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<title>Test Bench APA95ML</title>
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@ -26,30 +22,30 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org90a334e">1. Huddle Test</a>
<li><a href="#orgad16569">1. Huddle Test</a>
<ul>
<li><a href="#org285da21">1.1. Time Domain Data</a></li>
<li><a href="#org5e1c721">1.2. PSD of Measurement Noise</a></li>
<li><a href="#orgb19f340">1.1. Time Domain Data</a></li>
<li><a href="#org2899ef6">1.2. PSD of Measurement Noise</a></li>
</ul>
</li>
<li><a href="#orgd37467e">2. Identification of the dynamics from actuator to displacement</a>
<li><a href="#org3e5f64b">2. Identification of the dynamics from actuator to displacement</a>
<ul>
<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>
<li><a href="#org31a2faa">2.1. Load Data</a></li>
<li><a href="#org11eaa6a">2.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#org341d0d1">2.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org74d8741">2.4. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#orgcce11f7">3. Identification of the dynamics from actuator to force sensor</a>
<li><a href="#orgd1c03bf">3. Identification of the dynamics from actuator to force sensor</a>
<ul>
<li><a href="#org48d4bd0">3.1. System Identification</a></li>
<li><a href="#orge58d929">3.2. Integral Force Feedback</a></li>
<li><a href="#org7a3c2eb">3.1. System Identification</a></li>
<li><a href="#org9b871e7">3.2. Integral Force Feedback</a></li>
</ul>
</li>
<li><a href="#orgfe5bc71">4. Integral Force Feedback</a>
<li><a href="#orgfc2a4ed">4. Integral Force Feedback</a>
<ul>
<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>
<li><a href="#orgd017d15">4.1. First tests with few gains</a></li>
<li><a href="#org863493b">4.2. Second test with many Gains</a></li>
</ul>
</li>
</ul>
@ -57,31 +53,31 @@
</div>
<div id="org392f56d" class="figure">
<div id="orgc83aff0" 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="org6970f6d" class="figure">
<div id="orgc088b40" 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-org90a334e" class="outline-2">
<h2 id="org90a334e"><span class="section-number-2">1</span> Huddle Test</h2>
<div id="outline-container-orgad16569" class="outline-2">
<h2 id="orgad16569"><span class="section-number-2">1</span> Huddle Test</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="orga0e8ba1"></a>
<a id="org323bc97"></a>
</p>
</div>
<div id="outline-container-org285da21" class="outline-3">
<h3 id="org285da21"><span class="section-number-3">1.1</span> Time Domain Data</h3>
<div id="outline-container-orgb19f340" class="outline-3">
<h3 id="orgb19f340"><span class="section-number-3">1.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-1-1">
<div id="orgde9f524" class="figure">
<div id="orgb70cce7" 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>
@ -89,8 +85,8 @@
</div>
</div>
<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 id="outline-container-org2899ef6" class="outline-3">
<h3 id="org2899ef6"><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);
@ -106,7 +102,7 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
<div id="org71c1833" class="figure">
<div id="orgf47fe49" 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>
@ -115,15 +111,15 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
</div>
<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 id="outline-container-org3e5f64b" class="outline-2">
<h2 id="org3e5f64b"><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>
<a id="org71bfc39"></a>
</p>
</div>
<div id="outline-container-org9434b07" class="outline-3">
<h3 id="org9434b07"><span class="section-number-3">2.1</span> Load Data</h3>
<div id="outline-container-org31a2faa" class="outline-3">
<h3 id="org31a2faa"><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">'huddle_test.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'u'</span>, <span class="org-string">'y'</span>);
@ -143,8 +139,8 @@ ht.y = ht.y <span class="org-type">-</span> mean(ht.y);
</div>
</div>
<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 id="outline-container-org11eaa6a" class="outline-3">
<h3 id="org11eaa6a"><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);
@ -161,7 +157,7 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
<div id="orgd9832c1" class="figure">
<div id="org5cce219" 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>
@ -169,8 +165,8 @@ win = hanning(ceil(1<span class="org-type">*</span>Fs));
</div>
</div>
<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 id="outline-container-org341d0d1" class="outline-3">
<h3 id="org341d0d1"><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);
@ -188,14 +184,14 @@ Fs = 1<span class="org-type">/</span>Ts;
</div>
<div id="orgcd90594" class="figure">
<div id="orgdf9fef1" 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="org55f5177" class="figure">
<div id="org683c6bc" 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>
@ -203,8 +199,8 @@ Fs = 1<span class="org-type">/</span>Ts;
</div>
</div>
<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 id="outline-container-org74d8741" class="outline-3">
<h3 id="org74d8741"><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">'fem_model_5kg.mat'</span>, <span class="org-string">'G'</span>);
@ -212,7 +208,7 @@ Fs = 1<span class="org-type">/</span>Ts;
</div>
<div id="org7e7ad3c" class="figure">
<div id="org11f0001" 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>
@ -221,11 +217,11 @@ Fs = 1<span class="org-type">/</span>Ts;
</div>
</div>
<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 id="outline-container-orgd1c03bf" class="outline-2">
<h2 id="orgd1c03bf"><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>
<a id="orge7252db"></a>
</p>
<p>
Two measurements are performed:
@ -272,7 +268,7 @@ 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="#org93e238f">9</a>.
The transfer function from input voltage to output voltage are computed and shown in Figure <a href="#org044fb48">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);
@ -289,14 +285,14 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div>
<div id="org93e238f" class="figure">
<div id="org044fb48" 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-org48d4bd0" class="outline-3">
<h3 id="org48d4bd0"><span class="section-number-3">3.1</span> System Identification</h3>
<div id="outline-container-org7a3c2eb" class="outline-3">
<h3 id="org7a3c2eb"><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>
@ -310,7 +306,7 @@ Gi = G_inf<span class="org-type">*</span>(s<span class="org-type">^</span>2 <spa
</div>
<div id="orga3e3e7b" class="figure">
<div id="org2c26a21" 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>
@ -319,11 +315,11 @@ Gi = G_inf<span class="org-type">*</span>(s<span class="org-type">^</span>2 <spa
</div>
<div id="outline-container-orge58d929" class="outline-3">
<h3 id="orge58d929"><span class="section-number-3">3.2</span> Integral Force Feedback</h3>
<div id="outline-container-org9b871e7" class="outline-3">
<h3 id="org9b871e7"><span class="section-number-3">3.2</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-3-2">
<div id="org55e0695" class="figure">
<div id="orgf1840c0" 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>
@ -332,15 +328,15 @@ Gi = G_inf<span class="org-type">*</span>(s<span class="org-type">^</span>2 <spa
</div>
</div>
<div id="outline-container-orgfe5bc71" class="outline-2">
<h2 id="orgfe5bc71"><span class="section-number-2">4</span> Integral Force Feedback</h2>
<div id="outline-container-orgfc2a4ed" class="outline-2">
<h2 id="orgfc2a4ed"><span class="section-number-2">4</span> Integral Force Feedback</h2>
<div class="outline-text-2" id="text-4">
<p>
<a id="org9e016b1"></a>
<a id="org4a62205"></a>
</p>
</div>
<div id="outline-container-orgd854491" class="outline-3">
<h3 id="orgd854491"><span class="section-number-3">4.1</span> First tests with few gains</h3>
<div id="outline-container-orgd017d15" class="outline-3">
<h3 id="orgd017d15"><span class="section-number-3">4.1</span> First tests with few gains</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<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>);
@ -365,7 +361,7 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div>
<div id="org2c6892b" class="figure">
<div id="orge3b0697" class="figure">
<p><img src="figs/iff_first_test_coherence.png" alt="iff_first_test_coherence.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Coherence</p>
@ -373,7 +369,7 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
<div id="org91fa41a" class="figure">
<div id="orgd0ae2ae" class="figure">
<p><img src="figs/iff_first_test_bode_plot.png" alt="iff_first_test_bode_plot.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Bode plot for different values of IFF gain</p>
@ -381,8 +377,8 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div>
</div>
<div id="outline-container-org899fef5" class="outline-3">
<h3 id="org899fef5"><span class="section-number-3">4.2</span> Second test with many Gains</h3>
<div id="outline-container-org863493b" class="outline-3">
<h3 id="org863493b"><span class="section-number-3">4.2</span> Second test with many Gains</h3>
<div class="outline-text-3" id="text-4-2">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'apa95ml_iff_test.mat'</span>, <span class="org-string">'results'</span>);
@ -411,7 +407,7 @@ g_iff = [0, 1, 5, 10, 50, 100];
</div>
<div id="orgcf10be1" class="figure">
<div id="org3935454" class="figure">
<p><img src="figs/iff_results_bode_plots.png" alt="iff_results_bode_plots.png" />
</p>
</div>
@ -433,13 +429,13 @@ f_end = 500; <span class="org-comment">% [Hz]</span>
</div>
<div id="orgda781ba" class="figure">
<div id="org549cbcc" class="figure">
<p><img src="figs/iff_results_bode_plots_identification.png" alt="iff_results_bode_plots_identification.png" />
</p>
</div>
<div id="org473937a" class="figure">
<div id="orga00988a" class="figure">
<p><img src="figs/iff_results_root_locus.png" alt="iff_results_root_locus.png" />
</p>
</div>
@ -449,7 +445,7 @@ f_end = 500; <span class="org-comment">% [Hz]</span>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-12 jeu. 09:29</p>
<p class="date">Created: 2020-11-12 jeu. 09:50</p>
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