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<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="#org5e5b5f3">1. Identification</a></li>
<li><a href="#orge4ddae7">2. Cartesian Plot</a></li>
<li><a href="#orgc3f5223">3. From a force to force sensor</a></li>
<li><a href="#org1795f38">4. From a force applied in the leg to the displacement of the leg</a></li>
<li><a href="#org3e4873e">5. Transmissibility</a></li>
<li><a href="#org1ab2176">6. Compliance</a></li>
<li><a href="#orgf18ed8c">7. Inertial</a></li>
<li><a href="#org9ed65c5">8. identifyPlant</a></li>
</ul>
</div>
</div>
<div id="outline-container-org5e5b5f3" class="outline-2">
<h2 id="org5e5b5f3"><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">stewart = initializeGeneralConfiguration<span class="org-rainbow-delimiters-depth-1">()</span>;
stewart = computeGeometricalProperties<span class="org-rainbow-delimiters-depth-1">(</span>stewart<span class="org-rainbow-delimiters-depth-1">)</span>;
stewart = initializeMechanicalElements<span class="org-rainbow-delimiters-depth-1">(</span>stewart<span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/stewart.mat', 'stewart'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
initializeSample<span class="org-rainbow-delimiters-depth-1">()</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">G = identifyPlant<span class="org-rainbow-delimiters-depth-1">()</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">freqs = logspace<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orge4ddae7" class="outline-2">
<h2 id="orge4ddae7"><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 class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_cart<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_cart<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_cart<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
bode<span class="org-rainbow-delimiters-depth-1">(</span>G.G_cart, freqs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgc3f5223" class="outline-2">
<h2 id="orgc3f5223"><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 class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_forc<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k-', 'DisplayName', '$F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">m_i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">/F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">N/N</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'location', 'southeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_forc<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k-', 'DisplayName', '$F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">m_i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">/F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_forc<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'DisplayName', '$F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">m_j</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">/F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_forc<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_forc<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_forc<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_forc<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">N/N</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'location', 'southeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org1795f38" class="outline-2">
<h2 id="org1795f38"><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 class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_legs<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k-', 'DisplayName', '$D_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">/F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/N</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_legs<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k-', 'DisplayName', '$D_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">/F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_legs<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'DisplayName', '$D_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">j</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">/F_</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-string">i</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_legs<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_legs<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_legs<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_legs<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">, 'k--', 'HandleVisibility', 'off'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/N</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org3e4873e" class="outline-2">
<h2 id="org3e4873e"><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 class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">4</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>rad<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span>rad<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}</span>$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_tran<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org1ab2176" class="outline-2">
<h2 id="org1ab2176"><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 class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_comp<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_comp<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_comp<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/N</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf18ed8c" class="outline-2">
<h2 id="orgf18ed8c"><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 class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_iner<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_iner<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>freqs, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>G.G_iner<span class="org-rainbow-delimiters-depth-5">(</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-5">)</span>, freqs, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Amplitude </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/N</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org9ed65c5" class="outline-2">
<h2 id="org9ed65c5"><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 class="org-keyword">function</span> <span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">[</span></span><span class="org-variable-name">sys</span><span class="org-variable-name"><span class="org-rainbow-delimiters-depth-1">]</span></span> = <span class="org-function-name">identifyPlant</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">opts_param</span><span class="org-rainbow-delimiters-depth-1">)</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 class="org-matlab-cellbreak"><span class="org-comment">%% Default values for opts</span></span>
opts = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
<span class="org-matlab-cellbreak"><span class="org-comment">%% Populate opts with input parameters</span></span>
<span class="org-keyword">if</span> exist<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'opts_param','var'</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-keyword">for</span> <span class="org-variable-name">opt</span> = <span class="org-constant">fieldnames</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">opts_param</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-constant">'</span>
opts.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span> = opts_param.<span class="org-rainbow-delimiters-depth-1">(</span>opt<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-keyword">end</span>
<span class="org-keyword">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 class="org-highlight-numbers-number">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 class="org-string">'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 class="org-matlab-cellbreak"><span class="org-comment">%% Inputs</span></span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>F'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'input'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Cartesian forces</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>Fl'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'input'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Leg forces</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>Fd'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'input'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Direct forces</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>Dw'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'input'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Base motion</span>
<span class="org-matlab-cellbreak"><span class="org-comment">%% Outputs</span></span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>Dm'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'output'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Relative Motion</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>Dlm'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'output'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Displacement of each leg</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">7</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>Flm'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'output'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Force sensor in each leg</span>
io<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">8</span><span class="org-rainbow-delimiters-depth-1">)</span> = linio<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>mdl, '<span class="org-type">/</span>Xm'<span class="org-rainbow-delimiters-depth-2">]</span>, <span class="org-highlight-numbers-number">1</span>, 'output'<span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% 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 class="org-rainbow-delimiters-depth-1">(</span>mdl, io, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</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 class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'</span>, <span class="org-underline">...</span>
<span class="org-string">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span>, <span class="org-underline">...</span>
<span class="org-string">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span>, <span class="org-underline">...</span>
<span class="org-string">'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'</span><span class="org-rainbow-delimiters-depth-1">}</span>;
G.OutputName = <span class="org-rainbow-delimiters-depth-1">{</span><span class="org-string">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span>, <span class="org-underline">...</span>
<span class="org-string">'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'</span>, <span class="org-underline">...</span>
<span class="org-string">'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'</span>, <span class="org-underline">...</span>
<span class="org-string">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span class="org-rainbow-delimiters-depth-1">}</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 class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">, </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sys.G_forc = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'F1m', 'F2m', 'F3m', 'F4m', 'F5m', 'F6m'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">, </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sys.G_legs = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'D1m', 'D2m', 'D3m', 'D4m', 'D5m', 'D6m'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">, </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">'F1', 'F2', 'F3', 'F4', 'F5', 'F6'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sys.G_tran = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">, </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">'Dwx', 'Dwy', 'Dwz', 'Rwx', 'Rwy', 'Rwz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sys.G_comp = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dxm', 'Dym', 'Dzm', 'Rxm', 'Rym', 'Rzm'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">, </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sys.G_iner = minreal<span class="org-rainbow-delimiters-depth-1">(</span>G<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">{</span><span class="org-string">'Dxtm', 'Dytm', 'Dztm', 'Rxtm', 'Rytm', 'Rztm'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">, </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">'Fdx', 'Fdy', 'Fdz', 'Mdx', 'Mdy', 'Mdz'</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-comment">% sys.G_all = minreal(G);</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">end</span>
</pre>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-08-26 lun. 11:55</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
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