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Thomas Dehaeze
2020-11-12 09:30:03 +01:00
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@@ -3,17 +3,17 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-11-12 jeu. 09:18 -->
<!-- 2020-11-12 jeu. 09:29 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Test Bench APA95ML</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Dehaeze Thomas" />
<link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
<link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
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</head>
<body>
<div id="org-div-home-and-up">
@@ -26,42 +26,30 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orge1ce8ff">1. Setup</a>
<li><a href="#org90a334e">1. Huddle Test</a>
<ul>
<li><a href="#org4f8d088">1.1. Parameters</a></li>
<li><a href="#org92bcdf4">1.2. Filter White Noise</a></li>
<li><a href="#org285da21">1.1. Time Domain Data</a></li>
<li><a href="#org5e1c721">1.2. PSD of Measurement Noise</a></li>
</ul>
</li>
<li><a href="#org17a026f">2. Run Experiment and Save Data</a>
<li><a href="#orgd37467e">2. Identification of the dynamics from actuator to displacement</a>
<ul>
<li><a href="#org1b14494">2.1. Load Data</a></li>
<li><a href="#org59026b4">2.2. Save Data</a></li>
<li><a href="#org9434b07">2.1. Load Data</a></li>
<li><a href="#org1eba886">2.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgcfe0cb7">2.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org1cdc3bc">2.4. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#org1758121">3. Huddle Test</a>
<li><a href="#orgcce11f7">3. Identification of the dynamics from actuator to force sensor</a>
<ul>
<li><a href="#org7fcc745">3.1. Time Domain Data</a></li>
<li><a href="#org67ec115">3.2. PSD of Measurement Noise</a></li>
<li><a href="#org48d4bd0">3.1. System Identification</a></li>
<li><a href="#orge58d929">3.2. Integral Force Feedback</a></li>
</ul>
</li>
<li><a href="#org3be6abe">4. Transfer Function Estimation using the PI Amplifier</a>
<li><a href="#orgfe5bc71">4. Integral Force Feedback</a>
<ul>
<li><a href="#orgd263f64">4.1. Load Data</a></li>
<li><a href="#orga450ffc">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgc964fb2">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#orge2ba96a">4.4. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#org1988c0d">5. Transfer function from force actuator to force sensor</a>
<ul>
<li><a href="#org037188e">5.1. System Identification</a></li>
<li><a href="#org0a38226">5.2. Integral Force Feedback</a></li>
</ul>
</li>
<li><a href="#org5df0163">6. IFF Tests</a>
<ul>
<li><a href="#org26f64e8">6.1. First tests with few gains</a></li>
<li><a href="#orgda4dc48">6.2. Second test with many Gains</a></li>
<li><a href="#orgd854491">4.1. First tests with few gains</a></li>
<li><a href="#org899fef5">4.2. Second test with many Gains</a></li>
</ul>
</li>
</ul>
@@ -69,90 +57,31 @@
</div>
<div id="orgf655a68" class="figure">
<div id="org392f56d" 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="org9083f49" class="figure">
<div id="org6970f6d" 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-orge1ce8ff" class="outline-2">
<h2 id="orge1ce8ff"><span class="section-number-2">1</span> Setup</h2>
<div id="outline-container-org90a334e" class="outline-2">
<h2 id="org90a334e"><span class="section-number-2">1</span> Huddle Test</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="orga0e8ba1"></a>
</p>
</div>
<div id="outline-container-org4f8d088" class="outline-3">
<h3 id="org4f8d088"><span class="section-number-3">1.1</span> Parameters</h3>
<div id="outline-container-org285da21" class="outline-3">
<h3 id="org285da21"><span class="section-number-3">1.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
</pre>
</div>
</div>
</div>
<div id="outline-container-org92bcdf4" class="outline-3">
<h3 id="org92bcdf4"><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<span class="org-type">/</span>(1 <span class="org-type">+</span> s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>500);
Gz = c2d(Glpf, Ts, <span class="org-string">'tustin'</span>);
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org17a026f" class="outline-2">
<h2 id="org17a026f"><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-org1b14494" class="outline-3">
<h3 id="org1b14494"><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(<span class="org-string">'data/apa95ml.dat'</span>).data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org59026b4" class="outline-3">
<h3 id="org59026b4"><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(<span class="org-type">:</span>, 1); <span class="org-comment">% Input Voltage [V]</span>
y = data(<span class="org-type">:</span>, 2); <span class="org-comment">% Output Displacement [m]</span>
t = data(<span class="org-type">:</span>, 3); <span class="org-comment">% Time [s]</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">save(<span class="org-string">'./mat/huddle_test.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>, <span class="org-string">'Glpf'</span>);
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org1758121" class="outline-2">
<h2 id="org1758121"><span class="section-number-2">3</span> Huddle Test</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-org7fcc745" class="outline-3">
<h3 id="org7fcc745"><span class="section-number-3">3.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-3-1">
<div id="orge79b739" class="figure">
<div id="orgde9f524" 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>
@@ -160,9 +89,9 @@ t = data(<span class="org-type">:</span>, 3); <span class="org-comment">% Time [
</div>
</div>
<div id="outline-container-org67ec115" class="outline-3">
<h3 id="org67ec115"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3>
<div class="outline-text-3" id="text-3-2">
<div id="outline-container-org5e1c721" class="outline-3">
<h3 id="org5e1c721"><span class="section-number-3">1.2</span> PSD of Measurement Noise</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)<span class="org-type">/</span>(length(t)<span class="org-type">-</span>1);
Fs = 1<span class="org-type">/</span>Ts;
@@ -177,7 +106,7 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
<div id="org8f41c21" class="figure">
<div id="org71c1833" 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>
@@ -186,16 +115,19 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
</div>
<div id="outline-container-org3be6abe" class="outline-2">
<h2 id="org3be6abe"><span class="section-number-2">4</span> Transfer Function Estimation using the PI Amplifier</h2>
<div class="outline-text-2" id="text-4">
<div id="outline-container-orgd37467e" class="outline-2">
<h2 id="orgd37467e"><span class="section-number-2">2</span> Identification of the dynamics from actuator to displacement</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org7bb414b"></a>
</p>
</div>
<div id="outline-container-orgd263f64" class="outline-3">
<h3 id="orgd263f64"><span class="section-number-3">4.1</span> Load Data</h3>
<div class="outline-text-3" id="text-4-1">
<div id="outline-container-org9434b07" class="outline-3">
<h3 id="org9434b07"><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">ht = load(<span class="org-string">'./mat/huddle_test.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>);
load(<span class="org-string">'./mat/apa95ml_5kg_Amp_E505.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'um'</span>, <span class="org-string">'y'</span>);
<pre class="src src-matlab">ht = load(<span class="org-string">'huddle_test.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>);
load(<span class="org-string">'apa95ml_5kg_Amp_E505.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'um'</span>, <span class="org-string">'y'</span>);
</pre>
</div>
@@ -211,9 +143,9 @@ ht.y = ht.y <span class="org-type">-</span> mean(ht.y);
</div>
</div>
<div id="outline-container-orga450ffc" class="outline-3">
<h3 id="orga450ffc"><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 id="outline-container-org1eba886" class="outline-3">
<h3 id="org1eba886"><span class="section-number-3">2.2</span> Comparison of the PSD with Huddle Test</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)<span class="org-type">/</span>(length(t)<span class="org-type">-</span>1);
Fs = 1<span class="org-type">/</span>Ts;
@@ -229,7 +161,7 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
<div id="orge6cd415" class="figure">
<div id="orgd9832c1" 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 5: </span>Comparison of the ASD for the identification test and the huddle test</p>
@@ -237,9 +169,9 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
</div>
<div id="outline-container-orgc964fb2" class="outline-3">
<h3 id="orgc964fb2"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-4-3">
<div id="outline-container-orgcfe0cb7" class="outline-3">
<h3 id="orgcfe0cb7"><span class="section-number-3">2.3</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)<span class="org-type">/</span>(length(t)<span class="org-type">-</span>1);
Fs = 1<span class="org-type">/</span>Ts;
@@ -256,14 +188,14 @@ Fs = 1<span class="org-type">/</span>Ts;
</div>
<div id="orgc5081fd" class="figure">
<div id="orgcd90594" class="figure">
<p><img src="figs/apa95ml_5kg_PI_coh.png" alt="apa95ml_5kg_PI_coh.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Coherence</p>
</div>
<div id="orgef956d1" class="figure">
<div id="org55f5177" class="figure">
<p><img src="figs/apa95ml_5kg_PI_tf.png" alt="apa95ml_5kg_PI_tf.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Estimation of the transfer function from input voltage to displacement</p>
@@ -271,16 +203,16 @@ Fs = 1<span class="org-type">/</span>Ts;
</div>
</div>
<div id="outline-container-orge2ba96a" class="outline-3">
<h3 id="orge2ba96a"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3>
<div class="outline-text-3" id="text-4-4">
<div id="outline-container-org1cdc3bc" class="outline-3">
<h3 id="org1cdc3bc"><span class="section-number-3">2.4</span> Comparison with the FEM model</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'mat/fem_model_5kg.mat'</span>, <span class="org-string">'G'</span>);
<pre class="src src-matlab">load(<span class="org-string">'fem_model_5kg.mat'</span>, <span class="org-string">'G'</span>);
</pre>
</div>
<div id="org5df5018" class="figure">
<div id="org7e7ad3c" 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 8: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
@@ -289,9 +221,12 @@ Fs = 1<span class="org-type">/</span>Ts;
</div>
</div>
<div id="outline-container-org1988c0d" class="outline-2">
<h2 id="org1988c0d"><span class="section-number-2">5</span> Transfer function from force actuator to force sensor</h2>
<div class="outline-text-2" id="text-5">
<div id="outline-container-orgcce11f7" class="outline-2">
<h2 id="orgcce11f7"><span class="section-number-2">3</span> Identification of the dynamics from actuator to force sensor</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org7d9ec69"></a>
</p>
<p>
Two measurements are performed:
</p>
@@ -307,9 +242,9 @@ The obtained dynamics from force actuator to force sensor are compare with the F
The data are loaded:
</p>
<div class="org-src-container">
<pre class="src src-matlab">a_ss = load(<span class="org-string">'mat/apa95ml_5kg_1a_2s.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
aa_s = load(<span class="org-string">'mat/apa95ml_5kg_2a_1s.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
load(<span class="org-string">'mat/G_force_sensor_5kg.mat'</span>, <span class="org-string">'G'</span>);
<pre class="src src-matlab">a_ss = load(<span class="org-string">'apa95ml_5kg_1a_2s.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
aa_s = load(<span class="org-string">'apa95ml_5kg_2a_1s.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
load(<span class="org-string">'G_force_sensor_5kg.mat'</span>, <span class="org-string">'G'</span>);
</pre>
</div>
<p>
@@ -337,7 +272,7 @@ Gfem_a_ss = exp(<span class="org-type">-</span>s<span class="org-type">/</span>1
</pre>
</div>
<p>
The transfer function from input voltage to output voltage are computed and shown in Figure <a href="#orge6ce288">9</a>.
The transfer function from input voltage to output voltage are computed and shown in Figure <a href="#org93e238f">9</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Ts = a_ss.t(end)<span class="org-type">/</span>(length(a_ss.t)<span class="org-type">-</span>1);
@@ -354,16 +289,15 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div>
<div id="orge6ce288" class="figure">
<div id="org93e238f" class="figure">
<p><img src="figs/bode_plot_force_sensor_voltage_comp_fem.png" alt="bode_plot_force_sensor_voltage_comp_fem.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Comparison of the identified dynamics from voltage output to voltage input and the FEM</p>
</div>
</div>
<div id="outline-container-org037188e" class="outline-3">
<h3 id="org037188e"><span class="section-number-3">5.1</span> System Identification</h3>
<div class="outline-text-3" id="text-5-1">
<div id="outline-container-org48d4bd0" class="outline-3">
<h3 id="org48d4bd0"><span class="section-number-3">3.1</span> System Identification</h3>
<div class="outline-text-3" id="text-3-1">
<div class="org-src-container">
<pre class="src src-matlab">w_z = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>111; <span class="org-comment">% Zeros frequency [rad/s]</span>
w_p = 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>255; <span class="org-comment">% Pole frequency [rad/s]</span>
@@ -376,7 +310,7 @@ Gi = G_inf<span class="org-type">*</span>(s<span class="org-type">^</span>2 <spa
</div>
<div id="orged1dc40" class="figure">
<div id="orga3e3e7b" class="figure">
<p><img src="figs/iff_plant_identification_apa95ml.png" alt="iff_plant_identification_apa95ml.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Identification of the IFF plant</p>
@@ -385,11 +319,11 @@ Gi = G_inf<span class="org-type">*</span>(s<span class="org-type">^</span>2 <spa
</div>
<div id="outline-container-org0a38226" class="outline-3">
<h3 id="org0a38226"><span class="section-number-3">5.2</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-5-2">
<div id="outline-container-orge58d929" class="outline-3">
<h3 id="orge58d929"><span class="section-number-3">3.2</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-3-2">
<div id="org86c0c5b" class="figure">
<div id="org55e0695" class="figure">
<p><img src="figs/root_locus_iff_apa95ml_identification.png" alt="root_locus_iff_apa95ml_identification.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Root Locus for IFF</p>
@@ -398,17 +332,20 @@ Gi = G_inf<span class="org-type">*</span>(s<span class="org-type">^</span>2 <spa
</div>
</div>
<div id="outline-container-org5df0163" class="outline-2">
<h2 id="org5df0163"><span class="section-number-2">6</span> IFF Tests</h2>
<div class="outline-text-2" id="text-6">
<div id="outline-container-orgfe5bc71" class="outline-2">
<h2 id="orgfe5bc71"><span class="section-number-2">4</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-4">
<p>
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<h3 id="org26f64e8"><span class="section-number-3">6.1</span> First tests with few gains</h3>
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<h3 id="orgd854491"><span class="section-number-3">4.1</span> First tests with few gains</h3>
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<pre class="src src-matlab">iff_g10 = load(<span class="org-string">'./mat/apa95ml_iff_g10_res.mat'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
iff_g100 = load(<span class="org-string">'./mat/apa95ml_iff_g100_res.mat'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
iff_of = load(<span class="org-string">'./mat/apa95ml_iff_off_res.mat'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
<pre class="src src-matlab">iff_g10 = load(<span class="org-string">'apa95ml_iff_g10_res.mat'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
iff_g100 = load(<span class="org-string">'apa95ml_iff_g100_res.mat'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
iff_of = load(<span class="org-string">'apa95ml_iff_off_res.mat'</span>, <span class="org-string">'u'</span>, <span class="org-string">'t'</span>, <span class="org-string">'y'</span>, <span class="org-string">'v'</span>);
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@@ -428,7 +365,7 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
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<p><img src="figs/iff_first_test_coherence.png" alt="iff_first_test_coherence.png" />
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<p><span class="figure-number">Figure 12: </span>Coherence</p>
@@ -436,7 +373,7 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
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<p><img src="figs/iff_first_test_bode_plot.png" alt="iff_first_test_bode_plot.png" />
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<p><span class="figure-number">Figure 13: </span>Bode plot for different values of IFF gain</p>
@@ -444,11 +381,11 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
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<h3 id="orgda4dc48"><span class="section-number-3">6.2</span> Second test with many Gains</h3>
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<h3 id="org899fef5"><span class="section-number-3">4.2</span> Second test with many Gains</h3>
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<pre class="src src-matlab">load(<span class="org-string">'./mat/apa95ml_iff_test.mat'</span>, <span class="org-string">'results'</span>);
<pre class="src src-matlab">load(<span class="org-string">'apa95ml_iff_test.mat'</span>, <span class="org-string">'results'</span>);
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@@ -474,7 +411,7 @@ g_iff = [0, 1, 5, 10, 50, 100];
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<p><img src="figs/iff_results_bode_plots.png" alt="iff_results_bode_plots.png" />
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@@ -496,13 +433,13 @@ f_end = 500; <span class="org-comment">% [Hz]</span>
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<p><img src="figs/iff_results_bode_plots_identification.png" alt="iff_results_bode_plots_identification.png" />
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<div id="org9a011df" class="figure">
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<p><img src="figs/iff_results_root_locus.png" alt="iff_results_root_locus.png" />
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@@ -512,7 +449,7 @@ f_end = 500; <span class="org-comment">% [Hz]</span>
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-12 jeu. 09:18</p>
<p class="date">Created: 2020-11-12 jeu. 09:29</p>
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