371 lines
15 KiB
HTML
371 lines
15 KiB
HTML
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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">Stewart Platform - Tracking Control</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="#org4c793a2">1. First Control Architecture</a>
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<ul>
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<li><a href="#org49467e8">1.1. Control Schematic</a></li>
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<li><a href="#org67db718">1.2. Initialize the Stewart platform</a></li>
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<li><a href="#org641cba6">1.3. Identification of the plant</a></li>
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<li><a href="#orgd9d7b44">1.4. Plant Analysis</a></li>
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<li><a href="#orgfaf80fa">1.5. Controller Design</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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<div id="outline-container-org4c793a2" class="outline-2">
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<h2 id="org4c793a2"><span class="section-number-2">1</span> First Control Architecture</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-org49467e8" class="outline-3">
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<h3 id="org49467e8"><span class="section-number-3">1.1</span> Control Schematic</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="figure">
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<p><img src="figs/control_measure_rotating_2dof.png" alt="control_measure_rotating_2dof.png" />
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</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org67db718" class="outline-3">
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<h3 id="org67db718"><span class="section-number-3">1.2</span> Initialize the Stewart platform</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="org-src-container">
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<pre class="src src-matlab">stewart = initializeStewartPlatform();
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stewart = initializeFramesPositions(stewart, <span class="org-string">'H'</span>, 90e<span class="org-type">-</span>3, <span class="org-string">'MO_B'</span>, 45e<span class="org-type">-</span>3);
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stewart = generateGeneralConfiguration(stewart);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart);
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stewart = initializeJointDynamics(stewart, <span class="org-string">'type_F'</span>, <span class="org-string">'universal_p'</span>, <span class="org-string">'type_M'</span>, <span class="org-string">'spherical_p'</span>);
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stewart = initializeCylindricalPlatforms(stewart);
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stewart = initializeCylindricalStruts(stewart);
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stewart = computeJacobian(stewart);
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stewart = initializeStewartPose(stewart);
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stewart = initializeInertialSensor(stewart, <span class="org-string">'type'</span>, <span class="org-string">'accelerometer'</span>, <span class="org-string">'freq'</span>, 5e3);
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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">ground = initializeGround(<span class="org-string">'type'</span>, <span class="org-string">'none'</span>);
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payload = initializePayload(<span class="org-string">'type'</span>, <span class="org-string">'none'</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-org641cba6" class="outline-3">
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<h3 id="org641cba6"><span class="section-number-3">1.3</span> Identification of the plant</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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Let’s identify the transfer function from \(\bm{\tau}\) to \(\bm{L}\).
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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">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'stewart_platform_model'</span>;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
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clear io; io_i = 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Controller'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Actuator Force Inputs [N]</span>
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io(io_i) = linio([mdl, <span class="org-string">'/Stewart Platform'</span>], 1, <span class="org-string">'openoutput'</span>, [], <span class="org-string">'dLm'</span>); io_i = io_i <span class="org-type">+</span> 1; <span class="org-comment">% Relative Displacement Outputs [m]</span>
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
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G = linearize(mdl, io);
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G.InputName = {<span class="org-string">'F1'</span>, <span class="org-string">'F2'</span>, <span class="org-string">'F3'</span>, <span class="org-string">'F4'</span>, <span class="org-string">'F5'</span>, <span class="org-string">'F6'</span>};
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G.OutputName = {<span class="org-string">'L1'</span>, <span class="org-string">'L2'</span>, <span class="org-string">'L3'</span>, <span class="org-string">'L4'</span>, <span class="org-string">'L5'</span>, <span class="org-string">'L6'</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-orgd9d7b44" class="outline-3">
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<h3 id="orgd9d7b44"><span class="section-number-3">1.4</span> Plant Analysis</h3>
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<div class="outline-text-3" id="text-1-4">
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<p>
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Diagonal terms
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Compare to off-diagonal terms
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</p>
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</div>
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</div>
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<div id="outline-container-orgfaf80fa" class="outline-3">
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<h3 id="orgfaf80fa"><span class="section-number-3">1.5</span> Controller Design</h3>
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<div class="outline-text-3" id="text-1-5">
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<p>
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One integrator should be present in the controller.
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</p>
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<p>
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A lead is added around the crossover frequency which is set to be around 500Hz.
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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-comment">% wint = 2*pi*100; % Integrate until [rad]</span>
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<span class="org-comment">% wlead = 2*pi*500; % Location of the lead [rad]</span>
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<span class="org-comment">% hlead = 2; % Lead strengh</span>
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<span class="org-comment">% Kl = 1e6 * ... % Gain</span>
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<span class="org-comment">% (s + wint)/(s) * ... % Integrator until 100Hz</span>
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<span class="org-comment">% (1 + s/(wlead/hlead)/(1 + s/(wlead*hlead))); % Lead</span>
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wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100;
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Kl = 1<span class="org-type">/</span>abs(freqresp(G(1,1), wc)) <span class="org-type">*</span> wc<span class="org-type">/</span>s <span class="org-type">*</span> 1<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>(3<span class="org-type">*</span>wc));
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Kl = Kl <span class="org-type">*</span> eye(6);
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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>
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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: 2020-03-02 lun. 17:57</p>
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