-</span>K_iff;
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span>);
|
|
K_rmc = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span>);
|
|
K_dvf = tf(0);
|
|
save(<span class="org-string">'./mat/controllers_uniaxial.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
|
options = linearizeOptions;
|
|
options.SampleTime = 0;
|
|
|
|
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
|
mdl = <span class="org-string">'sim_nano_station_uniaxial'</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
|
io<span class="org-type">(1) </span>= linio([mdl, <span class="org-string">'/Dw'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Ground Motion</span>
|
|
io<span class="org-type">(2) </span>= linio([mdl, <span class="org-string">'/Fs'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied on the sample</span>
|
|
io<span class="org-type">(3) </span>= linio([mdl, <span class="org-string">'/Fnl'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Force applied by the NASS</span>
|
|
io<span class="org-type">(4) </span>= linio([mdl, <span class="org-string">'/Fdty'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Ty</span>
|
|
io<span class="org-type">(5) </span>= linio([mdl, <span class="org-string">'/Fdrz'</span>], 1, <span class="org-string">'input'</span>); <span class="org-comment">% Parasitic force Rz</span>
|
|
|
|
io<span class="org-type">(6) </span>= linio([mdl, <span class="org-string">'/Dsm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of the sample</span>
|
|
io<span class="org-type">(7) </span>= linio([mdl, <span class="org-string">'/Fnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Force sensor in NASS's legs</span>
|
|
io<span class="org-type">(8) </span>= linio([mdl, <span class="org-string">'/Dnlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Displacement of NASS's legs</span>
|
|
io<span class="org-type">(9) </span>= linio([mdl, <span class="org-string">'/Dgm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Absolute displacement of the granite</span>
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io<span class="org-type">(10) </span>= linio([mdl, <span class="org-string">'/Vlm'</span>], 1, <span class="org-string">'output'</span>); <span class="org-comment">% Measured absolute velocity of the top NASS platform</span>
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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G_vc_iff = linearize(mdl, io, options);
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G_vc_iff.InputName = {<span class="org-string">'Dw'</span>, ...<span class="org-comment"> % Ground Motion [m]</span>
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<span class="org-string">'Fs'</span>, ...<span class="org-comment"> % Force Applied on Sample [N]</span>
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|
<span class="org-string">'Fn'</span>, ...<span class="org-comment"> % Force applied by NASS [N]</span>
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|
<span class="org-string">'Fty'</span>, ...<span class="org-comment"> % Parasitic Force Ty [N]</span>
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|
<span class="org-string">'Frz'</span>}; <span class="org-comment">% Parasitic Force Rz [N]</span>
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G_vc_iff.OutputName = {<span class="org-string">'D'</span>, ...<span class="org-comment"> % Measured sample displacement x.r.t. granite [m]</span>
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|
<span class="org-string">'Fnm'</span>, ...<span class="org-comment"> % Force Sensor in NASS [N]</span>
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|
<span class="org-string">'Dnm'</span>, ...<span class="org-comment"> % Displacement Sensor in NASS [m]</span>
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|
<span class="org-string">'Dgm'</span>, ...<span class="org-comment"> % Asbolute displacement of Granite [m]</span>
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|
<span class="org-string">'Vlm'</span>}; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
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|
</pre>
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|
</div>
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|
</div>
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|
</div>
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|
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|
<div id="outline-container-org1ecc3e1" class="outline-3">
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|
<h3 id="org1ecc3e1"><span class="section-number-3">8.7</span> Noise Budget</h3>
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|
<div class="outline-text-3" id="text-8-7">
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|
<p>
|
|
We compute the obtain PSD of the displacement \(D\) when using IFF.
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|
</p>
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|
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|
<div id="org60accee" class="figure">
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|
<p><img src="figs/uniaxial-cas-iff-vc.png" alt="uniaxial-cas-iff-vc.png" />
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|
</p>
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|
<p><span class="figure-number">Figure 43: </span>CAS of the displacement \(D\) (<a href="./figs/uniaxial-cas-iff-vc.png">png</a>, <a href="./figs/uniaxial-cas-iff-vc.pdf">pdf</a>)</p>
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|
</div>
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|
</div>
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|
</div>
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|
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|
<div id="outline-container-org229e708" class="outline-3">
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<h3 id="org229e708"><span class="section-number-3">8.8</span> Conclusion</h3>
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|
<div class="outline-text-3" id="text-8-8">
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|
<div class="important">
|
|
<p>
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|
The use of voice coil actuators would allow a better disturbance rejection for a fixed bandwidth compared with a piezo-electric hexapod.
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|
</p>
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|
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|
<p>
|
|
Similarly, it would require much lower bandwidth to attain the same level of disturbance rejection for \(D\).
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|
</p>
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|
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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>
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|
<div id="postamble" class="status">
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|
<p class="author">Author: Dehaeze Thomas</p>
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|
<p class="date">Created: 2020-04-17 ven. 09:35</p>
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</div>
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</body>
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</html>
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