1103 lines
51 KiB
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1103 lines
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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">Identification of the Stewart Platform using Simscape</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="#org4f5919a">1. Identification</a>
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<ul>
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<li><a href="#org89ad201">1.1. Simscape Model</a></li>
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<li><a href="#orgf726654">1.2. Initialize the Stewart Platform</a></li>
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<li><a href="#org79afd8d">1.3. Identification</a></li>
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</ul>
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</li>
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<li><a href="#orge464de2">2. States as the motion of the mobile platform</a>
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<ul>
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<li><a href="#orge352695">2.1. Initialize the Stewart Platform</a></li>
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<li><a href="#org0dc382a">2.2. Identification</a></li>
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<li><a href="#orge68adea">2.3. Coordinate transformation</a></li>
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<li><a href="#org4973ae1">2.4. Analysis</a></li>
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<li><a href="#orge7b97c8">2.5. Visualizing the modes</a></li>
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<li><a href="#orgf6eca35">2.6. Identification</a></li>
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<li><a href="#orgf7a52cb">2.7. Change of states</a></li>
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</ul>
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</li>
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<li><a href="#org23d7e7b">3. Simple Model without any sensor</a>
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<ul>
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<li><a href="#org9366ba4">3.1. Simscape Model</a></li>
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<li><a href="#orgf4e4e80">3.2. Initialize the Stewart Platform</a></li>
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<li><a href="#org9b90cca">3.3. Identification</a></li>
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</ul>
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</li>
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<li><a href="#org0502cd2">4. Cartesian Plot</a></li>
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<li><a href="#org32e2eb3">5. From a force to force sensor</a></li>
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<li><a href="#org8ddfd2c">6. From a force applied in the leg to the displacement of the leg</a></li>
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<li><a href="#org5685537">7. Transmissibility</a></li>
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<li><a href="#org3335d1e">8. Compliance</a></li>
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<li><a href="#org5ca7af8">9. Inertial</a></li>
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</ul>
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</div>
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</div>
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<p>
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We would like to extract a state space model of the Stewart Platform from the Simscape model.
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</p>
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<p>
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The inputs are:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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<thead>
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<tr>
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<th scope="col" class="org-left">Symbol</th>
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<th scope="col" class="org-left">Meaning</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">\(\bm{\mathcal{F}}_{d}\)</td>
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<td class="org-left">External forces applied in {B}</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{\tau}\)</td>
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<td class="org-left">Joint forces</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{\mathcal{F}}\)</td>
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<td class="org-left">Cartesian forces applied by the Joints</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{D}_{w}\)</td>
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<td class="org-left">Fixed Based translation and rotations around {A}</td>
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</tr>
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</tbody>
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</table>
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<p>
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The outputs are:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left">Symbol</th>
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<th scope="col" class="org-left">Meaning</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">\(\bm{\mathcal{X}}\)</td>
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<td class="org-left">Relative Motion of {B} with respect to {A}</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{\mathcal{L}}\)</td>
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<td class="org-left">Joint Displacement</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{F}_{m}\)</td>
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<td class="org-left">Force Sensors in each strut</td>
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</tr>
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<tr>
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<td class="org-left">\(\bm{v}_{m}\)</td>
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<td class="org-left">Inertial Sensors located at \(b_i\) measuring in the direction of the strut</td>
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</tr>
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</tbody>
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</table>
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<blockquote>
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<p>
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An important difference from basic Simulink models is that the states in a physical network are not independent in general, because some states have dependencies on other states through constraints.
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</p>
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</blockquote>
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<div id="outline-container-org4f5919a" class="outline-2">
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<h2 id="org4f5919a"><span class="section-number-2">1</span> Identification</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-org89ad201" class="outline-3">
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<h3 id="org89ad201"><span class="section-number-3">1.1</span> Simscape Model</h3>
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</div>
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<div id="outline-container-orgf726654" class="outline-3">
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<h3 id="orgf726654"><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);
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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-org79afd8d" class="outline-3">
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<h3 id="org79afd8d"><span class="section-number-3">1.3</span> Identification</h3>
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<div class="outline-text-3" id="text-1-3">
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<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_identification'</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">'/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;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Vm'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Taum'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Lm'</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">'tau1'</span>, <span class="org-string">'tau2'</span>, <span class="org-string">'tau3'</span>, <span class="org-string">'tau4'</span>, <span class="org-string">'tau5'</span>, <span class="org-string">'tau6'</span>, ...
|
|
<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">'Xdx'</span>, <span class="org-string">'Xdy'</span>, <span class="org-string">'Xdz'</span>, <span class="org-string">'Xrx'</span>, <span class="org-string">'Xry'</span>, <span class="org-string">'Xrz'</span>, ...
|
|
<span class="org-string">'Vm1'</span>, <span class="org-string">'Vm2'</span>, <span class="org-string">'Vm3'</span>, <span class="org-string">'Vm4'</span>, <span class="org-string">'Vm5'</span>, <span class="org-string">'Vm6'</span>, ...
|
|
<span class="org-string">'taum1'</span>, <span class="org-string">'taum2'</span>, <span class="org-string">'taum3'</span>, <span class="org-string">'taum4'</span>, <span class="org-string">'taum5'</span>, <span class="org-string">'taum6'</span>, ...
|
|
<span class="org-string">'Lm1'</span>, <span class="org-string">'Lm2'</span>, <span class="org-string">'Lm3'</span>, <span class="org-string">'Lm4'</span>, <span class="org-string">'Lm5'</span>, <span class="org-string">'Lm6'</span>};
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge464de2" class="outline-2">
|
|
<h2 id="orge464de2"><span class="section-number-2">2</span> States as the motion of the mobile platform</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
</div>
|
|
<div id="outline-container-orge352695" class="outline-3">
|
|
<h3 id="orge352695"><span class="section-number-3">2.1</span> Initialize the Stewart Platform</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
|
stewart = initializeFramesPositions(stewart);
|
|
stewart = generateGeneralConfiguration(stewart);
|
|
stewart = computeJointsPose(stewart);
|
|
stewart = initializeStrutDynamics(stewart);
|
|
stewart = initializeCylindricalPlatforms(stewart);
|
|
stewart = initializeCylindricalStruts(stewart);
|
|
stewart = computeJacobian(stewart);
|
|
stewart = initializeStewartPose(stewart);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0dc382a" class="outline-3">
|
|
<h3 id="org0dc382a"><span class="section-number-3">2.2</span> Identification</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<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_identification_simple'</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">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Xdot'</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);
|
|
<span class="org-comment">% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};</span>
|
|
<span class="org-comment">% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Let’s check the size of <code>G</code>:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">size(G)
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
size(G)
|
|
State-space model with 12 outputs, 6 inputs, and 18 states.
|
|
'org_babel_eoe'
|
|
ans =
|
|
'org_babel_eoe'
|
|
</pre>
|
|
|
|
|
|
<p>
|
|
We expect to have only 12 states (corresponding to the 6dof of the mobile platform).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Gm = minreal(G);
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
Gm = minreal(G);
|
|
6 states removed.
|
|
</pre>
|
|
|
|
|
|
<p>
|
|
And indeed, we obtain 12 states.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge68adea" class="outline-3">
|
|
<h3 id="orge68adea"><span class="section-number-3">2.3</span> Coordinate transformation</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<p>
|
|
We can perform the following transformation using the <code>ss2ss</code> command.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Gt = ss2ss(Gm, Gm.C);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then, the <code>C</code> matrix of <code>Gt</code> is the unity matrix which means that the states of the state space model are equal to the measurements \(\bm{Y}\).
|
|
</p>
|
|
|
|
<p>
|
|
The measurements are the 6 displacement and 6 velocities of mobile platform with respect to \(\{B\}\).
|
|
</p>
|
|
|
|
<p>
|
|
We could perform the transformation by hand:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">At = Gm.C<span class="org-type">*</span>Gm.A<span class="org-type">*</span>pinv(Gm.C);
|
|
|
|
Bt = Gm.C<span class="org-type">*</span>Gm.B;
|
|
|
|
Ct = eye(12);
|
|
Dt = zeros(12, 6);
|
|
|
|
Gt = ss(At, Bt, Ct, Dt);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4973ae1" class="outline-3">
|
|
<h3 id="org4973ae1"><span class="section-number-3">2.4</span> Analysis</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">[V,D] = eig(Gt.A);
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-right">Mode Number</th>
|
|
<th scope="col" class="org-right">Resonance Frequency [Hz]</th>
|
|
<th scope="col" class="org-right">Damping Ratio [%]</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">1.0</td>
|
|
<td class="org-right">174.5</td>
|
|
<td class="org-right">0.9</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">2.0</td>
|
|
<td class="org-right">174.5</td>
|
|
<td class="org-right">0.7</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">3.0</td>
|
|
<td class="org-right">202.1</td>
|
|
<td class="org-right">0.7</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">4.0</td>
|
|
<td class="org-right">237.3</td>
|
|
<td class="org-right">0.6</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">5.0</td>
|
|
<td class="org-right">237.3</td>
|
|
<td class="org-right">0.5</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">6.0</td>
|
|
<td class="org-right">283.8</td>
|
|
<td class="org-right">0.5</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge7b97c8" class="outline-3">
|
|
<h3 id="orge7b97c8"><span class="section-number-3">2.5</span> Visualizing the modes</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<p>
|
|
To visualize the i’th mode, we may excite the system using the inputs \(U_i\) such that \(B U_i\) is co-linear to \(\xi_i\) (the mode we want to excite).
|
|
</p>
|
|
|
|
<p>
|
|
\[ U(t) = e^{\alpha t} ( ) \]
|
|
</p>
|
|
|
|
<p>
|
|
Let’s first sort the modes and just take the modes corresponding to a eigenvalue with a positive imaginary part.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">ws = imag(diag(D));
|
|
[ws,I] = sort(ws)
|
|
ws = ws(7<span class="org-type">:</span>end); I = I(7<span class="org-type">:</span>end);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(ws)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">i_mode = I(<span class="org-constant">i</span>); <span class="org-comment">% the argument is the i'th mode</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">lambda_i = D(i_mode, i_mode);
|
|
xi_i = V(<span class="org-type">:</span>,i_mode);
|
|
|
|
a_i = real(lambda_i);
|
|
b_i = imag(lambda_i);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Let do 10 periods of the mode.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">t = linspace(0, 10<span class="org-type">/</span>(imag(lambda_i)<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), 1000);
|
|
U_i = pinv(Gt.B) <span class="org-type">*</span> real(xi_i <span class="org-type">*</span> lambda_i <span class="org-type">*</span> (cos(b_i <span class="org-type">*</span> t) <span class="org-type">+</span> 1<span class="org-constant">i</span><span class="org-type">*</span>sin(b_i <span class="org-type">*</span> t)));
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">U = timeseries(U_i, t);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Simulation:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">load(<span class="org-string">'mat/conf_simscape.mat'</span>);
|
|
<span class="org-matlab-simulink-keyword">set_param</span>(<span class="org-variable-name">conf_simscape</span>, <span class="org-string">'StopTime'</span>, num2str(t(<span class="org-variable-name">end</span>)));
|
|
<span class="org-matlab-simulink-keyword">sim</span>(mdl);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Save the movie of the mode shape.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">smwritevideo(mdl, sprintf(<span class="org-string">'figs/mode%i'</span>, <span class="org-constant">i</span>), ...
|
|
<span class="org-string">'PlaybackSpeedRatio'</span>, 1<span class="org-type">/</span>(b_i<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>), ...
|
|
<span class="org-string">'FrameRate'</span>, 30, ...
|
|
<span class="org-string">'FrameSize'</span>, [800, 400]);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgb15855a" class="figure">
|
|
<p><img src="figs/mode1.gif" alt="mode1.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Identified mode - 1</p>
|
|
</div>
|
|
|
|
|
|
<div id="org1816e59" class="figure">
|
|
<p><img src="figs/mode3.gif" alt="mode3.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Identified mode - 3</p>
|
|
</div>
|
|
|
|
|
|
<div id="org01c8dca" class="figure">
|
|
<p><img src="figs/mode5.gif" alt="mode5.gif" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Identified mode - 5</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf6eca35" class="outline-3">
|
|
<h3 id="orgf6eca35"><span class="section-number-3">2.6</span> Identification</h3>
|
|
<div class="outline-text-3" id="text-2-6">
|
|
<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_identification'</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">'/Lm'</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);
|
|
<span class="org-comment">% G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};</span>
|
|
<span class="org-comment">% G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">size(G)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf7a52cb" class="outline-3">
|
|
<h3 id="orgf7a52cb"><span class="section-number-3">2.7</span> Change of states</h3>
|
|
<div class="outline-text-3" id="text-2-7">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">At = G.C<span class="org-type">*</span>G.A<span class="org-type">*</span>pinv(G.C);
|
|
|
|
Bt = G.C<span class="org-type">*</span>G.B;
|
|
|
|
Ct = eye(12);
|
|
Dt = zeros(12, 6);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Gt = ss(At, Bt, Ct, Dt);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">size(Gt)
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org23d7e7b" class="outline-2">
|
|
<h2 id="org23d7e7b"><span class="section-number-2">3</span> Simple Model without any sensor</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
</div>
|
|
<div id="outline-container-org9366ba4" class="outline-3">
|
|
<h3 id="org9366ba4"><span class="section-number-3">3.1</span> Simscape Model</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">open <span class="org-string">'stewart_identification_simple.slx'</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgf4e4e80" class="outline-3">
|
|
<h3 id="orgf4e4e80"><span class="section-number-3">3.2</span> Initialize the Stewart Platform</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stewart = initializeStewartPlatform();
|
|
stewart = initializeFramesPositions(stewart);
|
|
stewart = generateGeneralConfiguration(stewart);
|
|
stewart = computeJointsPose(stewart);
|
|
stewart = initializeStrutDynamics(stewart);
|
|
stewart = initializeCylindricalPlatforms(stewart);
|
|
stewart = initializeCylindricalStruts(stewart);
|
|
stewart = computeJacobian(stewart);
|
|
stewart = initializeStewartPose(stewart);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9b90cca" class="outline-3">
|
|
<h3 id="org9b90cca"><span class="section-number-3">3.3</span> Identification</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">stateorder = {...
|
|
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_1_1_1'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_2_1_1'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_3_1_1'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_4_1_1'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_5_1_1'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_6_1_1'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.p'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.v'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.Q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.w'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.Q'</span>,...
|
|
<span class="org-string">'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.w'</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_identification_simple'</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">'/X'</span>], 1, <span class="org-string">'openoutput'</span>); io_i = io_i <span class="org-type">+</span> 1;
|
|
io(io_i) = linio([mdl, <span class="org-string">'/Xdot'</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">'tau1'</span>, <span class="org-string">'tau2'</span>, <span class="org-string">'tau3'</span>, <span class="org-string">'tau4'</span>, <span class="org-string">'tau5'</span>, <span class="org-string">'tau6'</span>};
|
|
|
|
G.OutputName = {<span class="org-string">'Xdx'</span>, <span class="org-string">'Xdy'</span>, <span class="org-string">'Xdz'</span>, <span class="org-string">'Xrx'</span>, <span class="org-string">'Xry'</span>, <span class="org-string">'Xrz'</span>, <span class="org-string">'Vdx'</span>, <span class="org-string">'Vdy'</span>, <span class="org-string">'Vdz'</span>, <span class="org-string">'Vrx'</span>, <span class="org-string">'Vry'</span>, <span class="org-string">'Vrz'</span>};
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">size(G)
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">G.StateName
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0502cd2" class="outline-2">
|
|
<h2 id="org0502cd2"><span class="section-number-2">4</span> Cartesian Plot</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
From a force applied in the Cartesian frame to a displacement in the Cartesian frame.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_cart(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_cart(2, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_cart(3, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
bode(G.G_cart, freqs);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org32e2eb3" class="outline-2">
|
|
<h2 id="org32e2eb3"><span class="section-number-2">5</span> From a force to force sensor</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$F_{m_i}/F_{i}$'</span>);
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [N/N]'</span>);
|
|
legend(<span class="org-string">'location'</span>, <span class="org-string">'southeast'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$F_{m_i}/F_{i}$'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_forc(2, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$F_{m_j}/F_{i}$'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_forc(3, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_forc(4, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_forc(5, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_forc(6, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [N/N]'</span>);
|
|
legend(<span class="org-string">'location'</span>, <span class="org-string">'southeast'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8ddfd2c" class="outline-2">
|
|
<h2 id="org8ddfd2c"><span class="section-number-2">6</span> From a force applied in the leg to the displacement of the leg</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$D_{i}/F_{i}$'</span>);
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$D_{i}/F_{i}$'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_legs(2, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'$D_{j}/F_{i}$'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_legs(3, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_legs(4, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_legs(5, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
plot(freqs, abs(squeeze(freqresp(G.G_legs(6, 1), freqs, <span class="org-string">'Hz'</span>))), <span class="org-string">'k--'</span>, <span class="org-string">'HandleVisibility'</span>, <span class="org-string">'off'</span>);
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
legend(<span class="org-string">'location'</span>, <span class="org-string">'northeast'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5685537" class="outline-2">
|
|
<h2 id="org5685537"><span class="section-number-2">7</span> Transmissibility</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(2, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(3, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/m]'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(4, 4), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(5, 5), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(6, 6), freqs, <span class="org-string">'Hz'</span>))));
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [$\frac{rad/s}{rad/s}$]'</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/m]'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3335d1e" class="outline-2">
|
|
<h2 id="org3335d1e"><span class="section-number-2">8</span> Compliance</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
<p>
|
|
From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_comp(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_comp(2, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_comp(3, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org5ca7af8" class="outline-2">
|
|
<h2 id="org5ca7af8"><span class="section-number-2">9</span> Inertial</h2>
|
|
<div class="outline-text-2" id="text-9">
|
|
<p>
|
|
From a force applied on the Cartesian frame to the absolute displacement of the mobile platform.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot(freqs, abs(squeeze(freqresp(G.G_iner(1, 1), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_iner(2, 2), freqs, <span class="org-string">'Hz'</span>))));
|
|
plot(freqs, abs(squeeze(freqresp(G.G_iner(3, 3), freqs, <span class="org-string">'Hz'</span>))));
|
|
hold off;
|
|
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
|
|
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude [m/N]'</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2020-02-11 mar. 15:50</p>
|
|
</div>
|
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</body>
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</html>
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