Add Cedrat Actuator
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simscape/sim_nano_station_uniaxial_cedrat.slx
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src/initializeCedratPiezo.m
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src/initializeCedratPiezo.m
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@ -0,0 +1,38 @@
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% Cedrat Actuator
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% :PROPERTIES:
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% :header-args:matlab+: :tangle ../src/initializeCedratPiezo.m
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% :header-args:matlab+: :comments org :mkdirp yes
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% :header-args:matlab+: :eval no :results none
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% :END:
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% <<sec:initializeCedratPiezo>>
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% This Matlab function is accessible [[file:../src/initializeCedratPiezo.m][here]].
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function [cedrat] = initializeCedratPiezo(opts_param)
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%% Default values for opts
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opts = struct();
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%% Populate opts with input parameters
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if exist('opts_param','var')
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for opt = fieldnames(opts_param)'
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opts.(opt{1}) = opts_param.(opt{1});
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end
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end
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%% Stewart Object
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cedrat = struct();
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cedrat.k = 10e7; % Linear Stiffness of each "blade" [N/m]
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cedrat.ka = 10e7; % Linear Stiffness of the stack [N/m]
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cedrat.c = 0.1*sqrt(1*cedrat.k); % [N/(m/s)]
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cedrat.ca = 0.1*sqrt(1*cedrat.ka); % [N/(m/s)]
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cedrat.L = 80; % Total Width of the Actuator[mm]
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cedrat.H = 45; % Total Height of the Actuator [mm]
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cedrat.L2 = sqrt((cedrat.L/2)^2 + (cedrat.H/2)^2); % Length of the elipsoidal sections [mm]
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cedrat.alpha = 180/pi*atan2(cedrat.L/2, cedrat.H/2); % [deg]
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%% Save
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save('./mat/stages.mat', 'cedrat', '-append');
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end
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@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2019-10-25 ven. 16:02 -->
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<!-- 2019-10-28 lun. 17:34 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Simscape Uniaxial Model</title>
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@ -280,48 +280,58 @@ for the JavaScript code in this tag.
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org119d8dc">1. Simscape Model</a></li>
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<li><a href="#org95b633d">2. Undamped System</a>
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<li><a href="#orgfc3044a">1. Simscape Model</a></li>
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<li><a href="#org8da4eb0">2. Undamped System</a>
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<ul>
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<li><a href="#orga87af67">2.1. Init</a></li>
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<li><a href="#org2d53583">2.2. Identification</a></li>
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<li><a href="#orgc443c0b">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#orgdb21910">2.4. Plant</a></li>
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<li><a href="#orgcb2b0a1">2.1. Init</a></li>
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<li><a href="#org7f40bf7">2.2. Identification</a></li>
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<li><a href="#org7908bab">2.3. Sensitivity to Disturbances</a></li>
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<li><a href="#org5a57afd">2.4. Plant</a></li>
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</ul>
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</li>
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<li><a href="#org497a34a">3. Integral Force Feedback</a>
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<li><a href="#org68d1bb0">3. Integral Force Feedback</a>
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<ul>
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<li><a href="#org90d6383">3.1. Control Design</a></li>
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<li><a href="#orge5c43d3">3.2. Identification</a></li>
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<li><a href="#orgdc6e62f">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orgf2883d8">3.4. Damped Plant</a></li>
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<li><a href="#orgb766da3">3.5. Conclusion</a></li>
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<li><a href="#orga5e22eb">3.1. Control Design</a></li>
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<li><a href="#org0fdf2fd">3.2. Identification</a></li>
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<li><a href="#org8b81fd6">3.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org80d5d2d">3.4. Damped Plant</a></li>
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<li><a href="#orga9ed49c">3.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org0216063">4. Relative Motion Control</a>
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<li><a href="#org5d0bc94">4. Relative Motion Control</a>
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<ul>
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<li><a href="#orgda1c98e">4.1. Control Design</a></li>
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<li><a href="#orge3806a0">4.2. Identification</a></li>
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<li><a href="#orge58c47d">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org70ec2cf">4.4. Damped Plant</a></li>
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<li><a href="#orga845b21">4.5. Conclusion</a></li>
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<li><a href="#org4ffacc7">4.1. Control Design</a></li>
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<li><a href="#orgf86862c">4.2. Identification</a></li>
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<li><a href="#org0211838">4.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orgefb061f">4.4. Damped Plant</a></li>
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<li><a href="#org467a5d6">4.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org7666422">5. Direct Velocity Feedback</a>
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<li><a href="#org408eed0">5. Direct Velocity Feedback</a>
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<ul>
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<li><a href="#org58e4d64">5.1. Control Design</a></li>
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<li><a href="#org7e8b911">5.2. Identification</a></li>
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<li><a href="#org2adcafe">5.3. Sensitivity to Disturbance</a></li>
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<li><a href="#orge8b5bd9">5.4. Damped Plant</a></li>
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<li><a href="#org22d6515">5.5. Conclusion</a></li>
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<li><a href="#org64e7b3f">5.1. Control Design</a></li>
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<li><a href="#orga75fa6d">5.2. Identification</a></li>
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<li><a href="#org0d535fa">5.3. Sensitivity to Disturbance</a></li>
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<li><a href="#org9643807">5.4. Damped Plant</a></li>
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<li><a href="#org6e6fd47">5.5. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org55010b4">6. Comparison of Active Damping Techniques</a>
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<li><a href="#orgd792cab">6. With Cedrat Piezo-electric Actuators</a>
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<ul>
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<li><a href="#org5cb1e25">6.1. Load the plants</a></li>
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<li><a href="#orgc746216">6.2. Sensitivity to Disturbance</a></li>
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<li><a href="#orgcd1790f">6.3. Damped Plant</a></li>
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<li><a href="#org9a602cb">6.4. Conclusion</a></li>
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<li><a href="#org7707a0a">6.1. Identification</a></li>
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<li><a href="#orgd921ae7">6.2. Control Design</a></li>
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<li><a href="#org1d5a39c">6.3. Identification</a></li>
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<li><a href="#orgb163c6c">6.4. Sensitivity to Disturbance</a></li>
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<li><a href="#org552dcab">6.5. Damped Plant</a></li>
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<li><a href="#org5065aae">6.6. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org60dfb12">7. Comparison of Active Damping Techniques</a>
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<ul>
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<li><a href="#org249a650">7.1. Load the plants</a></li>
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<li><a href="#org0c1cccb">7.2. Sensitivity to Disturbance</a></li>
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<li><a href="#orgb54c9e3">7.3. Damped Plant</a></li>
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<li><a href="#org1c67523">7.4. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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@ -336,11 +346,11 @@ The idea is to use the same model as the full Simscape Model but to restrict the
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This is done in order to more easily study the system and evaluate control techniques.
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</p>
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<div id="outline-container-org119d8dc" class="outline-2">
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<h2 id="org119d8dc"><span class="section-number-2">1</span> Simscape Model</h2>
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<div id="outline-container-orgfc3044a" class="outline-2">
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<h2 id="orgfc3044a"><span class="section-number-2">1</span> Simscape Model</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#org20bfb11">1</a>.
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A schematic of the uniaxial model used for simulations is represented in figure <a href="#orgc5e0a56">1</a>.
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</p>
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<p>
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@ -384,7 +394,7 @@ The control signal \(u\) is:
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</ul>
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<div id="org20bfb11" class="figure">
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<div id="orgc5e0a56" 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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@ -393,11 +403,11 @@ The control signal \(u\) is:
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<p>
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Few active damping techniques will be compared in order to decide which sensor is to be included in the system.
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Schematics of the active damping techniques are displayed in figure <a href="#org2eb3599">2</a>.
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Schematics of the active damping techniques are displayed in figure <a href="#orgdb9985c">2</a>.
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</p>
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<div id="org2eb3599" class="figure">
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<div id="orgdb9985c" 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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@ -405,16 +415,16 @@ Schematics of the active damping techniques are displayed in figure <a href="#or
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</div>
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</div>
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<div id="outline-container-org95b633d" class="outline-2">
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<h2 id="org95b633d"><span class="section-number-2">2</span> Undamped System</h2>
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<div id="outline-container-org8da4eb0" class="outline-2">
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<h2 id="org8da4eb0"><span class="section-number-2">2</span> Undamped System</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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Let's start by study the undamped system.
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</p>
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</div>
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<div id="outline-container-orga87af67" class="outline-3">
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<h3 id="orga87af67"><span class="section-number-3">2.1</span> Init</h3>
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<div id="outline-container-orgcb2b0a1" class="outline-3">
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<h3 id="orgcb2b0a1"><span class="section-number-3">2.1</span> Init</h3>
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<div 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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@ -426,8 +436,8 @@ All the controllers are set to 0 (Open Loop).
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</p>
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</div>
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</div>
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<div id="outline-container-org2d53583" class="outline-3">
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<h3 id="org2d53583"><span class="section-number-3">2.2</span> Identification</h3>
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<div id="outline-container-org7f40bf7" class="outline-3">
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<h3 id="org7f40bf7"><span class="section-number-3">2.2</span> Identification</h3>
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<div 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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@ -490,19 +500,19 @@ Finally, we save the identified system dynamics for further analysis.
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</div>
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</div>
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<div id="outline-container-orgc443c0b" class="outline-3">
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<h3 id="orgc443c0b"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
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<div id="outline-container-org7908bab" class="outline-3">
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<h3 id="org7908bab"><span class="section-number-3">2.3</span> Sensitivity to Disturbances</h3>
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<div 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="#org4d3097e">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="#orgfd7633d">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
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<li>in figure <a href="#orgd82c2ce">3</a> the transfer functions from ground motion \(D_w\) to the sample position \(D\) and the transfer function from direct force on the sample \(F_s\) to the sample position \(D\) are shown</li>
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<li>in figure <a href="#org72d40e7">4</a>, it is the effect of parasitic forces of the positioning stages (\(F_{ty}\) and \(F_{rz}\)) on the position \(D\) of the sample that are shown</li>
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</ul>
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<div id="org4d3097e" class="figure">
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<div id="orgd82c2ce" 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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@ -510,7 +520,7 @@ We show several plots representing the sensitivity to disturbances:
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<div id="orgfd7633d" class="figure">
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<div id="org72d40e7" 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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@ -518,16 +528,16 @@ We show several plots representing the sensitivity to disturbances:
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</div>
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</div>
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<div id="outline-container-orgdb21910" class="outline-3">
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<h3 id="orgdb21910"><span class="section-number-3">2.4</span> Plant</h3>
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<div id="outline-container-org5a57afd" class="outline-3">
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<h3 id="org5a57afd"><span class="section-number-3">2.4</span> Plant</h3>
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<div class="outline-text-3" id="text-2-4">
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<p>
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The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#orgee21d6a">5</a>.
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The transfer function from the force \(F\) applied by the nano-hexapod to the position of the sample \(D\) is shown in figure <a href="#org5789c3f">5</a>.
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It corresponds to the plant to control.
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</p>
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<div id="orgee21d6a" class="figure">
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<div id="org5789c3f" class="figure">
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<p><img src="figs/uniaxial-plant.png" alt="uniaxial-plant.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Bode plot of the Plant (<a href="./figs/uniaxial-plant.png">png</a>, <a href="./figs/uniaxial-plant.pdf">pdf</a>)</p>
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@ -536,21 +546,21 @@ It corresponds to the plant to control.
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</div>
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</div>
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<div id="outline-container-org497a34a" class="outline-2">
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<h2 id="org497a34a"><span class="section-number-2">3</span> Integral Force Feedback</h2>
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<div id="outline-container-org68d1bb0" class="outline-2">
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<h2 id="org68d1bb0"><span class="section-number-2">3</span> Integral Force Feedback</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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<a id="org61a9736"></a>
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<a id="org36327e7"></a>
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</p>
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<div id="orgf30b3b3" class="figure">
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<div id="org6ca8a23" class="figure">
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<p><img src="figs/uniaxial-model-nass-flexible-iff.png" alt="uniaxial-model-nass-flexible-iff.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Uniaxial IFF Control Schematic</p>
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</div>
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</div>
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<div id="outline-container-org90d6383" class="outline-3">
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<h3 id="org90d6383"><span class="section-number-3">3.1</span> Control Design</h3>
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<div id="outline-container-orga5e22eb" class="outline-3">
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<h3 id="orga5e22eb"><span class="section-number-3">3.1</span> Control Design</h3>
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<div class="outline-text-3" id="text-3-1">
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<div class="org-src-container">
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<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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@ -562,7 +572,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
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</p>
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<div id="org13e2d05" class="figure">
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<div id="org5063cb4" class="figure">
|
||||
<p><img src="figs/uniaxial_iff_plant.png" alt="uniaxial_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_iff_plant.png">png</a>, <a href="./figs/uniaxial_iff_plant.pdf">pdf</a>)</p>
|
||||
@ -577,7 +587,7 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org928425f" class="figure">
|
||||
<div id="org495687f" class="figure">
|
||||
<p><img src="figs/uniaxial_iff_open_loop.png" alt="uniaxial_iff_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_iff_open_loop.png">png</a>, <a href="./figs/uniaxial_iff_open_loop.pdf">pdf</a>)</p>
|
||||
@ -585,8 +595,8 @@ The controller for each pair of actuator/sensor is:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge5c43d3" class="outline-3">
|
||||
<h3 id="orge5c43d3"><span class="section-number-3">3.2</span> Identification</h3>
|
||||
<div id="outline-container-org0fdf2fd" class="outline-3">
|
||||
<h3 id="org0fdf2fd"><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.
|
||||
@ -669,18 +679,18 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgdc6e62f" class="outline-3">
|
||||
<h3 id="orgdc6e62f"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org8b81fd6" class="outline-3">
|
||||
<h3 id="org8b81fd6"><span class="section-number-3">3.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
|
||||
<div id="org8df8488" class="figure">
|
||||
<div id="org307c8d8" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_iff.png" alt="uniaxial_sensitivity_dist_iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Sensitivity to disturbance once the IFF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_iff.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6003ced" class="figure">
|
||||
<div id="orgabd6245" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_iff.png" alt="uniaxial_sensitivity_dist_stages_iff.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Sensitivity to force disturbances in various stages when IFF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_iff.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_iff.pdf">pdf</a>)</p>
|
||||
@ -688,11 +698,11 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf2883d8" class="outline-3">
|
||||
<h3 id="orgf2883d8"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-org80d5d2d" class="outline-3">
|
||||
<h3 id="org80d5d2d"><span class="section-number-3">3.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
|
||||
<div id="org2071f90" class="figure">
|
||||
<div id="org35f8f43" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_iff_damped.png" alt="uniaxial_plant_iff_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Damped Plant after IFF is applied (<a href="./figs/uniaxial_plant_iff_damped.png">png</a>, <a href="./figs/uniaxial_plant_iff_damped.pdf">pdf</a>)</p>
|
||||
@ -700,8 +710,8 @@ G_iff.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb766da3" class="outline-3">
|
||||
<h3 id="orgb766da3"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||
<div id="outline-container-orga9ed49c" class="outline-3">
|
||||
<h3 id="orga9ed49c"><span class="section-number-3">3.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-3-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -713,25 +723,25 @@ Integral Force Feedback:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0216063" class="outline-2">
|
||||
<h2 id="org0216063"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||
<div id="outline-container-org5d0bc94" class="outline-2">
|
||||
<h2 id="org5d0bc94"><span class="section-number-2">4</span> Relative Motion Control</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="orgcf7a709"></a>
|
||||
<a id="org5737634"></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="org8ed07c5" class="figure">
|
||||
<div id="org742e0c1" class="figure">
|
||||
<p><img src="figs/uniaxial-model-nass-flexible-rmc.png" alt="uniaxial-model-nass-flexible-rmc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Uniaxial RMC Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgda1c98e" class="outline-3">
|
||||
<h3 id="orgda1c98e"><span class="section-number-3">4.1</span> Control Design</h3>
|
||||
<div id="outline-container-org4ffacc7" class="outline-3">
|
||||
<h3 id="org4ffacc7"><span class="section-number-3">4.1</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
@ -743,7 +753,7 @@ Let's look at the transfer function from actuator forces in the nano-hexapod to
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org75fbb9f" class="figure">
|
||||
<div id="org9fd5b87" class="figure">
|
||||
<p><img src="figs/uniaxial_rmc_plant.png" alt="uniaxial_rmc_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Transfer function from forces applied in the legs to leg displacement sensor (<a href="./figs/uniaxial_rmc_plant.png">png</a>, <a href="./figs/uniaxial_rmc_plant.pdf">pdf</a>)</p>
|
||||
@ -759,7 +769,7 @@ A Low pass Filter is added to make the controller transfer function proper.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgc5d2eb6" class="figure">
|
||||
<div id="org7d6a1ae" class="figure">
|
||||
<p><img src="figs/uniaxial_rmc_open_loop.png" alt="uniaxial_rmc_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_rmc_open_loop.png">png</a>, <a href="./figs/uniaxial_rmc_open_loop.pdf">pdf</a>)</p>
|
||||
@ -767,8 +777,8 @@ A Low pass Filter is added to make the controller transfer function proper.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge3806a0" class="outline-3">
|
||||
<h3 id="orge3806a0"><span class="section-number-3">4.2</span> Identification</h3>
|
||||
<div id="outline-container-orgf86862c" class="outline-3">
|
||||
<h3 id="orgf86862c"><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.
|
||||
@ -852,18 +862,18 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-orge58c47d" class="outline-3">
|
||||
<h3 id="orge58c47d"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org0211838" class="outline-3">
|
||||
<h3 id="org0211838"><span class="section-number-3">4.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
|
||||
<div id="orgd910119" class="figure">
|
||||
<div id="org00d0d6e" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_rmc.png" alt="uniaxial_sensitivity_dist_rmc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Sensitivity to disturbance once the RMC controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_rmc.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6610f06" class="figure">
|
||||
<div id="org0006b16" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_rmc.png" alt="uniaxial_sensitivity_dist_stages_rmc.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Sensitivity to force disturbances in various stages when RMC is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_rmc.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_rmc.pdf">pdf</a>)</p>
|
||||
@ -871,11 +881,11 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org70ec2cf" class="outline-3">
|
||||
<h3 id="org70ec2cf"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-orgefb061f" class="outline-3">
|
||||
<h3 id="orgefb061f"><span class="section-number-3">4.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
|
||||
<div id="org7508a42" class="figure">
|
||||
<div id="org2092a67" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_rmc_damped.png" alt="uniaxial_plant_rmc_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </span>Damped Plant after RMC is applied (<a href="./figs/uniaxial_plant_rmc_damped.png">png</a>, <a href="./figs/uniaxial_plant_rmc_damped.pdf">pdf</a>)</p>
|
||||
@ -883,8 +893,8 @@ G_rmc.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga845b21" class="outline-3">
|
||||
<h3 id="orga845b21"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org467a5d6" class="outline-3">
|
||||
<h3 id="org467a5d6"><span class="section-number-3">4.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-4-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -896,25 +906,25 @@ Relative Motion Control:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7666422" class="outline-2">
|
||||
<h2 id="org7666422"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||
<div id="outline-container-org408eed0" class="outline-2">
|
||||
<h2 id="org408eed0"><span class="section-number-2">5</span> Direct Velocity Feedback</h2>
|
||||
<div class="outline-text-2" id="text-5">
|
||||
<p>
|
||||
<a id="org6b8afcf"></a>
|
||||
<a id="orgfc1ffa1"></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="orga86445d" class="figure">
|
||||
<div id="org070b73d" class="figure">
|
||||
<p><img src="figs/uniaxial-model-nass-flexible-dvf.png" alt="uniaxial-model-nass-flexible-dvf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 18: </span>Uniaxial DVF Control Schematic</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org58e4d64" class="outline-3">
|
||||
<h3 id="org58e4d64"><span class="section-number-3">5.1</span> Control Design</h3>
|
||||
<div id="outline-container-org64e7b3f" class="outline-3">
|
||||
<h3 id="org64e7b3f"><span class="section-number-3">5.1</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-5-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
@ -922,7 +932,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgf4888fb" class="figure">
|
||||
<div id="org56e8509" class="figure">
|
||||
<p><img src="figs/uniaxial_dvf_plant.png" alt="uniaxial_dvf_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_plant.png">png</a>, <a href="./figs/uniaxial_dvf_plant.pdf">pdf</a>)</p>
|
||||
@ -934,7 +944,7 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org1a62235" class="figure">
|
||||
<div id="orgc80a1c2" class="figure">
|
||||
<p><img src="figs/uniaxial_dvf_loop_gain.png" alt="uniaxial_dvf_loop_gain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Transfer function from forces applied in the legs to leg velocity sensor (<a href="./figs/uniaxial_dvf_loop_gain.png">png</a>, <a href="./figs/uniaxial_dvf_loop_gain.pdf">pdf</a>)</p>
|
||||
@ -942,8 +952,8 @@ In the Relative Motion Control (RMC), a feedback is applied between the measured
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7e8b911" class="outline-3">
|
||||
<h3 id="org7e8b911"><span class="section-number-3">5.2</span> Identification</h3>
|
||||
<div id="outline-container-orga75fa6d" class="outline-3">
|
||||
<h3 id="orga75fa6d"><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.
|
||||
@ -1026,18 +1036,18 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2adcafe" class="outline-3">
|
||||
<h3 id="org2adcafe"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||
<div id="outline-container-org0d535fa" class="outline-3">
|
||||
<h3 id="org0d535fa"><span class="section-number-3">5.3</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-5-3">
|
||||
|
||||
<div id="org9ca6224" class="figure">
|
||||
<div id="org30e1316" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_dvf.png" alt="uniaxial_sensitivity_dist_dvf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 21: </span>Sensitivity to disturbance once the DVF controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_dvf.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd0ada58" class="figure">
|
||||
<div id="orge40e605" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_dvf.png" alt="uniaxial_sensitivity_dist_stages_dvf.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 22: </span>Sensitivity to force disturbances in various stages when DVF is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_dvf.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_dvf.pdf">pdf</a>)</p>
|
||||
@ -1045,11 +1055,11 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge8b5bd9" class="outline-3">
|
||||
<h3 id="orge8b5bd9"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||
<div id="outline-container-org9643807" class="outline-3">
|
||||
<h3 id="org9643807"><span class="section-number-3">5.4</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-5-4">
|
||||
|
||||
<div id="org55c6262" class="figure">
|
||||
<div id="org48982d0" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_dvf_damped.png" alt="uniaxial_plant_dvf_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 23: </span>Damped Plant after DVF is applied (<a href="./figs/uniaxial_plant_dvf_damped.png">png</a>, <a href="./figs/uniaxial_plant_dvf_damped.pdf">pdf</a>)</p>
|
||||
@ -1057,8 +1067,8 @@ G_dvf.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span cl
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org22d6515" class="outline-3">
|
||||
<h3 id="org22d6515"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||
<div id="outline-container-org6e6fd47" class="outline-3">
|
||||
<h3 id="org6e6fd47"><span class="section-number-3">5.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-5-5">
|
||||
<div class="important">
|
||||
<p>
|
||||
@ -1069,16 +1079,235 @@ Direct Velocity Feedback:
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-org55010b4" class="outline-2">
|
||||
<h2 id="org55010b4"><span class="section-number-2">6</span> Comparison of Active Damping Techniques</h2>
|
||||
<div id="outline-container-orgd792cab" class="outline-2">
|
||||
<h2 id="orgd792cab"><span class="section-number-2">6</span> With Cedrat Piezo-electric Actuators</h2>
|
||||
<div class="outline-text-2" id="text-6">
|
||||
</div>
|
||||
<div id="outline-container-org7707a0a" class="outline-3">
|
||||
<h3 id="org7707a0a"><span class="section-number-3">6.1</span> Identification</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<p>
|
||||
<a id="org9b9c235"></a>
|
||||
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 = <span class="org-highlight-numbers-number">0</span>;
|
||||
|
||||
<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'</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-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fs'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied on the sample</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnl'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied by the NASS</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdty'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Ty</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdrz'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Rz</span>
|
||||
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dsm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of the sample</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in NASS's legs</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of NASS's legs</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">9</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dgm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute displacement of the granite</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Vlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</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<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
G.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><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-rainbow-delimiters-depth-1">}</span>; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
||||
G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><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-rainbow-delimiters-depth-1">}</span>; ...<span class="org-comment"> % Absolute Velocity of NASS [m/s]</span>
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd921ae7" class="outline-3">
|
||||
<h3 id="orgd921ae7"><span class="section-number-3">6.2</span> Control Design</h3>
|
||||
<div class="outline-text-3" id="text-6-2">
|
||||
<p>
|
||||
Let's look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org8bae400" class="figure">
|
||||
<p><img src="figs/uniaxial_cedrat_plant.png" alt="uniaxial_cedrat_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 24: </span>Transfer function from forces applied in the legs to force sensor (<a href="./figs/uniaxial_cedrat_plant.png">png</a>, <a href="./figs/uniaxial_cedrat_plant.pdf">pdf</a>)</p>
|
||||
</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-highlight-numbers-number">1000</span><span class="org-type">/</span>s;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0e53970" class="figure">
|
||||
<p><img src="figs/uniaxial_cedrat_open_loop.png" alt="uniaxial_cedrat_open_loop.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 25: </span>Loop Gain for the Integral Force Feedback (<a href="./figs/uniaxial_cedrat_open_loop.png">png</a>, <a href="./figs/uniaxial_cedrat_open_loop.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1d5a39c" class="outline-3">
|
||||
<h3 id="org1d5a39c"><span class="section-number-3">6.3</span> Identification</h3>
|
||||
<div 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<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeGranite<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeTy<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeRy<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeRz<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeMicroHexapod<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeAxisc<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeMirror<span class="org-rainbow-delimiters-depth-1">()</span>;
|
||||
initializeNanoHexapod<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'actuator'</span>, <span class="org-string">'piezo'</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
initializeSample<span class="org-rainbow-delimiters-depth-1">(</span>struct<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mass'</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
All the controllers are set to 0.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">K = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
K_iff = <span class="org-type">-</span>K_cedrat;
|
||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_iff'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
K_rmc = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_rmc'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
K_dvf = tf<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/controllers.mat'</span>, <span class="org-string">'K_dvf'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div 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 = <span class="org-highlight-numbers-number">0</span>;
|
||||
|
||||
<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'</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-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dw'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Ground Motion</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fs'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied on the sample</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnl'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force applied by the NASS</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdty'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Ty</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fdrz'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'input'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Parasitic force Rz</span>
|
||||
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dsm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of the sample</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Fnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in NASS's legs</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dnlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of NASS's legs</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">9</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Dgm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Absolute displacement of the granite</span>
|
||||
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, <span class="org-string">'/Vlm'</span><span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-string">'output'</span><span class="org-rainbow-delimiters-depth-1">)</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<span class="org-rainbow-delimiters-depth-1">(</span>mdl, io, options<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
G_cedrat.InputName = <span class="org-rainbow-delimiters-depth-1">{</span><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-rainbow-delimiters-depth-1">}</span>; <span class="org-comment">% Parasitic Force Rz [N]</span>
|
||||
G_cedrat.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><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-rainbow-delimiters-depth-1">}</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-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G_cedrat'</span>, <span class="org-string">'-append'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb163c6c" class="outline-3">
|
||||
<h3 id="orgb163c6c"><span class="section-number-3">6.4</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-6-4">
|
||||
|
||||
<div id="org6c93b19" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_cedrat.png" alt="uniaxial_sensitivity_dist_cedrat.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 26: </span>Sensitivity to disturbance once the CEDRAT controller is applied to the system (<a href="./figs/uniaxial_sensitivity_dist_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_cedrat.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org1b2d2df" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_dist_stages_cedrat.png" alt="uniaxial_sensitivity_dist_stages_cedrat.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 27: </span>Sensitivity to force disturbances in various stages when CEDRAT is applied (<a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.png">png</a>, <a href="./figs/uniaxial_sensitivity_dist_stages_cedrat.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org552dcab" class="outline-3">
|
||||
<h3 id="org552dcab"><span class="section-number-3">6.5</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-6-5">
|
||||
|
||||
<div id="orge59303f" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_cedrat_damped.png" alt="uniaxial_plant_cedrat_damped.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 28: </span>Damped Plant after CEDRAT is applied (<a href="./figs/uniaxial_plant_cedrat_damped.png">png</a>, <a href="./figs/uniaxial_plant_cedrat_damped.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5065aae" class="outline-3">
|
||||
<h3 id="org5065aae"><span class="section-number-3">6.6</span> Conclusion</h3>
|
||||
<div 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-org60dfb12" class="outline-2">
|
||||
<h2 id="org60dfb12"><span class="section-number-2">7</span> Comparison of Active Damping Techniques</h2>
|
||||
<div class="outline-text-2" id="text-7">
|
||||
<p>
|
||||
<a id="orgc7002a8"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org5cb1e25" class="outline-3">
|
||||
<h3 id="org5cb1e25"><span class="section-number-3">6.1</span> Load the plants</h3>
|
||||
<div class="outline-text-3" id="text-6-1">
|
||||
<div id="outline-container-org249a650" class="outline-3">
|
||||
<h3 id="org249a650"><span class="section-number-3">7.1</span> Load the plants</h3>
|
||||
<div class="outline-text-3" id="text-7-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./uniaxial/mat/plants.mat'</span>, <span class="org-string">'G'</span>, <span class="org-string">'G_iff'</span>, <span class="org-string">'G_rmc'</span>, <span class="org-string">'G_dvf'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
@ -1086,56 +1315,59 @@ Direct Velocity Feedback:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc746216" class="outline-3">
|
||||
<h3 id="orgc746216"><span class="section-number-3">6.2</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-6-2">
|
||||
<div id="outline-container-org0c1cccb" class="outline-3">
|
||||
<h3 id="org0c1cccb"><span class="section-number-3">7.2</span> Sensitivity to Disturbance</h3>
|
||||
<div class="outline-text-3" id="text-7-2">
|
||||
|
||||
<div id="orga056e76" class="figure">
|
||||
<div id="org9992967" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_ground_motion.png" alt="uniaxial_sensitivity_ground_motion.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 24: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 29: </span>Sensitivity to Ground Motion - Comparison (<a href="./figs/uniaxial_sensitivity_ground_motion.png">png</a>, <a href="./figs/uniaxial_sensitivity_ground_motion.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div id="org5bfe138" class="figure">
|
||||
<div id="orgc7a133b" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_direct_force.png" alt="uniaxial_sensitivity_direct_force.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 25: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 30: </span>Sensitivity to disturbance - Comparison (<a href="./figs/uniaxial_sensitivity_direct_force.png">png</a>, <a href="./figs/uniaxial_sensitivity_direct_force.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org4e0c629" class="figure">
|
||||
<div id="org8eaf52e" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_fty.png" alt="uniaxial_sensitivity_fty.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 26: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 31: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_fty.png">png</a>, <a href="./figs/uniaxial_sensitivity_fty.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgae22af6" class="figure">
|
||||
<div id="orgb554437" class="figure">
|
||||
<p><img src="figs/uniaxial_sensitivity_frz.png" alt="uniaxial_sensitivity_frz.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 27: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 32: </span>Sensitivity to force disturbances - Comparison (<a href="./figs/uniaxial_sensitivity_frz.png">png</a>, <a href="./figs/uniaxial_sensitivity_frz.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcd1790f" class="outline-3">
|
||||
<h3 id="orgcd1790f"><span class="section-number-3">6.3</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-6-3">
|
||||
<div id="outline-container-orgb54c9e3" class="outline-3">
|
||||
<h3 id="orgb54c9e3"><span class="section-number-3">7.3</span> Damped Plant</h3>
|
||||
<div class="outline-text-3" id="text-7-3">
|
||||
|
||||
<div id="org38fbe3d" class="figure">
|
||||
<div id="org9375b1e" class="figure">
|
||||
<p><img src="figs/uniaxial_plant_damped_comp.png" alt="uniaxial_plant_damped_comp.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 28: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
|
||||
<p><span class="figure-number">Figure 33: </span>Damped Plant - Comparison (<a href="./figs/uniaxial_plant_damped_comp.png">png</a>, <a href="./figs/uniaxial_plant_damped_comp.pdf">pdf</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9a602cb" class="outline-3">
|
||||
<h3 id="org9a602cb"><span class="section-number-3">6.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-6-4">
|
||||
<table id="orgf039db4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<div id="outline-container-org1c67523" class="outline-3">
|
||||
<h3 id="org1c67523"><span class="section-number-3">7.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-7-4">
|
||||
<p>
|
||||
#name: tab:active<sub>damping</sub><sub>comparison</sub>
|
||||
</p>
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
<caption class="t-above"><span class="table-number">Table 1:</span> Comparison of proposed active damping techniques</caption>
|
||||
|
||||
<colgroup>
|
||||
@ -1205,7 +1437,7 @@ The next step is to take into account the power spectral density of each disturb
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-10-25 ven. 16:02</p>
|
||||
<p class="date">Created: 2019-10-28 lun. 17:34</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
@ -2106,6 +2106,314 @@ And initialize the controllers.
|
||||
#+begin_important
|
||||
Direct Velocity Feedback:
|
||||
#+end_important
|
||||
* With Cedrat Piezo-electric Actuators
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
simulinkproject('../');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
open 'simscape/sim_nano_station_uniaxial_cedrat.slx'
|
||||
#+end_src
|
||||
|
||||
** Identification
|
||||
We identify the dynamics of the system.
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'sim_nano_station_uniaxial_cedrat';
|
||||
#+end_src
|
||||
|
||||
The inputs and outputs are defined below and corresponds to the name of simulink blocks.
|
||||
#+begin_src matlab
|
||||
%% Input/Output definition
|
||||
io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion
|
||||
io(2) = linio([mdl, '/Fs'], 1, 'input'); % Force applied on the sample
|
||||
io(3) = linio([mdl, '/Fnl'], 1, 'input'); % Force applied by the NASS
|
||||
io(4) = linio([mdl, '/Fdty'], 1, 'input'); % Parasitic force Ty
|
||||
io(5) = linio([mdl, '/Fdrz'], 1, 'input'); % Parasitic force Rz
|
||||
|
||||
io(6) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample
|
||||
io(7) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs
|
||||
io(8) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs
|
||||
io(9) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute displacement of the granite
|
||||
io(10) = linio([mdl, '/Vlm'], 1, 'output'); % Measured absolute velocity of the top NASS platform
|
||||
#+end_src
|
||||
|
||||
Finally, we use the =linearize= Matlab function to extract a state space model from the simscape model.
|
||||
#+begin_src matlab
|
||||
%% Run the linearization
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {'Dw', ... % Ground Motion [m]
|
||||
'Fs', ... % Force Applied on Sample [N]
|
||||
'Fn', ... % Force applied by NASS [N]
|
||||
'Fty', ... % Parasitic Force Ty [N]
|
||||
'Frz'}; % Parasitic Force Rz [N]
|
||||
G.OutputName = {'D', ... % Measured sample displacement x.r.t. granite [m]
|
||||
'Fnm', ... % Force Sensor in NASS [N]
|
||||
'Dnm', ... % Displacement Sensor in NASS [m]
|
||||
'Dgm', ... % Asbolute displacement of Granite [m]
|
||||
'Vlm'}; ... % Absolute Velocity of NASS [m/s]
|
||||
#+end_src
|
||||
|
||||
** Control Design
|
||||
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.
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
plot(freqs, abs(squeeze(freqresp(G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial_cedrat_plant.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial_cedrat_plant
|
||||
#+CAPTION: Transfer function from forces applied in the legs to force sensor ([[./figs/uniaxial_cedrat_plant.png][png]], [[./figs/uniaxial_cedrat_plant.pdf][pdf]])
|
||||
[[file:figs/uniaxial_cedrat_plant.png]]
|
||||
|
||||
The controller for each pair of actuator/sensor is:
|
||||
#+begin_src matlab
|
||||
K_cedrat = 1000/s;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
plot(freqs, abs(squeeze(freqresp(K_cedrat*G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]);
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(K_cedrat*G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial_cedrat_open_loop.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial_cedrat_open_loop
|
||||
#+CAPTION: Loop Gain for the Integral Force Feedback ([[./figs/uniaxial_cedrat_open_loop.png][png]], [[./figs/uniaxial_cedrat_open_loop.pdf][pdf]])
|
||||
[[file:figs/uniaxial_cedrat_open_loop.png]]
|
||||
|
||||
** Identification
|
||||
Let's initialize the system prior to identification.
|
||||
#+begin_src matlab
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
initializeNanoHexapod(struct('actuator', 'piezo'));
|
||||
initializeSample(struct('mass', 50));
|
||||
#+end_src
|
||||
|
||||
All the controllers are set to 0.
|
||||
#+begin_src matlab
|
||||
K = tf(0);
|
||||
save('./mat/controllers.mat', 'K', '-append');
|
||||
K_iff = -K_cedrat;
|
||||
save('./mat/controllers.mat', 'K_iff', '-append');
|
||||
K_rmc = tf(0);
|
||||
save('./mat/controllers.mat', 'K_rmc', '-append');
|
||||
K_dvf = tf(0);
|
||||
save('./mat/controllers.mat', 'K_dvf', '-append');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'sim_nano_station_uniaxial_cedrat';
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
%% Input/Output definition
|
||||
io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion
|
||||
io(2) = linio([mdl, '/Fs'], 1, 'input'); % Force applied on the sample
|
||||
io(3) = linio([mdl, '/Fnl'], 1, 'input'); % Force applied by the NASS
|
||||
io(4) = linio([mdl, '/Fdty'], 1, 'input'); % Parasitic force Ty
|
||||
io(5) = linio([mdl, '/Fdrz'], 1, 'input'); % Parasitic force Rz
|
||||
|
||||
io(6) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample
|
||||
io(7) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs
|
||||
io(8) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs
|
||||
io(9) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute displacement of the granite
|
||||
io(10) = linio([mdl, '/Vlm'], 1, 'output'); % Measured absolute velocity of the top NASS platform
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
%% Run the linearization
|
||||
G_cedrat = linearize(mdl, io, options);
|
||||
G_cedrat.InputName = {'Dw', ... % Ground Motion [m]
|
||||
'Fs', ... % Force Applied on Sample [N]
|
||||
'Fn', ... % Force applied by NASS [N]
|
||||
'Fty', ... % Parasitic Force Ty [N]
|
||||
'Frz'}; % Parasitic Force Rz [N]
|
||||
G_cedrat.OutputName = {'D', ... % Measured sample displacement x.r.t. granite [m]
|
||||
'Fnm', ... % Force Sensor in NASS [N]
|
||||
'Dnm', ... % Displacement Sensor in NASS [m]
|
||||
'Dgm', ... % Asbolute displacement of Granite [m]
|
||||
'Vlm'}; ... % Absolute Velocity of NASS [m/s]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
save('./uniaxial/mat/plants.mat', 'G_cedrat', '-append');
|
||||
#+end_src
|
||||
|
||||
** Sensitivity to Disturbance
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
subplot(2, 1, 1);
|
||||
title('$D_w$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('D', 'Dw'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL');
|
||||
plot(freqs, abs(squeeze(freqresp(G_cedrat('D', 'Dw'), freqs, 'Hz'))), 'k--', 'DisplayName', 'CEDRAT');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
subplot(2, 1, 2);
|
||||
title('$F_s$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('D', 'Fs'), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, abs(squeeze(freqresp(G_cedrat('D', 'Fs'), freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_cedrat.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial_sensitivity_dist_cedrat
|
||||
#+CAPTION: Sensitivity to disturbance once the CEDRAT controller is applied to the system ([[./figs/uniaxial_sensitivity_dist_cedrat.png][png]], [[./figs/uniaxial_sensitivity_dist_cedrat.pdf][pdf]])
|
||||
[[file:figs/uniaxial_sensitivity_dist_cedrat.png]]
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
subplot(2, 1, 1);
|
||||
title('$F_{ty}$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('D', 'Fty'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL');
|
||||
plot(freqs, abs(squeeze(freqresp(G_cedrat('D', 'Fty'), freqs, 'Hz'))), 'k--', 'DisplayName', 'CEDRAT');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
subplot(2, 1, 2);
|
||||
title('$F_{rz}$ to $D$');
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('D', 'Frz'), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, abs(squeeze(freqresp(G_cedrat('D', 'Frz'), freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_stages_cedrat.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial_sensitivity_dist_stages_cedrat
|
||||
#+CAPTION: Sensitivity to force disturbances in various stages when CEDRAT is applied ([[./figs/uniaxial_sensitivity_dist_stages_cedrat.png][png]], [[./figs/uniaxial_sensitivity_dist_stages_cedrat.pdf][pdf]])
|
||||
[[file:figs/uniaxial_sensitivity_dist_stages_cedrat.png]]
|
||||
|
||||
** Damped Plant
|
||||
#+begin_src matlab :exports none
|
||||
freqs = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
|
||||
ax1 = subplot(2, 1, 1);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL');
|
||||
plot(freqs, abs(squeeze(freqresp(G_cedrat('D', 'Fn'), freqs, 'Hz'))), 'k--', 'DisplayName', 'CEDRAT');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]);
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
hold on;
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-');
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_cedrat('D', 'Fn'), freqs, 'Hz'))), 'k--');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
#+end_src
|
||||
|
||||
#+HEADER: :tangle no :exports results :results none :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/uniaxial_plant_cedrat_damped.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:uniaxial_plant_cedrat_damped
|
||||
#+CAPTION: Damped Plant after CEDRAT is applied ([[./figs/uniaxial_plant_cedrat_damped.png][png]], [[./figs/uniaxial_plant_cedrat_damped.pdf][pdf]])
|
||||
[[file:figs/uniaxial_plant_cedrat_damped.png]]
|
||||
|
||||
** Conclusion
|
||||
#+begin_important
|
||||
This gives similar results than with a classical force sensor.
|
||||
#+end_important
|
||||
|
||||
* Comparison of Active Damping Techniques
|
||||
<<sec:comparison>>
|
||||
** Matlab Init :noexport:ignore:
|
||||
@ -2278,7 +2586,7 @@ Direct Velocity Feedback:
|
||||
|
||||
** Conclusion
|
||||
|
||||
#+name: tab:active_damping_comparison
|
||||
#name: tab:active_damping_comparison
|
||||
#+caption: Comparison of proposed active damping techniques
|
||||
| | IFF | RMC | DVF |
|
||||
|---------------------------+-----------------+-----------------+----------|
|
||||
|
||||
Loading…
Reference in New Issue
Block a user