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<title>Stewart Platform - Active Damping</title>
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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 - Active Damping</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="#orgbab9da7">1. Inertial Control</a>
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<ul>
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<li><a href="#orgd9e8d20">1.1. Simscape Model</a></li>
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<li><a href="#orge6285ea">1.2. Initialize the Stewart model</a></li>
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<li><a href="#org471f4bb">1.3. Identification of the Dynamics</a></li>
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<li><a href="#org30b2e11">1.4. Analysis</a></li>
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<li><a href="#org7f07dca">1.5. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgbab9da7" class="outline-2">
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<h2 id="orgbab9da7"><span class="section-number-2">1</span> Inertial Control</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-orgd9e8d20" class="outline-3">
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<h3 id="orgd9e8d20"><span class="section-number-3">1.1</span> Simscape Model</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">open(<span class="org-string">'simulink/stewart_active_damping.slx'</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-orge6285ea" class="outline-3">
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<h3 id="orge6285ea"><span class="section-number-3">1.2</span> Initialize the Stewart model</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 = initializeFramesPositions(<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 = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 40e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
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stewart = computeJointsPose(stewart);
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stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
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stewart = computeJacobian(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-org471f4bb" class="outline-3">
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<h3 id="org471f4bb"><span class="section-number-3">1.3</span> Identification of the Dynamics</h3>
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<div class="outline-text-3" id="text-1-3">
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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_active_damping'</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">'/F'</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">'/WVB'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
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io(io_i) = linio([mdl, <span class="org-string">'/Dm'</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);
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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">'Vx'</span>, <span class="org-string">'Vy'</span>, <span class="org-string">'Vz'</span>, <span class="org-string">'Wx'</span>, <span class="org-string">'Wy'</span>, <span class="org-string">'Wz'</span>, ...
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<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</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-org30b2e11" class="outline-3">
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<h3 id="org30b2e11"><span class="section-number-3">1.4</span> Analysis</h3>
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<div class="outline-text-3" id="text-1-4">
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<div class="org-src-container">
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<pre class="src src-matlab">freqs = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>logspace(1, 4, 1000);
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<span class="org-type">figure</span>;
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bode(G({<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>}, {<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>}), freqs)
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<span class="org-type">figure</span>;
|
||||
bode(stewart.J<span class="org-type">*</span>G({<span class="org-string">'Vx'</span>, <span class="org-string">'Vy'</span>, <span class="org-string">'Vz'</span>, <span class="org-string">'Wx'</span>, <span class="org-string">'Wy'</span>, <span class="org-string">'Wz'</span>}, {<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>}), freqs)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
bode(G({<span class="org-string">'D1'</span>, <span class="org-string">'D2'</span>, <span class="org-string">'D3'</span>, <span class="org-string">'D4'</span>, <span class="org-string">'D5'</span>, <span class="org-string">'D6'</span>}, {<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>}), stewart.J<span class="org-type">*</span>G({<span class="org-string">'Vx'</span>, <span class="org-string">'Vy'</span>, <span class="org-string">'Vz'</span>, <span class="org-string">'Wx'</span>, <span class="org-string">'Wy'</span>, <span class="org-string">'Wz'</span>}, {<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>}), freqs)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7f07dca" class="outline-3">
|
||||
<h3 id="org7f07dca"><span class="section-number-3">1.5</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<p>
|
||||
It is similar to use:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>one 6dof inertial sensor and the Jacobian the have the velocity of each lim</li>
|
||||
<li>6 1dof inertial sensor in each top part of the limbs</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-01-22 mer. 16:31</p>
|
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</div>
|
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</body>
|
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|
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430
control-study.html
Normal file
430
control-study.html
Normal file
@ -0,0 +1,430 @@
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<body>
|
||||
<div id="org-div-home-and-up">
|
||||
<a accesskey="h" href="./index.html"> UP </a>
|
||||
|
|
||||
<a accesskey="H" href="./index.html"> HOME </a>
|
||||
</div><div id="content">
|
||||
<h1 class="title">Stewart Platform - Control Study</h1>
|
||||
<div id="table-of-contents">
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgd132186">1. First Control Architecture</a>
|
||||
<ul>
|
||||
<li><a href="#orgf511610">1.1. Control Schematic</a></li>
|
||||
<li><a href="#org210df0e">1.2. Initialize the Stewart platform</a></li>
|
||||
<li><a href="#org2be78af">1.3. Initialize the Simulation</a></li>
|
||||
<li><a href="#org032eb91">1.4. Identification of the plant</a></li>
|
||||
<li><a href="#org7cd44a9">1.5. Plant Analysis</a></li>
|
||||
<li><a href="#orgcff4d92">1.6. Controller Design</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd132186" class="outline-2">
|
||||
<h2 id="orgd132186"><span class="section-number-2">1</span> First Control Architecture</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
</div>
|
||||
<div id="outline-container-orgf511610" class="outline-3">
|
||||
<h3 id="orgf511610"><span class="section-number-3">1.1</span> Control Schematic</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<div class="org-src-container">
|
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|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (J.east) -- (subr.west) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bm</span></span><span class="org-font-latex-math">{r}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_{L}</span></span><span class="org-font-latex-math">$</span>};
|
||||
<span class="org-font-latex-sedate">\draw</span>[->] (subr.east) -- (K.west) node[above left]{<span class="org-font-latex-math">$</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\bm</span></span><span class="org-font-latex-math">{</span><span class="org-font-latex-sedate"><span class="org-font-latex-math">\epsilon</span></span><span class="org-font-latex-math">}</span><span class="org-font-latex-math"><span class="org-font-latex-script-char">_{L}</span></span><span class="org-font-latex-math">$</span>};
|
||||
<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>};
|
||||
<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);
|
||||
<span class="org-font-latex-sedate"><span class="org-keyword">\end</span></span>{<span class="org-function-name">tikzpicture</span>}
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div class="figure">
|
||||
<p><img src="figs/control_measure_rotating_2dof.png" alt="control_measure_rotating_2dof.png" />
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org210df0e" class="outline-3">
|
||||
<h3 id="org210df0e"><span class="section-number-3">1.2</span> Initialize the Stewart platform</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">stewart = initializeFramesPositions(<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);
|
||||
<span class="org-comment">% stewart = generateCubicConfiguration(stewart, 'Hc', 60e-3, 'FOc', 45e-3, 'FHa', 5e-3, 'MHb', 5e-3);</span>
|
||||
stewart = generateGeneralConfiguration(stewart);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2be78af" class="outline-3">
|
||||
<h3 id="org2be78af"><span class="section-number-3">1.3</span> Initialize the Simulation</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org032eb91" class="outline-3">
|
||||
<h3 id="org032eb91"><span class="section-number-3">1.4</span> Identification of the plant</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<p>
|
||||
Let’s identify the transfer function from \(\bm{\tau}}\) to \(\bm{L}\).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_control'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
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;
|
||||
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;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'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-org7cd44a9" class="outline-3">
|
||||
<h3 id="org7cd44a9"><span class="section-number-3">1.5</span> Plant Analysis</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<p>
|
||||
Diagonal terms
|
||||
Compare to off-diagonal terms
|
||||
</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgcff4d92" class="outline-3">
|
||||
<h3 id="orgcff4d92"><span class="section-number-3">1.6</span> Controller Design</h3>
|
||||
<div class="outline-text-3" id="text-1-6">
|
||||
<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: 2020-01-22 mer. 16:31</p>
|
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</div>
|
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</body>
|
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748
dynamics-study.html
Normal file
748
dynamics-study.html
Normal file
@ -0,0 +1,748 @@
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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">
|
||||
<h1 class="title">Stewart Platform - Dynamics Study</h1>
|
||||
<div id="table-of-contents">
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgf59f0f9">1. Some tests</a>
|
||||
<ul>
|
||||
<li><a href="#orgaf3d924">1.1. Simscape Model</a></li>
|
||||
<li><a href="#org7312203">1.2. test</a></li>
|
||||
<li><a href="#org9daf767">1.3. Compare external forces and forces applied by the actuators</a></li>
|
||||
<li><a href="#org2a5345f">1.4. Comparison of the static transfer function and the Compliance matrix</a></li>
|
||||
<li><a href="#org089f223">1.5. Transfer function from forces applied in the legs to the displacement of the legs</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf59f0f9" class="outline-2">
|
||||
<h2 id="orgf59f0f9"><span class="section-number-2">1</span> Some tests</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
</div>
|
||||
<div id="outline-container-orgaf3d924" class="outline-3">
|
||||
<h3 id="orgaf3d924"><span class="section-number-3">1.1</span> Simscape Model</h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">open(<span class="org-string">'stewart_platform_dynamics.slx'</span>)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org7312203" class="outline-3">
|
||||
<h3 id="org7312203"><span class="section-number-3">1.2</span> test</h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">stewart = initializeFramesPositions(<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);
|
||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Estimation of the transfer function from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\):
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_dynamics'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
|
||||
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_dynamics'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/J-T'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'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">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">G_cart = minreal(G<span class="org-type">*</span>inv(stewart.J<span class="org-type">'</span>));
|
||||
G_cart.InputName = {<span class="org-string">'Fnx'</span>, <span class="org-string">'Fny'</span>, <span class="org-string">'Fnz'</span>, <span class="org-string">'Mnx'</span>, <span class="org-string">'Mny'</span>, <span class="org-string">'Mnz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>; bode(G, G_cart)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_dynamics'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Fext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
Gd = linearize(mdl, io, options);
|
||||
Gd.InputName = {<span class="org-string">'Fex'</span>, <span class="org-string">'Fey'</span>, <span class="org-string">'Fez'</span>, <span class="org-string">'Mex'</span>, <span class="org-string">'Mey'</span>, <span class="org-string">'Mez'</span>};
|
||||
Gd.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">freqs = logspace(0, 3, 1000);
|
||||
|
||||
<span class="org-type">figure</span>;
|
||||
bode(Gd, G)
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9daf767" class="outline-3">
|
||||
<h3 id="org9daf767"><span class="section-number-3">1.3</span> Compare external forces and forces applied by the actuators</h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
Initialization of the Stewart platform.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">stewart = initializeFramesPositions(<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);
|
||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Estimation of the transfer function from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\):
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_dynamics'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
|
||||
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Estimation of the transfer function from \(\mathcal{\bm{F}}_{d}\) to \(\mathcal{\bm{X}}\):
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_dynamics'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/Fext'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
Gd = linearize(mdl, io, options);
|
||||
Gd.InputName = {<span class="org-string">'Fex'</span>, <span class="org-string">'Fey'</span>, <span class="org-string">'Fez'</span>, <span class="org-string">'Mex'</span>, <span class="org-string">'Mey'</span>, <span class="org-string">'Mez'</span>};
|
||||
Gd.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Comparison of the two transfer function matrices.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">freqs = logspace(0, 4, 1000);
|
||||
|
||||
<span class="org-type">figure</span>;
|
||||
bode(Gd, G, freqs)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="important">
|
||||
<p>
|
||||
Seems quite similar.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2a5345f" class="outline-3">
|
||||
<h3 id="org2a5345f"><span class="section-number-3">1.4</span> Comparison of the static transfer function and the Compliance matrix</h3>
|
||||
<div class="outline-text-3" id="text-1-4">
|
||||
<p>
|
||||
Initialization of the Stewart platform.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">stewart = initializeFramesPositions(<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);
|
||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Estimation of the transfer function from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\):
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_dynamics'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/F'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'Fx'</span>, <span class="org-string">'Fy'</span>, <span class="org-string">'Fz'</span>, <span class="org-string">'Mx'</span>, <span class="org-string">'My'</span>, <span class="org-string">'Mz'</span>};
|
||||
G.OutputName = {<span class="org-string">'Edx'</span>, <span class="org-string">'Edy'</span>, <span class="org-string">'Edz'</span>, <span class="org-string">'Erx'</span>, <span class="org-string">'Ery'</span>, <span class="org-string">'Erz'</span>};
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Let’s first look at the low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\).
|
||||
</p>
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
|
||||
<colgroup>
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-right">2.0e-06</td>
|
||||
<td class="org-right">-9.1e-19</td>
|
||||
<td class="org-right">-5.3e-12</td>
|
||||
<td class="org-right">7.3e-18</td>
|
||||
<td class="org-right">1.7e-05</td>
|
||||
<td class="org-right">1.3e-18</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">-1.7e-18</td>
|
||||
<td class="org-right">2.0e-06</td>
|
||||
<td class="org-right">8.6e-19</td>
|
||||
<td class="org-right">-1.7e-05</td>
|
||||
<td class="org-right">-1.5e-17</td>
|
||||
<td class="org-right">6.7e-12</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">3.6e-13</td>
|
||||
<td class="org-right">3.2e-19</td>
|
||||
<td class="org-right">5.0e-07</td>
|
||||
<td class="org-right">-2.5e-18</td>
|
||||
<td class="org-right">8.1e-12</td>
|
||||
<td class="org-right">-1.5e-19</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">1.0e-17</td>
|
||||
<td class="org-right">-1.7e-05</td>
|
||||
<td class="org-right">-5.0e-18</td>
|
||||
<td class="org-right">1.9e-04</td>
|
||||
<td class="org-right">9.1e-17</td>
|
||||
<td class="org-right">-3.5e-11</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">1.7e-05</td>
|
||||
<td class="org-right">-6.9e-19</td>
|
||||
<td class="org-right">-5.3e-11</td>
|
||||
<td class="org-right">6.9e-18</td>
|
||||
<td class="org-right">1.9e-04</td>
|
||||
<td class="org-right">4.8e-18</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">-3.5e-18</td>
|
||||
<td class="org-right">-4.5e-12</td>
|
||||
<td class="org-right">1.5e-18</td>
|
||||
<td class="org-right">7.1e-11</td>
|
||||
<td class="org-right">-3.4e-17</td>
|
||||
<td class="org-right">4.6e-05</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<p>
|
||||
And now at the Compliance matrix.
|
||||
</p>
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
|
||||
<colgroup>
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
|
||||
<col class="org-right" />
|
||||
</colgroup>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-right">2.0e-06</td>
|
||||
<td class="org-right">2.9e-22</td>
|
||||
<td class="org-right">2.8e-22</td>
|
||||
<td class="org-right">-3.2e-21</td>
|
||||
<td class="org-right">1.7e-05</td>
|
||||
<td class="org-right">1.5e-37</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">-2.1e-22</td>
|
||||
<td class="org-right">2.0e-06</td>
|
||||
<td class="org-right">-1.8e-23</td>
|
||||
<td class="org-right">-1.7e-05</td>
|
||||
<td class="org-right">-2.3e-21</td>
|
||||
<td class="org-right">1.1e-22</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">3.1e-22</td>
|
||||
<td class="org-right">-1.6e-23</td>
|
||||
<td class="org-right">5.0e-07</td>
|
||||
<td class="org-right">1.7e-22</td>
|
||||
<td class="org-right">2.2e-21</td>
|
||||
<td class="org-right">-8.1e-39</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">2.1e-21</td>
|
||||
<td class="org-right">-1.7e-05</td>
|
||||
<td class="org-right">2.0e-22</td>
|
||||
<td class="org-right">1.9e-04</td>
|
||||
<td class="org-right">2.3e-20</td>
|
||||
<td class="org-right">-8.7e-21</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">1.7e-05</td>
|
||||
<td class="org-right">2.5e-21</td>
|
||||
<td class="org-right">2.0e-21</td>
|
||||
<td class="org-right">-2.8e-20</td>
|
||||
<td class="org-right">1.9e-04</td>
|
||||
<td class="org-right">1.3e-36</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">3.7e-23</td>
|
||||
<td class="org-right">3.1e-22</td>
|
||||
<td class="org-right">-6.0e-39</td>
|
||||
<td class="org-right">-1.0e-20</td>
|
||||
<td class="org-right">3.1e-22</td>
|
||||
<td class="org-right">4.6e-05</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<div class="important">
|
||||
<p>
|
||||
The low frequency transfer function matrix from \(\mathcal{\bm{F}}\) to \(\mathcal{\bm{X}}\) corresponds to the compliance matrix of the Stewart platform.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org089f223" class="outline-3">
|
||||
<h3 id="org089f223"><span class="section-number-3">1.5</span> Transfer function from forces applied in the legs to the displacement of the legs</h3>
|
||||
<div class="outline-text-3" id="text-1-5">
|
||||
<p>
|
||||
Initialization of the Stewart platform.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">stewart = initializeFramesPositions(<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);
|
||||
stewart = generateCubicConfiguration(stewart, <span class="org-string">'Hc'</span>, 60e<span class="org-type">-</span>3, <span class="org-string">'FOc'</span>, 45e<span class="org-type">-</span>3, <span class="org-string">'FHa'</span>, 5e<span class="org-type">-</span>3, <span class="org-string">'MHb'</span>, 5e<span class="org-type">-</span>3);
|
||||
stewart = computeJointsPose(stewart);
|
||||
stewart = initializeStrutDynamics(stewart, <span class="org-string">'Ki'</span>, 1e6<span class="org-type">*</span>ones(6,1), <span class="org-string">'Ci'</span>, 1e2<span class="org-type">*</span>ones(6,1));
|
||||
stewart = computeJacobian(stewart);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Estimation of the transfer function from \(\bm{\tau}\) to \(\bm{L}\):
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Options for Linearized</span></span>
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Name of the Simulink File</span></span>
|
||||
mdl = <span class="org-string">'stewart_platform_dynamics'</span>;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Input/Output definition</span></span>
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, <span class="org-string">'/J-T'</span>], 1, <span class="org-string">'openinput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
||||
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;
|
||||
|
||||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Run the linearization</span></span>
|
||||
G = linearize(mdl, io, options);
|
||||
G.InputName = {<span class="org-string">'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 class="org-src-container">
|
||||
<pre class="src src-matlab">freqs = logspace(1, 3, 1000);
|
||||
<span class="org-type">figure</span>; bode(G, 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs)
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">bodeFig({G(1,1), G(1,2)}, freqs, struct(<span class="org-string">'phase'</span>, <span class="org-constant">true</span>));
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-01-22 mer. 16:31</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
Loading…
Reference in New Issue
Block a user