589 lines
36 KiB
HTML
589 lines
36 KiB
HTML
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</head>
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<body>
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<div id="content">
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<h1 class="title">Cercalo Test Bench</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="#org25712dd">1. Identification</a>
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<ul>
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<li><a href="#orgc595eec">1.1. Excitation Data</a></li>
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<li><a href="#orgd0be9c1">1.2. Input / Output data</a></li>
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<li><a href="#org6ef1d0f">1.3. Estimation of the Frequency Response Function Matrix</a></li>
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<li><a href="#orgb893c50">1.4. Coherence</a></li>
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<li><a href="#org57d6ee3">1.5. Extraction of a transfer function matrix</a></li>
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</ul>
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</li>
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<li><a href="#org6115789">2. Plant Analysis</a></li>
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<li><a href="#orgcdff0c9">3. Control</a></li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org25712dd" class="outline-2">
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<h2 id="org25712dd"><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-orgc595eec" class="outline-3">
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<h3 id="orgc595eec"><span class="section-number-3">1.1</span> Excitation Data</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">fs = <span class="org-highlight-numbers-number">1e4</span>;
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Ts = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>fs;
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</pre>
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</div>
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<p>
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We generate white noise with the "random number" simulink block, and we filter that noise.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Gi = <span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">c2d<span class="org-rainbow-delimiters-depth-1">(</span>Gi, Ts, <span class="org-string">'tustin'</span><span class="org-rainbow-delimiters-depth-1">)</span>
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</pre>
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</div>
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<pre class="example">
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c2d(Gi, Ts, 'tustin')
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ans =
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0.030459 (z+1)
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--------------
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(z-0.9391)
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Sample time: 0.0001 seconds
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Discrete-time zero/pole/gain model.
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</pre>
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</div>
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</div>
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<div id="outline-container-orgd0be9c1" class="outline-3">
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<h3 id="orgd0be9c1"><span class="section-number-3">1.2</span> Input / Output data</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
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The identification data is loaded
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">ux = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'ux', 'yx', 'yy'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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uy = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_002.mat', 't', 'uy', 'yx', 'yy'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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<p>
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We remove the first seconds where the Cercalo is turned on.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">i0x = <span class="org-highlight-numbers-number">20</span><span class="org-type">*</span>fs;
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i0y = <span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>fs;
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ux.t = ux.t<span class="org-rainbow-delimiters-depth-1">(</span> i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> ux.t<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-rainbow-delimiters-depth-1">)</span>;
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ux.ux = ux.ux<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
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ux.yx = ux.yx<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
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ux.yy = ux.yy<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
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uy.t = uy.t<span class="org-rainbow-delimiters-depth-1">(</span> i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> uy.t<span class="org-rainbow-delimiters-depth-1">(</span>i0x<span class="org-rainbow-delimiters-depth-1">)</span>;
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uy.uy = uy.uy<span class="org-rainbow-delimiters-depth-1">(</span>i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
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uy.yx = uy.yx<span class="org-rainbow-delimiters-depth-1">(</span>i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
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uy.yy = uy.yy<span class="org-rainbow-delimiters-depth-1">(</span>i0y<span class="org-type">:</span>end<span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">ux.ux = ux.ux<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux<span class="org-rainbow-delimiters-depth-1">)</span>;
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ux.yx = ux.yx<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>ux.yx<span class="org-rainbow-delimiters-depth-1">)</span>;
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ux.yy = ux.yy<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>ux.yy<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
uy.ux = uy.ux<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>uy.ux<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
uy.yx = uy.yx<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>uy.yx<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
uy.yy = uy.yy<span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-1">(</span>uy.yy<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgdd27b44" class="figure">
|
|
<p><img src="figs/identification_ux.png" alt="identification_ux.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Identification signals when exciting the \(x\) axis (<a href="./figs/identification_ux.png">png</a>, <a href="./figs/identification_ux.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgc1aa49f" class="figure">
|
|
<p><img src="figs/identification_uy.png" alt="identification_uy.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Identification signals when exciting the \(y\) axis (<a href="./figs/identification_uy.png">png</a>, <a href="./figs/identification_uy.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6ef1d0f" class="outline-3">
|
|
<h3 id="org6ef1d0f"><span class="section-number-3">1.3</span> Estimation of the Frequency Response Function Matrix</h3>
|
|
<div class="outline-text-3" id="text-1-3">
|
|
<p>
|
|
We compute an estimate of the transfer functions.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>tf_ux_yx, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>tf_ux_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>tf_uy_yx, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>tf_uy_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org26ecff4" class="figure">
|
|
<p><img src="figs/frequency_response_matrix.png" alt="frequency_response_matrix.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Frequency Response Matrix (<a href="./figs/frequency_response_matrix.png">png</a>, <a href="./figs/frequency_response_matrix.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb893c50" class="outline-3">
|
|
<h3 id="orgb893c50"><span class="section-number-3">1.4</span> Coherence</h3>
|
|
<div class="outline-text-3" id="text-1-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh_ux_yx, f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>coh_ux_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ux.ux, ux.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>coh_uy_yx, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yx, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>coh_uy_yy, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>uy.uy, uy.yy, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>fs<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org2a5d4ff" class="figure">
|
|
<p><img src="figs/identification_coherence.png" alt="identification_coherence.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Coherence (<a href="./figs/identification_coherence.png">png</a>, <a href="./figs/identification_coherence.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org57d6ee3" class="outline-3">
|
|
<h3 id="org57d6ee3"><span class="section-number-3">1.5</span> Extraction of a transfer function matrix</h3>
|
|
<div class="outline-text-3" id="text-1-5">
|
|
<p>
|
|
First we define the initial guess for the resonance frequencies and the weights associated.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">freqs_res = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">410</span>, <span class="org-highlight-numbers-number">250</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [Hz]</span>
|
|
freqs_res_weights = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-1">]</span>; <span class="org-comment">% [Hz]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
From the number of resonance frequency we want to fit, we define the order <code>N</code> of the system we want to obtain.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">N = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>length<span class="org-rainbow-delimiters-depth-1">(</span>freqs_res<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We then make an initial guess on the complex values of the poles.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">xi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">001</span>; <span class="org-comment">% Approximate modal damping</span>
|
|
poles = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs_res<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>xi <span class="org-type">+</span> <span class="org-highlight-numbers-number">1i</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs_res<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>xi <span class="org-type">-</span> <span class="org-highlight-numbers-number">1i</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We then define the weight that will be used for the fitting.
|
|
Basically, we want more weight around the resonance and at low frequency (below the first resonance).
|
|
Also, we want more importance where we have a better coherence.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">weight = ones<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, length<span class="org-rainbow-delimiters-depth-2">(</span>f<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-comment">% weight = G_coh';</span>
|
|
|
|
% alpha = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>;
|
|
|
|
% <span class="org-keyword">for</span> <span class="org-variable-name">freq_i</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length(freqs_res)</span>
|
|
% weight(f<span class="org-type">></span>(<span class="org-highlight-numbers-number">1</span><span class="org-type">-</span>alpha)<span class="org-type">*</span>freqs_res(freq_i) <span class="org-type">&</span> omega<span class="org-type"><</span>(<span class="org-highlight-numbers-number">1</span> <span class="org-type">+</span> alpha)<span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freqs_res(freq_i)) = freqs_res_weights(freq_i);
|
|
<span class="org-comment">% end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Ignore data above some frequency.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">weight<span class="org-rainbow-delimiters-depth-1">(</span>f<span class="org-type">></span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-highlight-numbers-number">0</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgd766a83" class="figure">
|
|
<p><img src="figs/weights.png" alt="weights.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Weights amplitude (<a href="./figs/weights.png">png</a>, <a href="./figs/weights.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
When we set some options for <code>vfit3</code>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">opts = struct<span class="org-rainbow-delimiters-depth-1">()</span>;
|
|
|
|
opts.stable = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% Enforce stable poles</span>
|
|
opts.asymp = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% Force D matrix to be null</span>
|
|
opts.relax = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% Use vector fitting with relaxed non-triviality constraint</span>
|
|
opts.skip_pole = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Do NOT skip pole identification</span>
|
|
opts.skip_res = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Do NOT skip identification of residues (C,D,E)</span>
|
|
opts.cmplx_ss = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Create real state space model with block diagonal A</span>
|
|
|
|
opts.spy1 = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% No plotting for first stage of vector fitting</span>
|
|
opts.spy2 = <span class="org-highlight-numbers-number">0</span>; <span class="org-comment">% Create magnitude plot for fitting of f(s)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
We define the number of iteration.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Niter = <span class="org-highlight-numbers-number">5</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
An we run the <code>vectfit3</code> algorithm.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_ux_yx, poles, <span class="org-type">~</span>, fit_ux_yx<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_ux_yx<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-keyword">end</span>
|
|
<span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_uy_yx, poles, <span class="org-type">~</span>, fit_uy_yx<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_uy_yx<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-keyword">end</span>
|
|
<span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_ux_yy, poles, <span class="org-type">~</span>, fit_ux_yy<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_ux_yy<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-keyword">end</span>
|
|
<span class="org-keyword">for</span> <span class="org-variable-name">iter</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:Niter</span>
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>SER_uy_yy, poles, <span class="org-type">~</span>, fit_uy_yy<span class="org-rainbow-delimiters-depth-1">]</span> = vectfit3<span class="org-rainbow-delimiters-depth-1">(</span>tf_uy_yy<span class="org-type">.'</span>, <span class="org-highlight-numbers-number">1i</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f, poles, weight, opts<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-keyword">end</span>
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgc6407a4" class="figure">
|
|
<p><img src="figs/identification_matrix_fit.png" alt="identification_matrix_fit.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Transfer Function Extraction of the FRF matrix (<a href="./figs/identification_matrix_fit.png">png</a>, <a href="./figs/identification_matrix_fit.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
And finally, we create the identified state space model:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">G_ux_yx = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_ux_yx.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_ux_yx.B,SER_ux_yx.C,SER_ux_yx.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
G_uy_yx = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_uy_yx.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_uy_yx.B,SER_uy_yx.C,SER_uy_yx.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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G_ux_yy = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_ux_yy.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_ux_yy.B,SER_ux_yy.C,SER_ux_yy.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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G_uy_yy = minreal<span class="org-rainbow-delimiters-depth-1">(</span>ss<span class="org-rainbow-delimiters-depth-2">(</span>full<span class="org-rainbow-delimiters-depth-3">(</span>SER_uy_yy.A<span class="org-rainbow-delimiters-depth-3">)</span>,SER_uy_yy.B,SER_uy_yy.C,SER_uy_yy.D<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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G = <span class="org-rainbow-delimiters-depth-1">[</span>G_ux_yx, G_uy_yx;
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G_ux_yy, G_uy_yy<span class="org-rainbow-delimiters-depth-1">]</span>;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/plant.mat', 'G'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org6115789" class="outline-2">
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<h2 id="org6115789"><span class="section-number-2">2</span> Plant Analysis</h2>
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</div>
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<div id="outline-container-orgcdff0c9" class="outline-2">
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<h2 id="orgcdff0c9"><span class="section-number-2">3</span> Control</h2>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2019-09-10 mar. 18:15</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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