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<div id="content">
<h1 class="title">Identification of the Stewart Platform using Simscape</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org0c15748">1. Identification</a></li>
<li><a href="#orgb51bebd">2. Cartesian Plot</a></li>
<li><a href="#org8822347">3. From a force to force sensor</a></li>
<li><a href="#orgb3f97c3">4. From a force applied in the leg to the displacement of the leg</a></li>
<li><a href="#org4f7f749">5. Transmissibility</a></li>
<li><a href="#orgc027ff6">6. Compliance</a></li>
<li><a href="#orgeb43267">7. Inertial</a></li>
<li><a href="#org702dc6c">8. identifyPlant</a></li>
</ul>
</div>
</div>
<div id="outline-container-org0c15748" class="outline-2">
<h2 id="org0c15748"><span class="section-number-2">1</span> Identification</h2>
<div class="outline-text-2" id="text-1">
<p>
The hexapod structure and Sample structure are initialized.
</p>
<div class="org-src-container">
<pre class="src src-matlab">initializeHexapod<span style="color: #DCDCCC;">()</span>;
initializeSample<span style="color: #DCDCCC;">()</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">G = identifyPlant<span style="color: #DCDCCC;">()</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb51bebd" class="outline-2">
<h2 id="orgb51bebd"><span class="section-number-2">2</span> Cartesian Plot</h2>
<div class="outline-text-2" id="text-2">
<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 style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_cart<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_cart<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
</div>
</div>
<div id="outline-container-org8822347" class="outline-2">
<h2 id="org8822347"><span class="section-number-2">3</span> From a force to force sensor</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">4</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">5</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_forc<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgb3f97c3" class="outline-2">
<h2 id="orgb3f97c3"><span class="section-number-2">4</span> From a force applied in the leg to the displacement of the leg</h2>
<div class="outline-text-2" id="text-4">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">4</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">5</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_legs<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
</div>
</div>
<div id="outline-container-org4f7f749" class="outline-2">
<h2 id="org4f7f749"><span class="section-number-2">5</span> Transmissibility</h2>
<div class="outline-text-2" id="text-5">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">4</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">5</span>, <span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">6</span>, <span style="color: #BFEBBF;">6</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_tran<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgc027ff6" class="outline-2">
<h2 id="orgc027ff6"><span class="section-number-2">6</span> Compliance</h2>
<div class="outline-text-2" id="text-6">
<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 style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_comp<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_comp<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_comp<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgeb43267" class="outline-2">
<h2 id="orgeb43267"><span class="section-number-2">7</span> Inertial</h2>
<div class="outline-text-2" id="text-7">
<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 style="color: #7CB8BB;">figure</span>;
hold on;
bode<span style="color: #DCDCCC;">(</span>G.G_iner<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_iner<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">2</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
bode<span style="color: #DCDCCC;">(</span>G.G_iner<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">3</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
</pre>
</div>
</div>
</div>
<div id="outline-container-org702dc6c" class="outline-2">
<h2 id="org702dc6c"><span class="section-number-2">8</span> identifyPlant</h2>
<div class="outline-text-2" id="text-8">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">function</span> <span style="color: #DCDCCC;">[</span><span style="color: #DFAF8F;">sys</span><span style="color: #DCDCCC;">]</span> = <span style="color: #93E0E3;">identifyPlant</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">opts_param</span><span style="color: #DCDCCC;">)</span>
</pre>
</div>
<p>
We use this code block to pass optional parameters.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Default values for opts</span>
opts = struct<span style="color: #DCDCCC;">()</span>;
<span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Populate opts with input parameters</span>
<span style="color: #F0DFAF; font-weight: bold;">if</span> exist<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'opts_param','var'</span><span style="color: #DCDCCC;">)</span>
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">opt</span> = <span style="color: #BFEBBF;">fieldnames</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">opts_param</span><span style="color: #DCDCCC;">)</span><span style="color: #BFEBBF;">'</span>
opts.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span> = opts_param.<span style="color: #DCDCCC;">(</span>opt<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
<span style="color: #F0DFAF; font-weight: bold;">end</span>
</pre>
</div>
<p>
We defined the options for the <code>linearize</code> command.
Here, we just identify the system at time \(t = 0\).
</p>
<div class="org-src-container">
<pre class="src src-matlab">options = linearizeOptions;
options.SampleTime = <span style="color: #BFEBBF;">0</span>;
</pre>
</div>
<p>
We define the name of the Simulink File used to identification.
</p>
<div class="org-src-container">
<pre class="src src-matlab">mdl = <span style="color: #CC9393;">'stewart'</span>;
</pre>
</div>
<p>
Then we defined the input/output of the transfer function we want to identify.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Inputs</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>F'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Cartesian forces</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Fl'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Leg forces</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Fd'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Direct forces</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Dw'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'input'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Base motion</span>
<span style="color: #7F9F7F; font-weight: bold; text-decoration: overline;">%% Outputs</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">5</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Dm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Relative Motion</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">6</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Dlm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Displacement of each leg</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">7</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Flm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Force sensor in each leg</span>
io<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">8</span><span style="color: #DCDCCC;">)</span> = linio<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">[</span>mdl, '<span style="color: #7CB8BB;">/</span>Xm'<span style="color: #BFEBBF;">]</span>, <span style="color: #BFEBBF;">1</span>, 'output'<span style="color: #DCDCCC;">)</span>; <span style="color: #7F9F7F;">% Absolute motion of platform</span>
</pre>
</div>
<p>
The linearization is run.
</p>
<div class="org-src-container">
<pre class="src src-matlab">G = linearize<span style="color: #DCDCCC;">(</span>mdl, io, <span style="color: #BFEBBF;">0</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
We defined all the Input/Output names of the identified transfer function.
</p>
<div class="org-src-container">
<pre class="src src-matlab">G.InputName = <span style="color: #DCDCCC;">{</span><span style="color: #CC9393;">'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'</span>, <span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span>, <span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span>, <span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'</span><span style="color: #DCDCCC;">}</span>;
G.OutputName = <span style="color: #DCDCCC;">{</span><span style="color: #CC9393;">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span>, <span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'</span>, <span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'</span>, <span style="text-decoration: underline;">...</span>
<span style="color: #CC9393;">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span style="color: #DCDCCC;">}</span>;
</pre>
</div>
<p>
We split the transfer function into sub transfer functions and we compute their minimum realization.
</p>
<div class="org-src-container">
<pre class="src src-matlab">sys.G_cart = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
sys.G_forc = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
sys.G_legs = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
sys.G_tran = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
sys.G_comp = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
sys.G_iner = minreal<span style="color: #DCDCCC;">(</span>G<span style="color: #BFEBBF;">(</span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span style="color: #D0BF8F;">}</span><span style="color: #CC9393;">, </span><span style="color: #D0BF8F;">{</span><span style="color: #CC9393;">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span><span style="color: #D0BF8F;">}</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #7F9F7F;">% sys.G_all = minreal(G);</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #F0DFAF; font-weight: bold;">end</span>
</pre>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-03-22 ven. 12:03</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
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