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Add Comparison with the FEM

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Thomas Dehaeze 2020-07-20 13:29:36 +02:00
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<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>
<!-- 2020-07-20 lun. 13:22 --> <!-- 2020-07-20 lun. 13:29 -->
<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" />
@ -15,6 +15,14 @@
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</head> </head>
<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -27,29 +35,30 @@
<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="#org5904e1c">1. Setup</a> <li><a href="#orge11c5dc">1. Setup</a>
<ul> <ul>
<li><a href="#org9cb828d">1.1. Parameters</a></li> <li><a href="#org6653e08">1.1. Parameters</a></li>
<li><a href="#org55efde3">1.2. Filter White Noise</a></li> <li><a href="#orge01c6e9">1.2. Filter White Noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org8af571a">2. Run Experiment and Save Data</a> <li><a href="#org26dcd8d">2. Run Experiment and Save Data</a>
<ul> <ul>
<li><a href="#orgc26f768">2.1. Load Data</a></li> <li><a href="#orgc671538">2.1. Load Data</a></li>
<li><a href="#org184b70d">2.2. Save Data</a></li> <li><a href="#orge426d6c">2.2. Save Data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orga844fc8">3. Huddle Test</a> <li><a href="#org29fccbc">3. Huddle Test</a>
<ul> <ul>
<li><a href="#org7873825">3.1. Time Domain Data</a></li> <li><a href="#org1a509f0">3.1. Time Domain Data</a></li>
<li><a href="#org4799d62">3.2. PSD of Measurement Noise</a></li> <li><a href="#org99da013">3.2. PSD of Measurement Noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf667003">4. Transfer Function Estimation with m=5kg</a> <li><a href="#orgfa5e8ee">4. Transfer Function Estimation with \(m=5kg\)</a>
<ul> <ul>
<li><a href="#org1c0e9d1">4.1. Time Domain Data</a></li> <li><a href="#orgf861073">4.1. Time Domain Data</a></li>
<li><a href="#org303f615">4.2. Comparison of the PSD with Huddle Test</a></li> <li><a href="#org65d8a9f">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgeb52c9a">4.3. Compute TF estimate and Coherence</a></li> <li><a href="#orgc82a6e8">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org4b0a791">4.4. Comparison with the FEM model</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -57,26 +66,26 @@
</div> </div>
<div id="org2e20e62" class="figure"> <div id="org63ea785" 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="org5723466" class="figure"> <div id="org285264c" 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-org5904e1c" class="outline-2"> <div id="outline-container-orge11c5dc" class="outline-2">
<h2 id="org5904e1c"><span class="section-number-2">1</span> Setup</h2> <h2 id="orge11c5dc"><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-org9cb828d" class="outline-3"> <div id="outline-container-org6653e08" class="outline-3">
<h3 id="org9cb828d"><span class="section-number-3">1.1</span> Parameters</h3> <h3 id="org6653e08"><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;
@ -85,8 +94,8 @@
</div> </div>
</div> </div>
<div id="outline-container-org55efde3" class="outline-3"> <div id="outline-container-orge01c6e9" class="outline-3">
<h3 id="org55efde3"><span class="section-number-3">1.2</span> Filter White Noise</h3> <h3 id="orge01c6e9"><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);
@ -98,13 +107,13 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div> </div>
</div> </div>
<div id="outline-container-org8af571a" class="outline-2"> <div id="outline-container-org26dcd8d" class="outline-2">
<h2 id="org8af571a"><span class="section-number-2">2</span> Run Experiment and Save Data</h2> <h2 id="org26dcd8d"><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-orgc26f768" class="outline-3"> <div id="outline-container-orgc671538" class="outline-3">
<h3 id="orgc26f768"><span class="section-number-3">2.1</span> Load Data</h3> <h3 id="orgc671538"><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;
@ -113,8 +122,8 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div> </div>
</div> </div>
<div id="outline-container-org184b70d" class="outline-3"> <div id="outline-container-orge426d6c" class="outline-3">
<h3 id="org184b70d"><span class="section-number-3">2.2</span> Save Data</h3> <h3 id="orge426d6c"><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]
@ -131,16 +140,16 @@ t = data(:, 3); % Time [s]
</div> </div>
</div> </div>
<div id="outline-container-orga844fc8" class="outline-2"> <div id="outline-container-org29fccbc" class="outline-2">
<h2 id="orga844fc8"><span class="section-number-2">3</span> Huddle Test</h2> <h2 id="org29fccbc"><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-org7873825" class="outline-3"> <div id="outline-container-org1a509f0" class="outline-3">
<h3 id="org7873825"><span class="section-number-3">3.1</span> Time Domain Data</h3> <h3 id="org1a509f0"><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="orge1a69cc" class="figure"> <div id="orgf1f51e5" 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>
@ -148,8 +157,8 @@ t = data(:, 3); % Time [s]
</div> </div>
</div> </div>
<div id="outline-container-org4799d62" class="outline-3"> <div id="outline-container-org99da013" class="outline-3">
<h3 id="org4799d62"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3> <h3 id="org99da013"><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);
@ -165,7 +174,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="org251d419" class="figure"> <div id="orgc5a6acc" 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>
@ -174,16 +183,16 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-orgf667003" class="outline-2"> <div id="outline-container-orgfa5e8ee" class="outline-2">
<h2 id="orgf667003"><span class="section-number-2">4</span> Transfer Function Estimation with m=5kg</h2> <h2 id="orgfa5e8ee"><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-org1c0e9d1" class="outline-3"> <div id="outline-container-orgf861073" class="outline-3">
<h3 id="org1c0e9d1"><span class="section-number-3">4.1</span> Time Domain Data</h3> <h3 id="orgf861073"><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="org6773b72" class="figure"> <div id="orga6ff075" 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>
@ -191,8 +200,8 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-org303f615" class="outline-3"> <div id="outline-container-org65d8a9f" class="outline-3">
<h3 id="org303f615"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3> <h3 id="org65d8a9f"><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);
@ -209,7 +218,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="org001b938" class="figure"> <div id="org63805be" 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>
@ -217,8 +226,8 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-orgeb52c9a" class="outline-3"> <div id="outline-container-orgc82a6e8" class="outline-3">
<h3 id="orgeb52c9a"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3> <h3 id="orgc82a6e8"><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">win = hann(ceil(1/Ts)); <pre class="src src-matlab">win = hann(ceil(1/Ts));
@ -229,25 +238,42 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="orgbfd3d36" class="figure"> <div id="orgf57d3dd" 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="orgbd7052e" class="figure"> <div id="org3409282" 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>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org4b0a791" class="outline-3">
<h3 id="org4b0a791"><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="org-src-container">
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
</pre>
</div>
<div id="org7509557" class="figure">
<p><img src="figs/apa95ml_5kg_comp_fem.png" alt="apa95ml_5kg_comp_fem.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
</div>
</div>
</div>
</div> </div>
</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: 2020-07-20 lun. 13:22</p> <p class="date">Created: 2020-07-20 lun. 13:29</p>
</div> </div>
</body> </body>
</html> </html>

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@ -156,7 +156,7 @@
#+RESULTS: #+RESULTS:
[[file:figs/huddle_test_pdf.png]] [[file:figs/huddle_test_pdf.png]]
* Transfer Function Estimation with m=5kg * Transfer Function Estimation with $m=5kg$
:PROPERTIES: :PROPERTIES:
:header-args:matlab+: :tangle matlab/tf_estimation.m :header-args:matlab+: :tangle matlab/tf_estimation.m
:header-args:matlab+: :comments org :mkdirp yes :header-args:matlab+: :comments org :mkdirp yes
@ -290,3 +290,40 @@
#+caption: Estimation of the transfer function from input voltage to displacement #+caption: Estimation of the transfer function from input voltage to displacement
#+RESULTS: #+RESULTS:
[[file:figs/apa95ml_5kg_10V_tf.png]] [[file:figs/apa95ml_5kg_10V_tf.png]]
** Comparison with the FEM model
#+begin_src matlab
load('mat/fem_model_5kg.mat', 'Ghm');
#+end_src
#+begin_src matlab :exports none
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(tf_est), 'DisplayName', 'Identification')
plot(f, abs(squeeze(freqresp(Ghm, f, 'Hz'))), 'DisplayName', 'FEM')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
legend('location', 'northeast')
hold off;
ax2 = subplot(2, 1, 2);
hold on;
plot(f, 180/pi*angle(tf_est))
plot(f, 180/pi*angle(squeeze(freqresp(Ghm, f, 'Hz'))))
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
linkaxes([ax1,ax2], 'x');
xlim([10, 5e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/apa95ml_5kg_comp_fem.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:apa95ml_5kg_comp_fem
#+caption: Comparison of the identified transfer function and the one estimated from the FE model
#+RESULTS:
[[file:figs/apa95ml_5kg_comp_fem.png]]

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