408 lines
18 KiB
HTML
408 lines
18 KiB
HTML
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<body>
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<div id="org-div-home-and-up">
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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 - Control Study</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="#orgc1805a8">First Control Architecture</a>
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<ul>
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<li><a href="#org066d914">Control Schematic</a></li>
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<li><a href="#org64f6d6b">Initialize the Stewart platform</a></li>
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<li><a href="#org4493ec7">Identification of the plant</a></li>
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<li><a href="#org72dad5c">Plant Analysis</a></li>
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<li><a href="#orga9fb0f5">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-orgc1805a8" class="outline-2">
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<h2 id="orgc1805a8">First Control Architecture</h2>
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<div class="outline-text-2" id="text-orgc1805a8">
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</div>
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<div id="outline-container-org066d914" class="outline-3">
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<h3 id="org066d914">Control Schematic</h3>
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<div class="outline-text-3" id="text-org066d914">
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<div class="org-src-container">
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<pre class="src src-latex"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
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<span class="org-comment">% Blocs</span>
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<span class="org-comment">% Connections and labels</span>
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<span class="org-font-latex-sedate">\draw</span>[->] (subr.east) -- (K.west) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bm</span></span><span class="org-font-latex-math">{</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\epsilon</span></span><span class="org-font-latex-math">}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_</span></span><span class="org-font-latex-math">{L}$</span>};
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<span class="org-font-latex-sedate">\draw</span>[->] (K.east) -- (G.west) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bm</span></span><span class="org-font-latex-math">{</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\tau</span></span><span class="org-font-latex-math">}$</span>};
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<span class="org-font-latex-sedate">\draw</span>[->] (G.east) node[above right]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bm</span></span><span class="org-font-latex-math">{L}$</span>} -| (<span class="org-font-latex-math">$(G.east)+(1, -1)$</span>) -| (subr.south);
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<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
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</pre>
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</div>
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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-org64f6d6b" class="outline-3">
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<h3 id="org64f6d6b">Initialize the Stewart platform</h3>
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<div class="outline-text-3" id="text-org64f6d6b">
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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);
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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 = 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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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org4493ec7" class="outline-3">
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<h3 id="org4493ec7">Identification of the plant</h3>
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<div class="outline-text-3" id="text-org4493ec7">
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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">%% Options for Linearized</span></span>
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options = linearizeOptions;
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options.SampleTime = 0;
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<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
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mdl = <span class="org-string">'stewart_platform_control'</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">'/tau'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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io(io_i) = linio([mdl, <span class="org-string">'/L'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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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, options);
|
|
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>};
|
|
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>};
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org72dad5c" class="outline-3">
|
|
<h3 id="org72dad5c">Plant Analysis</h3>
|
|
<div class="outline-text-3" id="text-org72dad5c">
|
|
<p>
|
|
Diagonal terms
|
|
Compare to off-diagonal terms
|
|
</p>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-orga9fb0f5" class="outline-3">
|
|
<h3 id="orga9fb0f5">Controller Design</h3>
|
|
<div class="outline-text-3" id="text-orga9fb0f5">
|
|
<p>
|
|
One integrator should be present in the controller.
|
|
</p>
|
|
|
|
<p>
|
|
A lead is added around the crossover frequency which is set to be around 500Hz.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-comment">% wint = 2*pi*100; % Integrate until [rad]</span>
|
|
<span class="org-comment">% wlead = 2*pi*500; % Location of the lead [rad]</span>
|
|
<span class="org-comment">% hlead = 2; % Lead strengh</span>
|
|
|
|
<span class="org-comment">% Kl = 1e6 * ... % Gain</span>
|
|
<span class="org-comment">% (s + wint)/(s) * ... % Integrator until 100Hz</span>
|
|
<span class="org-comment">% (1 + s/(wlead/hlead)/(1 + s/(wlead*hlead))); % Lead</span>
|
|
|
|
wc = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>100;
|
|
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));
|
|
Kl = Kl <span class="org-type">*</span> eye(6);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-02-11 mar. 15:23</p>
|
|
</div>
|
|
</body>
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</html>
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