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Add time delay estimation

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Thomas Dehaeze 2020-07-24 13:06:02 +02:00
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-07-24 ven. 11:34 --> <!-- 2020-07-24 ven. 13:06 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Test Bench APA95ML</title> <title>Test Bench APA95ML</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -35,42 +35,42 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgfe82cc3">1. Setup</a> <li><a href="#org2723d81">1. Setup</a>
<ul> <ul>
<li><a href="#org1c0f5ab">1.1. Parameters</a></li> <li><a href="#orgfd55c36">1.1. Parameters</a></li>
<li><a href="#orgaa4583f">1.2. Filter White Noise</a></li> <li><a href="#org292fe55">1.2. Filter White Noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org14fbfb3">2. Run Experiment and Save Data</a> <li><a href="#orge27b441">2. Run Experiment and Save Data</a>
<ul> <ul>
<li><a href="#orgad744cf">2.1. Load Data</a></li> <li><a href="#orgba39bc1">2.1. Load Data</a></li>
<li><a href="#orgecaca8d">2.2. Save Data</a></li> <li><a href="#orga7db326">2.2. Save Data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org6882b50">3. Huddle Test</a> <li><a href="#orgca23311">3. Huddle Test</a>
<ul> <ul>
<li><a href="#orgb5af256">3.1. Time Domain Data</a></li> <li><a href="#org28c4ff9">3.1. Time Domain Data</a></li>
<li><a href="#org40d323a">3.2. PSD of Measurement Noise</a></li> <li><a href="#org61d66e9">3.2. PSD of Measurement Noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgbd5d691">4. Transfer Function Estimation with \(m=5kg\)</a> <li><a href="#orgd62d5d5">4. Transfer Function Estimation with \(m=5kg\)</a>
<ul> <ul>
<li><a href="#org227c117">4.1. Time Domain Data</a></li> <li><a href="#orgd195c16">4.1. Time Domain Data</a></li>
<li><a href="#org6113f77">4.2. Comparison of the PSD with Huddle Test</a></li> <li><a href="#org008a2d9">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgd0a66e9">4.3. Compute TF estimate and Coherence</a></li> <li><a href="#orgb223df5">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org0a09881">4.4. Comparison with the FEM model</a></li> <li><a href="#orgf0b54fc">4.4. Comparison with the FEM model</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org67f151f">5. Transfer function of the PI Amplifier</a> <li><a href="#org189b278">5. Transfer function of the PI Amplifier</a>
<ul> <ul>
<li><a href="#orgf5e228d">5.1. Compute TF estimate and Coherence</a></li> <li><a href="#org970db83">5.1. Compute TF estimate and Coherence</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org1290d70">6. PI Amplifier</a> <li><a href="#orgea1748b">6. PI Amplifier</a>
<ul> <ul>
<li><a href="#orgd4ba330">6.1. Comparison of the PSD with Huddle Test</a></li> <li><a href="#org53f7284">6.1. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#org16df457">6.2. Compute TF estimate and Coherence</a></li> <li><a href="#org9081582">6.2. Compute TF estimate and Coherence</a></li>
<li><a href="#orgb02981d">6.3. Comparison with the FEM model</a></li> <li><a href="#org52ebb83">6.3. Comparison with the FEM model</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -78,26 +78,26 @@
</div> </div>
<div id="org06e99b8" class="figure"> <div id="org059b319" class="figure">
<p><img src="figs/setup_picture.png" alt="setup_picture.png" /> <p><img src="figs/setup_picture.png" alt="setup_picture.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the Setup</p> <p><span class="figure-number">Figure 1: </span>Picture of the Setup</p>
</div> </div>
<div id="orgdb17066" class="figure"> <div id="org64743ab" class="figure">
<p><img src="figs/setup_zoom.png" alt="setup_zoom.png" /> <p><img src="figs/setup_zoom.png" alt="setup_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Zoom on the APA</p> <p><span class="figure-number">Figure 2: </span>Zoom on the APA</p>
</div> </div>
<div id="outline-container-orgfe82cc3" class="outline-2"> <div id="outline-container-org2723d81" class="outline-2">
<h2 id="orgfe82cc3"><span class="section-number-2">1</span> Setup</h2> <h2 id="org2723d81"><span class="section-number-2">1</span> Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div> </div>
<div id="outline-container-org1c0f5ab" class="outline-3"> <div id="outline-container-orgfd55c36" class="outline-3">
<h3 id="org1c0f5ab"><span class="section-number-3">1.1</span> Parameters</h3> <h3 id="orgfd55c36"><span class="section-number-3">1.1</span> Parameters</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = 1e-4; <pre class="src src-matlab">Ts = 1e-4;
@ -106,8 +106,8 @@
</div> </div>
</div> </div>
<div id="outline-container-orgaa4583f" class="outline-3"> <div id="outline-container-org292fe55" class="outline-3">
<h3 id="orgaa4583f"><span class="section-number-3">1.2</span> Filter White Noise</h3> <h3 id="org292fe55"><span class="section-number-3">1.2</span> Filter White Noise</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Glpf = 1/(1 + s/2/pi/500); <pre class="src src-matlab">Glpf = 1/(1 + s/2/pi/500);
@ -119,13 +119,13 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div> </div>
</div> </div>
<div id="outline-container-org14fbfb3" class="outline-2"> <div id="outline-container-orge27b441" class="outline-2">
<h2 id="org14fbfb3"><span class="section-number-2">2</span> Run Experiment and Save Data</h2> <h2 id="orge27b441"><span class="section-number-2">2</span> Run Experiment and Save Data</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> </div>
<div id="outline-container-orgad744cf" class="outline-3"> <div id="outline-container-orgba39bc1" class="outline-3">
<h3 id="orgad744cf"><span class="section-number-3">2.1</span> Load Data</h3> <h3 id="orgba39bc1"><span class="section-number-3">2.1</span> Load Data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data; <pre class="src src-matlab">data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data;
@ -134,8 +134,8 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div> </div>
</div> </div>
<div id="outline-container-orgecaca8d" class="outline-3"> <div id="outline-container-orga7db326" class="outline-3">
<h3 id="orgecaca8d"><span class="section-number-3">2.2</span> Save Data</h3> <h3 id="orga7db326"><span class="section-number-3">2.2</span> Save Data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">u = data(:, 1); % Input Voltage [V] <pre class="src src-matlab">u = data(:, 1); % Input Voltage [V]
@ -152,16 +152,16 @@ t = data(:, 3); % Time [s]
</div> </div>
</div> </div>
<div id="outline-container-org6882b50" class="outline-2"> <div id="outline-container-orgca23311" class="outline-2">
<h2 id="org6882b50"><span class="section-number-2">3</span> Huddle Test</h2> <h2 id="orgca23311"><span class="section-number-2">3</span> Huddle Test</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
</div> </div>
<div id="outline-container-orgb5af256" class="outline-3"> <div id="outline-container-org28c4ff9" class="outline-3">
<h3 id="orgb5af256"><span class="section-number-3">3.1</span> Time Domain Data</h3> <h3 id="org28c4ff9"><span class="section-number-3">3.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<div id="orgbd7db15" class="figure"> <div id="org8b0837a" class="figure">
<p><img src="figs/huddle_test_time_domain.png" alt="huddle_test_time_domain.png" /> <p><img src="figs/huddle_test_time_domain.png" alt="huddle_test_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Measurement of the Mass displacement during Huddle Test</p> <p><span class="figure-number">Figure 3: </span>Measurement of the Mass displacement during Huddle Test</p>
@ -169,8 +169,8 @@ t = data(:, 3); % Time [s]
</div> </div>
</div> </div>
<div id="outline-container-org40d323a" class="outline-3"> <div id="outline-container-org61d66e9" class="outline-3">
<h3 id="org40d323a"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3> <h3 id="org61d66e9"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1); <pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@ -186,7 +186,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="orgd39e732" class="figure"> <div id="orge35cf94" class="figure">
<p><img src="figs/huddle_test_pdf.png" alt="huddle_test_pdf.png" /> <p><img src="figs/huddle_test_pdf.png" alt="huddle_test_pdf.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the Displacement during Huddle Test</p> <p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the Displacement during Huddle Test</p>
@ -195,16 +195,16 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-orgbd5d691" class="outline-2"> <div id="outline-container-orgd62d5d5" class="outline-2">
<h2 id="orgbd5d691"><span class="section-number-2">4</span> Transfer Function Estimation with \(m=5kg\)</h2> <h2 id="orgd62d5d5"><span class="section-number-2">4</span> Transfer Function Estimation with \(m=5kg\)</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
</div> </div>
<div id="outline-container-org227c117" class="outline-3"> <div id="outline-container-orgd195c16" class="outline-3">
<h3 id="org227c117"><span class="section-number-3">4.1</span> Time Domain Data</h3> <h3 id="orgd195c16"><span class="section-number-3">4.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<div id="org71839ef" class="figure"> <div id="orgb8b0684" class="figure">
<p><img src="figs/apa95ml_5kg_10V_time_domain.png" alt="apa95ml_5kg_10V_time_domain.png" /> <p><img src="figs/apa95ml_5kg_10V_time_domain.png" alt="apa95ml_5kg_10V_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Time domain signals during the test</p> <p><span class="figure-number">Figure 5: </span>Time domain signals during the test</p>
@ -212,8 +212,8 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-org6113f77" class="outline-3"> <div id="outline-container-org008a2d9" class="outline-3">
<h3 id="org6113f77"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3> <h3 id="org008a2d9"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1); <pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@ -230,7 +230,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="orgb5f4391" class="figure"> <div id="org3189602" class="figure">
<p><img src="figs/apa95ml_5kg_10V_pdf_comp_huddle.png" alt="apa95ml_5kg_10V_pdf_comp_huddle.png" /> <p><img src="figs/apa95ml_5kg_10V_pdf_comp_huddle.png" alt="apa95ml_5kg_10V_pdf_comp_huddle.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD for the identification test and the huddle test</p> <p><span class="figure-number">Figure 6: </span>Comparison of the ASD for the identification test and the huddle test</p>
@ -238,8 +238,8 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-orgd0a66e9" class="outline-3"> <div id="outline-container-orgb223df5" class="outline-3">
<h3 id="orgd0a66e9"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3> <h3 id="orgb223df5"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1); <pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@ -256,14 +256,14 @@ Fs = 1/Ts;
</div> </div>
<div id="org24bac83" class="figure"> <div id="orgc74f977" class="figure">
<p><img src="figs/apa95ml_5kg_10V_coh.png" alt="apa95ml_5kg_10V_coh.png" /> <p><img src="figs/apa95ml_5kg_10V_coh.png" alt="apa95ml_5kg_10V_coh.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Coherence</p> <p><span class="figure-number">Figure 7: </span>Coherence</p>
</div> </div>
<div id="orgb21f9f8" class="figure"> <div id="orgc54bab7" class="figure">
<p><img src="figs/apa95ml_5kg_10V_tf.png" alt="apa95ml_5kg_10V_tf.png" /> <p><img src="figs/apa95ml_5kg_10V_tf.png" alt="apa95ml_5kg_10V_tf.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Estimation of the transfer function from input voltage to displacement</p> <p><span class="figure-number">Figure 8: </span>Estimation of the transfer function from input voltage to displacement</p>
@ -271,8 +271,8 @@ Fs = 1/Ts;
</div> </div>
</div> </div>
<div id="outline-container-org0a09881" class="outline-3"> <div id="outline-container-orgf0b54fc" class="outline-3">
<h3 id="org0a09881"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3> <h3 id="orgf0b54fc"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3>
<div class="outline-text-3" id="text-4-4"> <div class="outline-text-3" id="text-4-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm'); <pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
@ -280,7 +280,7 @@ Fs = 1/Ts;
</div> </div>
<div id="org780d0cb" class="figure"> <div id="orge0b2a40" class="figure">
<p><img src="figs/apa95ml_5kg_comp_fem.png" alt="apa95ml_5kg_comp_fem.png" /> <p><img src="figs/apa95ml_5kg_comp_fem.png" alt="apa95ml_5kg_comp_fem.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Comparison of the identified transfer function and the one estimated from the FE model</p> <p><span class="figure-number">Figure 9: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
@ -299,12 +299,12 @@ In the next section, a current amplifier is used.
</div> </div>
</div> </div>
<div id="outline-container-org67f151f" class="outline-2"> <div id="outline-container-org189b278" class="outline-2">
<h2 id="org67f151f"><span class="section-number-2">5</span> Transfer function of the PI Amplifier</h2> <h2 id="org189b278"><span class="section-number-2">5</span> Transfer function of the PI Amplifier</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
</div> </div>
<div id="outline-container-orgf5e228d" class="outline-3"> <div id="outline-container-org970db83" class="outline-3">
<h3 id="orgf5e228d"><span class="section-number-3">5.1</span> Compute TF estimate and Coherence</h3> <h3 id="org970db83"><span class="section-number-3">5.1</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1); <pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@ -317,11 +317,11 @@ The coherence and the transfer function are estimate from the voltage input of t
</p> </p>
<p> <p>
The coherence is very good as expected (Figure <a href="#orgf66ca3c">10</a>). The coherence is very good as expected (Figure <a href="#org1877c12">10</a>).
</p> </p>
<p> <p>
The transfer function show a low pass filter behavior with a lot of phase drop (Figure <a href="#org0f454bc">11</a>). The transfer function show a low pass filter behavior with a lot of phase drop (Figure <a href="#org76c3cb3">11</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -333,28 +333,40 @@ The transfer function show a low pass filter behavior with a lot of phase drop (
</div> </div>
<div id="orgf66ca3c" class="figure"> <div id="org1877c12" class="figure">
<p><img src="figs/PI_E505_coh.png" alt="PI_E505_coh.png" /> <p><img src="figs/PI_E505_coh.png" alt="PI_E505_coh.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Coherence</p> <p><span class="figure-number">Figure 10: </span>Coherence</p>
</div> </div>
<div id="org0f454bc" class="figure"> <div id="org76c3cb3" class="figure">
<p><img src="figs/PI_E505_tf.png" alt="PI_E505_tf.png" /> <p><img src="figs/PI_E505_tf.png" alt="PI_E505_tf.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Estimation of the transfer function from input voltage to displacement</p> <p><span class="figure-number">Figure 11: </span>Estimation of the transfer function from input voltage to displacement</p>
</div> </div>
<p>
The delay can be estimated as follow:
</p>
<div class="org-src-container">
<pre class="src src-matlab">finddelay(u, um)*Ts
</pre>
</div>
<pre class="example">
0.0004
</pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1290d70" class="outline-2"> <div id="outline-container-orgea1748b" class="outline-2">
<h2 id="org1290d70"><span class="section-number-2">6</span> PI Amplifier</h2> <h2 id="orgea1748b"><span class="section-number-2">6</span> PI Amplifier</h2>
<div class="outline-text-2" id="text-6"> <div class="outline-text-2" id="text-6">
</div> </div>
<div id="outline-container-orgd4ba330" class="outline-3"> <div id="outline-container-org53f7284" class="outline-3">
<h3 id="orgd4ba330"><span class="section-number-3">6.1</span> Comparison of the PSD with Huddle Test</h3> <h3 id="org53f7284"><span class="section-number-3">6.1</span> Comparison of the PSD with Huddle Test</h3>
<div class="outline-text-3" id="text-6-1"> <div class="outline-text-3" id="text-6-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1); <pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@ -371,7 +383,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="orgee44531" class="figure"> <div id="org1d7bc05" class="figure">
<p><img src="figs/apa95ml_5kg_PI_pdf_comp_huddle.png" alt="apa95ml_5kg_PI_pdf_comp_huddle.png" /> <p><img src="figs/apa95ml_5kg_PI_pdf_comp_huddle.png" alt="apa95ml_5kg_PI_pdf_comp_huddle.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Comparison of the ASD for the identification test and the huddle test</p> <p><span class="figure-number">Figure 12: </span>Comparison of the ASD for the identification test and the huddle test</p>
@ -379,8 +391,8 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-org16df457" class="outline-3"> <div id="outline-container-org9081582" class="outline-3">
<h3 id="org16df457"><span class="section-number-3">6.2</span> Compute TF estimate and Coherence</h3> <h3 id="org9081582"><span class="section-number-3">6.2</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-6-2"> <div class="outline-text-3" id="text-6-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1); <pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@ -397,14 +409,14 @@ Fs = 1/Ts;
</div> </div>
<div id="org1b63f2b" class="figure"> <div id="orge505858" class="figure">
<p><img src="figs/apa95ml_5kg_PI_coh.png" alt="apa95ml_5kg_PI_coh.png" /> <p><img src="figs/apa95ml_5kg_PI_coh.png" alt="apa95ml_5kg_PI_coh.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Coherence</p> <p><span class="figure-number">Figure 13: </span>Coherence</p>
</div> </div>
<div id="orgd6c6bfa" class="figure"> <div id="org5754167" class="figure">
<p><img src="figs/apa95ml_5kg_PI_tf.png" alt="apa95ml_5kg_PI_tf.png" /> <p><img src="figs/apa95ml_5kg_PI_tf.png" alt="apa95ml_5kg_PI_tf.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Estimation of the transfer function from input voltage to displacement</p> <p><span class="figure-number">Figure 14: </span>Estimation of the transfer function from input voltage to displacement</p>
@ -412,8 +424,8 @@ Fs = 1/Ts;
</div> </div>
</div> </div>
<div id="outline-container-orgb02981d" class="outline-3"> <div id="outline-container-org52ebb83" class="outline-3">
<h3 id="orgb02981d"><span class="section-number-3">6.3</span> Comparison with the FEM model</h3> <h3 id="org52ebb83"><span class="section-number-3">6.3</span> Comparison with the FEM model</h3>
<div class="outline-text-3" id="text-6-3"> <div class="outline-text-3" id="text-6-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm'); <pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
@ -421,7 +433,7 @@ Fs = 1/Ts;
</div> </div>
<div id="org44c4863" class="figure"> <div id="orge0e655f" class="figure">
<p><img src="figs/apa95ml_5kg_pi_comp_fem.png" alt="apa95ml_5kg_pi_comp_fem.png" /> <p><img src="figs/apa95ml_5kg_pi_comp_fem.png" alt="apa95ml_5kg_pi_comp_fem.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Comparison of the identified transfer function and the one estimated from the FE model</p> <p><span class="figure-number">Figure 15: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
@ -432,7 +444,7 @@ Fs = 1/Ts;
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-07-24 ven. 11:34</p> <p class="date">Created: 2020-07-24 ven. 13:06</p>
</div> </div>
</body> </body>
</html> </html>

10
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@ -405,7 +405,7 @@ The transfer function show a low pass filter behavior with a lot of phase drop (
ax2 = subplot(2, 1, 2); ax2 = subplot(2, 1, 2);
hold on; hold on;
plot(f, 180/pi*angle(tf_est), 'k-') plot(f, 180/pi*angle(tf_est), 'k-')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin'); set(gca, 'Xscale', 'lin'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]'); ylabel('Phase'); xlabel('Frequency [Hz]');
hold off; hold off;
ylim([-180, 180]); ylim([-180, 180]);
@ -424,6 +424,14 @@ The transfer function show a low pass filter behavior with a lot of phase drop (
#+RESULTS: #+RESULTS:
[[file:figs/PI_E505_tf.png]] [[file:figs/PI_E505_tf.png]]
The delay can be estimated as follow:
#+begin_src matlab :results replace value
finddelay(u, um)*Ts
#+end_src
#+RESULTS:
: 0.0004
* PI Amplifier * PI Amplifier
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)