diff --git a/figs/apa95ml_5kg_comp_fem.pdf b/figs/apa95ml_5kg_comp_fem.pdf
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diff --git a/figs/apa95ml_5kg_comp_fem.png b/figs/apa95ml_5kg_comp_fem.png
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diff --git a/index.html b/index.html
index 6ad649f..a8fe6ea 100644
--- a/index.html
+++ b/index.html
@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
-<!-- 2020-07-20 lun. 13:22 -->
+<!-- 2020-07-20 lun. 13:29 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Test Bench APA95ML</title>
<meta name="generator" content="Org mode" />
@@ -15,6 +15,14 @@
<script type="text/javascript" src="./js/bootstrap.min.js"></script>
<script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
<script type="text/javascript" src="./js/readtheorg.js"></script>
+<script>MathJax = {
+ tex: {
+ tags: 'ams',
+ macros: {bm: ["\\boldsymbol{#1}",1],}
+ }
+ };
+ </script>
+ <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head>
<body>
<div id="org-div-home-and-up">
@@ -27,29 +35,30 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
-<li><a href="#org5904e1c">1. Setup</a>
+<li><a href="#orge11c5dc">1. Setup</a>
<ul>
-<li><a href="#org9cb828d">1.1. Parameters</a></li>
-<li><a href="#org55efde3">1.2. Filter White Noise</a></li>
+<li><a href="#org6653e08">1.1. Parameters</a></li>
+<li><a href="#orge01c6e9">1.2. Filter White Noise</a></li>
</ul>
</li>
-<li><a href="#org8af571a">2. Run Experiment and Save Data</a>
+<li><a href="#org26dcd8d">2. Run Experiment and Save Data</a>
<ul>
-<li><a href="#orgc26f768">2.1. Load Data</a></li>
-<li><a href="#org184b70d">2.2. Save Data</a></li>
+<li><a href="#orgc671538">2.1. Load Data</a></li>
+<li><a href="#orge426d6c">2.2. Save Data</a></li>
</ul>
</li>
-<li><a href="#orga844fc8">3. Huddle Test</a>
+<li><a href="#org29fccbc">3. Huddle Test</a>
<ul>
-<li><a href="#org7873825">3.1. Time Domain Data</a></li>
-<li><a href="#org4799d62">3.2. PSD of Measurement Noise</a></li>
+<li><a href="#org1a509f0">3.1. Time Domain Data</a></li>
+<li><a href="#org99da013">3.2. PSD of Measurement Noise</a></li>
</ul>
</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>
-<li><a href="#org1c0e9d1">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="#orgeb52c9a">4.3. Compute TF estimate and Coherence</a></li>
+<li><a href="#orgf861073">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="#orgc82a6e8">4.3. Compute TF estimate and Coherence</a></li>
+<li><a href="#org4b0a791">4.4. Comparison with the FEM model</a></li>
</ul>
</li>
</ul>
@@ -57,26 +66,26 @@
</div>
-<div id="org2e20e62" class="figure">
+<div id="org63ea785" class="figure">
<p><img src="figs/setup_picture.png" alt="setup_picture.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the Setup</p>
</div>
-<div id="org5723466" class="figure">
+<div id="org285264c" class="figure">
<p><img src="figs/setup_zoom.png" alt="setup_zoom.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Zoom on the APA</p>
</div>
-<div id="outline-container-org5904e1c" class="outline-2">
-<h2 id="org5904e1c"><span class="section-number-2">1</span> Setup</h2>
+<div id="outline-container-orge11c5dc" class="outline-2">
+<h2 id="orge11c5dc"><span class="section-number-2">1</span> Setup</h2>
<div class="outline-text-2" id="text-1">
</div>
-<div id="outline-container-org9cb828d" class="outline-3">
-<h3 id="org9cb828d"><span class="section-number-3">1.1</span> Parameters</h3>
+<div id="outline-container-org6653e08" class="outline-3">
+<h3 id="org6653e08"><span class="section-number-3">1.1</span> Parameters</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-matlab">Ts = 1e-4;
@@ -85,8 +94,8 @@
</div>
</div>
-<div id="outline-container-org55efde3" class="outline-3">
-<h3 id="org55efde3"><span class="section-number-3">1.2</span> Filter White Noise</h3>
+<div id="outline-container-orge01c6e9" class="outline-3">
+<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="org-src-container">
<pre class="src src-matlab">Glpf = 1/(1 + s/2/pi/500);
@@ -98,13 +107,13 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div>
</div>
-<div id="outline-container-org8af571a" class="outline-2">
-<h2 id="org8af571a"><span class="section-number-2">2</span> Run Experiment and Save Data</h2>
+<div id="outline-container-org26dcd8d" class="outline-2">
+<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>
-<div id="outline-container-orgc26f768" class="outline-3">
-<h3 id="orgc26f768"><span class="section-number-3">2.1</span> Load Data</h3>
+<div id="outline-container-orgc671538" class="outline-3">
+<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="org-src-container">
<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 id="outline-container-org184b70d" class="outline-3">
-<h3 id="org184b70d"><span class="section-number-3">2.2</span> Save Data</h3>
+<div id="outline-container-orge426d6c" class="outline-3">
+<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="org-src-container">
<pre class="src src-matlab">u = data(:, 1); % Input Voltage [V]
@@ -131,16 +140,16 @@ t = data(:, 3); % Time [s]
</div>
</div>
-<div id="outline-container-orga844fc8" class="outline-2">
-<h2 id="orga844fc8"><span class="section-number-2">3</span> Huddle Test</h2>
+<div id="outline-container-org29fccbc" class="outline-2">
+<h2 id="org29fccbc"><span class="section-number-2">3</span> Huddle Test</h2>
<div class="outline-text-2" id="text-3">
</div>
-<div id="outline-container-org7873825" class="outline-3">
-<h3 id="org7873825"><span class="section-number-3">3.1</span> Time Domain Data</h3>
+<div id="outline-container-org1a509f0" class="outline-3">
+<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 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>
<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 id="outline-container-org4799d62" class="outline-3">
-<h3 id="org4799d62"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3>
+<div id="outline-container-org99da013" class="outline-3">
+<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="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@@ -165,7 +174,7 @@ win = hanning(ceil(1*Fs));
</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>
<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 id="outline-container-orgf667003" class="outline-2">
-<h2 id="orgf667003"><span class="section-number-2">4</span> Transfer Function Estimation with m=5kg</h2>
+<div id="outline-container-orgfa5e8ee" class="outline-2">
+<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>
-<div id="outline-container-org1c0e9d1" class="outline-3">
-<h3 id="org1c0e9d1"><span class="section-number-3">4.1</span> Time Domain Data</h3>
+<div id="outline-container-orgf861073" class="outline-3">
+<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 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>
<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 id="outline-container-org303f615" class="outline-3">
-<h3 id="org303f615"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3>
+<div id="outline-container-org65d8a9f" class="outline-3">
+<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="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
@@ -209,7 +218,7 @@ win = hanning(ceil(1*Fs));
</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>
<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 id="outline-container-orgeb52c9a" class="outline-3">
-<h3 id="orgeb52c9a"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3>
+<div id="outline-container-orgc82a6e8" class="outline-3">
+<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="org-src-container">
<pre class="src src-matlab">win = hann(ceil(1/Ts));
@@ -229,25 +238,42 @@ win = hanning(ceil(1*Fs));
</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>
<p><span class="figure-number">Figure 7: </span>Coherence</p>
</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>
<p><span class="figure-number">Figure 8: </span>Estimation of the transfer function from input voltage to displacement</p>
</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 id="postamble" class="status">
<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>
</body>
</html>
diff --git a/index.org b/index.org
index aa5688a..991c82e 100644
--- a/index.org
+++ b/index.org
@@ -156,7 +156,7 @@
#+RESULTS:
[[file:figs/huddle_test_pdf.png]]
-* Transfer Function Estimation with m=5kg
+* Transfer Function Estimation with $m=5kg$
:PROPERTIES:
:header-args:matlab+: :tangle matlab/tf_estimation.m
:header-args:matlab+: :comments org :mkdirp yes
@@ -290,3 +290,40 @@
#+caption: Estimation of the transfer function from input voltage to displacement
#+RESULTS:
[[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]]
diff --git a/mat/fem_model_5kg.mat b/mat/fem_model_5kg.mat
new file mode 100644
index 0000000..281b5b6
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