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Add figures for when using the PI amplifier

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Thomas Dehaeze 2020-07-23 09:43:42 +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>
<!-- 2020-07-20 lun. 13:29 --> <!-- 2020-07-23 jeu. 09:33 -->
<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" />
@ -35,30 +35,37 @@
<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="#orge11c5dc">1. Setup</a> <li><a href="#org6d01a62">1. Setup</a>
<ul> <ul>
<li><a href="#org6653e08">1.1. Parameters</a></li> <li><a href="#org7f6c52e">1.1. Parameters</a></li>
<li><a href="#orge01c6e9">1.2. Filter White Noise</a></li> <li><a href="#orgf78bcf3">1.2. Filter White Noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org26dcd8d">2. Run Experiment and Save Data</a> <li><a href="#org3920c8f">2. Run Experiment and Save Data</a>
<ul> <ul>
<li><a href="#orgc671538">2.1. Load Data</a></li> <li><a href="#org48afa54">2.1. Load Data</a></li>
<li><a href="#orge426d6c">2.2. Save Data</a></li> <li><a href="#org6dd5e8b">2.2. Save Data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org29fccbc">3. Huddle Test</a> <li><a href="#orgb856102">3. Huddle Test</a>
<ul> <ul>
<li><a href="#org1a509f0">3.1. Time Domain Data</a></li> <li><a href="#orgbdccf6c">3.1. Time Domain Data</a></li>
<li><a href="#org99da013">3.2. PSD of Measurement Noise</a></li> <li><a href="#org555147e">3.2. PSD of Measurement Noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgfa5e8ee">4. Transfer Function Estimation with \(m=5kg\)</a> <li><a href="#orgb67c277">4. Transfer Function Estimation with \(m=5kg\)</a>
<ul> <ul>
<li><a href="#orgf861073">4.1. Time Domain Data</a></li> <li><a href="#org3f71fa1">4.1. Time Domain Data</a></li>
<li><a href="#org65d8a9f">4.2. Comparison of the PSD with Huddle Test</a></li> <li><a href="#org8e6db12">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgc82a6e8">4.3. Compute TF estimate and Coherence</a></li> <li><a href="#org4ac16d4">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org4b0a791">4.4. Comparison with the FEM model</a></li> <li><a href="#org6938b52">4.4. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#org98add36">5. PI Amplifier</a>
<ul>
<li><a href="#org68ab283">5.1. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orga8db91a">5.2. Compute TF estimate and Coherence</a></li>
<li><a href="#org7272539">5.3. Comparison with the FEM model</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -66,26 +73,26 @@
</div> </div>
<div id="org63ea785" class="figure"> <div id="orgfe6ddf9" 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="org285264c" class="figure"> <div id="orgde5ae22" 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-orge11c5dc" class="outline-2"> <div id="outline-container-org6d01a62" class="outline-2">
<h2 id="orge11c5dc"><span class="section-number-2">1</span> Setup</h2> <h2 id="org6d01a62"><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-org6653e08" class="outline-3"> <div id="outline-container-org7f6c52e" class="outline-3">
<h3 id="org6653e08"><span class="section-number-3">1.1</span> Parameters</h3> <h3 id="org7f6c52e"><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;
@ -94,8 +101,8 @@
</div> </div>
</div> </div>
<div id="outline-container-orge01c6e9" class="outline-3"> <div id="outline-container-orgf78bcf3" class="outline-3">
<h3 id="orge01c6e9"><span class="section-number-3">1.2</span> Filter White Noise</h3> <h3 id="orgf78bcf3"><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);
@ -107,13 +114,13 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div> </div>
</div> </div>
<div id="outline-container-org26dcd8d" class="outline-2"> <div id="outline-container-org3920c8f" class="outline-2">
<h2 id="org26dcd8d"><span class="section-number-2">2</span> Run Experiment and Save Data</h2> <h2 id="org3920c8f"><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-orgc671538" class="outline-3"> <div id="outline-container-org48afa54" class="outline-3">
<h3 id="orgc671538"><span class="section-number-3">2.1</span> Load Data</h3> <h3 id="org48afa54"><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;
@ -122,8 +129,8 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div> </div>
</div> </div>
<div id="outline-container-orge426d6c" class="outline-3"> <div id="outline-container-org6dd5e8b" class="outline-3">
<h3 id="orge426d6c"><span class="section-number-3">2.2</span> Save Data</h3> <h3 id="org6dd5e8b"><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]
@ -140,16 +147,16 @@ t = data(:, 3); % Time [s]
</div> </div>
</div> </div>
<div id="outline-container-org29fccbc" class="outline-2"> <div id="outline-container-orgb856102" class="outline-2">
<h2 id="org29fccbc"><span class="section-number-2">3</span> Huddle Test</h2> <h2 id="orgb856102"><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-org1a509f0" class="outline-3"> <div id="outline-container-orgbdccf6c" class="outline-3">
<h3 id="org1a509f0"><span class="section-number-3">3.1</span> Time Domain Data</h3> <h3 id="orgbdccf6c"><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="orgf1f51e5" class="figure"> <div id="orgfef1212" 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>
@ -157,8 +164,8 @@ t = data(:, 3); % Time [s]
</div> </div>
</div> </div>
<div id="outline-container-org99da013" class="outline-3"> <div id="outline-container-org555147e" class="outline-3">
<h3 id="org99da013"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3> <h3 id="org555147e"><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);
@ -174,7 +181,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="orgc5a6acc" class="figure"> <div id="orgd17271b" 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>
@ -183,16 +190,16 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-orgfa5e8ee" class="outline-2"> <div id="outline-container-orgb67c277" class="outline-2">
<h2 id="orgfa5e8ee"><span class="section-number-2">4</span> Transfer Function Estimation with \(m=5kg\)</h2> <h2 id="orgb67c277"><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-orgf861073" class="outline-3"> <div id="outline-container-org3f71fa1" class="outline-3">
<h3 id="orgf861073"><span class="section-number-3">4.1</span> Time Domain Data</h3> <h3 id="org3f71fa1"><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="orga6ff075" class="figure"> <div id="orga603410" 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>
@ -200,8 +207,8 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-org65d8a9f" class="outline-3"> <div id="outline-container-org8e6db12" class="outline-3">
<h3 id="org65d8a9f"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3> <h3 id="org8e6db12"><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);
@ -218,7 +225,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="org63805be" class="figure"> <div id="orgf16dfcd" 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>
@ -226,9 +233,15 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-orgc82a6e8" class="outline-3"> <div id="outline-container-org4ac16d4" class="outline-3">
<h3 id="orgc82a6e8"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3> <h3 id="org4ac16d4"><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">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
</pre>
</div>
<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));
@ -238,14 +251,14 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="orgf57d3dd" class="figure"> <div id="org93041d8" 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="org3409282" class="figure"> <div id="orgf2a7b3e" 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>
@ -253,8 +266,8 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
<div id="outline-container-org4b0a791" class="outline-3"> <div id="outline-container-org6938b52" class="outline-3">
<h3 id="org4b0a791"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3> <h3 id="org6938b52"><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');
@ -262,7 +275,7 @@ win = hanning(ceil(1*Fs));
</div> </div>
<div id="org7509557" class="figure"> <div id="orgfcc57fa" 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>
@ -270,10 +283,91 @@ win = hanning(ceil(1*Fs));
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org98add36" class="outline-2">
<h2 id="org98add36"><span class="section-number-2">5</span> PI Amplifier</h2>
<div class="outline-text-2" id="text-5">
</div>
<div id="outline-container-org68ab283" class="outline-3">
<h3 id="org68ab283"><span class="section-number-3">5.1</span> Comparison of the PSD with Huddle Test</h3>
<div class="outline-text-3" id="text-5-1">
<div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
win = hanning(ceil(1*Fs));
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">[pxx, f] = pwelch(y, win, [], [], Fs);
[pht, ~] = pwelch(ht.y, win, [], [], Fs);
</pre>
</div>
<div id="org5dff36b" class="figure">
<p><img src="figs/apa95ml_5kg_PI_pdf_comp_huddle.png" alt="apa95ml_5kg_PI_pdf_comp_huddle.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Comparison of the ASD for the identification test and the huddle test</p>
</div>
</div>
</div>
<div id="outline-container-orga8db91a" class="outline-3">
<h3 id="orga8db91a"><span class="section-number-3">5.2</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-5-2">
<div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(10/Ts));
[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts);
</pre>
</div>
<div id="org6e49e56" class="figure">
<p><img src="figs/apa95ml_5kg_PI_coh.png" alt="apa95ml_5kg_PI_coh.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Coherence</p>
</div>
<div id="org34f3b6c" class="figure">
<p><img src="figs/apa95ml_5kg_PI_tf.png" alt="apa95ml_5kg_PI_tf.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Estimation of the transfer function from input voltage to displacement</p>
</div>
</div>
</div>
<div id="outline-container-org7272539" class="outline-3">
<h3 id="org7272539"><span class="section-number-3">5.3</span> Comparison with the FEM model</h3>
<div class="outline-text-3" id="text-5-3">
<div class="org-src-container">
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
</pre>
</div>
<div id="orga88c7dc" class="figure">
<p><img src="figs/apa95ml_5kg_pi_comp_fem.png" alt="apa95ml_5kg_pi_comp_fem.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
</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. 13:29</p> <p class="date">Created: 2020-07-23 jeu. 09:33</p>
</div> </div>
</body> </body>
</html> </html>

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@ -235,6 +235,11 @@
[[file:figs/apa95ml_5kg_10V_pdf_comp_huddle.png]] [[file:figs/apa95ml_5kg_10V_pdf_comp_huddle.png]]
** Compute TF estimate and Coherence ** Compute TF estimate and Coherence
#+begin_src matlab
Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
#+end_src
#+begin_src matlab #+begin_src matlab
win = hann(ceil(1/Ts)); win = hann(ceil(1/Ts));
@ -327,3 +332,160 @@
#+caption: Comparison of the identified transfer function and the one estimated from the FE model #+caption: Comparison of the identified transfer function and the one estimated from the FE model
#+RESULTS: #+RESULTS:
[[file:figs/apa95ml_5kg_comp_fem.png]] [[file:figs/apa95ml_5kg_comp_fem.png]]
** Conclusion :ignore:
#+begin_important
The problem comes from the fact that the piezo is driven directly by the DAC that cannot deliver enought current.
In the next section, a current amplifier is used.
#+end_important
* PI Amplifier
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
** Load Data :noexport:
#+begin_src matlab
ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'y');
#+end_src
** Comparison of the PSD with Huddle Test
#+begin_src matlab
Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
win = hanning(ceil(1*Fs));
#+end_src
#+begin_src matlab
[pxx, f] = pwelch(y, win, [], [], Fs);
[pht, ~] = pwelch(ht.y, win, [], [], Fs);
#+end_src
#+begin_src matlab :exports none
figure;
hold on;
plot(f, sqrt(pxx), 'DisplayName', '5kg');
plot(f, sqrt(pht), 'DisplayName', 'Huddle Test');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
legend('location', 'northeast');
xlim([1, Fs/2]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/apa95ml_5kg_PI_pdf_comp_huddle.pdf', 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:apa95ml_5kg_PI_pdf_comp_huddle
#+caption: Comparison of the ASD for the identification test and the huddle test
#+RESULTS:
[[file:figs/apa95ml_5kg_PI_pdf_comp_huddle.png]]
** Compute TF estimate and Coherence
#+begin_src matlab
Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
#+end_src
#+begin_src matlab
win = hann(ceil(10/Ts));
[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts);
#+end_src
#+begin_src matlab :exports none
figure;
hold on;
plot(f, co_est, 'k-')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Coherence'); xlabel('Frequency [Hz]');
hold off;
xlim([10, 5e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/apa95ml_5kg_PI_coh.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:apa95ml_5kg_PI_coh
#+caption: Coherence
#+RESULTS:
[[file:figs/apa95ml_5kg_PI_coh.png]]
#+begin_src matlab :exports none
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(tf_est), 'k-')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
ax2 = subplot(2, 1, 2);
hold on;
plot(f, 180/pi*angle(tf_est), 'k-')
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_PI_tf.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:apa95ml_5kg_PI_tf
#+caption: Estimation of the transfer function from input voltage to displacement
#+RESULTS:
[[file:figs/apa95ml_5kg_PI_tf.png]]
** Comparison with the FEM model
#+begin_src matlab
load('mat/fem_model_5kg.mat', 'Ghm');
#+end_src
#+begin_src matlab :exports none
freqs = logspace(0, 4, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, 1/10*170/1400*abs(tf_est), 'DisplayName', 'Identification')
plot(freqs, abs(squeeze(freqresp(Ghm, freqs, '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(freqs, 180/pi*angle(squeeze(freqresp(Ghm, freqs, 'Hz'))))
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
ylim([-180, 180]);
linkaxes([ax1,ax2], 'x');
xlim([10, 5e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/apa95ml_5kg_pi_comp_fem.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:apa95ml_5kg_pi_comp_fem
#+caption: Comparison of the identified transfer function and the one estimated from the FE model
#+RESULTS:
[[file:figs/apa95ml_5kg_pi_comp_fem.png]]

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