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Thomas Dehaeze 2020-11-03 10:11:21 +01:00
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@ -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>
<!-- 2020-08-21 ven. 15:26 -->
<!-- 2020-11-03 mar. 10:11 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Test Bench APA95ML</title>
<meta name="generator" content="Org mode" />
@ -27,50 +27,50 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org6c2cfcc">1. Setup</a>
<li><a href="#orgdcc1f5c">1. Setup</a>
<ul>
<li><a href="#org9e42c6d">1.1. Parameters</a></li>
<li><a href="#org8bb3ebf">1.2. Filter White Noise</a></li>
<li><a href="#orgf7defdc">1.1. Parameters</a></li>
<li><a href="#org6e2beab">1.2. Filter White Noise</a></li>
</ul>
</li>
<li><a href="#org229c57e">2. Run Experiment and Save Data</a>
<li><a href="#org6fb223c">2. Run Experiment and Save Data</a>
<ul>
<li><a href="#org79522ee">2.1. Load Data</a></li>
<li><a href="#org050454c">2.2. Save Data</a></li>
<li><a href="#orge108931">2.1. Load Data</a></li>
<li><a href="#org4c370ec">2.2. Save Data</a></li>
</ul>
</li>
<li><a href="#org178348e">3. Huddle Test</a>
<li><a href="#org78464fb">3. Huddle Test</a>
<ul>
<li><a href="#org7eb915d">3.1. Time Domain Data</a></li>
<li><a href="#org959048f">3.2. PSD of Measurement Noise</a></li>
<li><a href="#org1d3dde0">3.1. Time Domain Data</a></li>
<li><a href="#org01c740a">3.2. PSD of Measurement Noise</a></li>
</ul>
</li>
<li><a href="#org4742221">4. Transfer Function Estimation using the DAC as the driver</a>
<li><a href="#orgf4b384a">4. Transfer Function Estimation using the DAC as the driver</a>
<ul>
<li><a href="#org3d81de2">4.1. Time Domain Data</a></li>
<li><a href="#org39e0140">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#org8b00bfb">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#orgbf49872">4.4. Comparison with the FEM model</a></li>
<li><a href="#orgc3e175d">4.1. Time Domain Data</a></li>
<li><a href="#orge6e7a4a">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#org4fe238a">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#orgdfa1999">4.4. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#orga133ef0">5. Transfer Function Estimation using the PI Amplifier</a>
<li><a href="#org3a522d2">5. Transfer Function Estimation using the PI Amplifier</a>
<ul>
<li><a href="#orgb86aac7">5.1. Load Data</a></li>
<li><a href="#orgf221216">5.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgeb0ef60">5.3. Compute TF estimate and Coherence</a></li>
<li><a href="#orgc786d54">5.4. Comparison with the FEM model</a></li>
<li><a href="#org37ebc58">5.1. Load Data</a></li>
<li><a href="#org96481d0">5.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#org0d0f5af">5.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org3e6bc68">5.4. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#org7363765">6. Transfer function from force actuator to force sensor</a>
<li><a href="#org97bbea0">6. Transfer function from force actuator to force sensor</a>
<ul>
<li><a href="#org5ad8bf1">6.1. System Identification</a></li>
<li><a href="#orgf1d7d77">6.2. Integral Force Feedback</a></li>
<li><a href="#org89a469b">6.1. System Identification</a></li>
<li><a href="#org5101bab">6.2. Integral Force Feedback</a></li>
</ul>
</li>
<li><a href="#orgabc1447">7. IFF Tests</a>
<li><a href="#orgea75537">7. IFF Tests</a>
<ul>
<li><a href="#org8a1d06a">7.1. First tests with few gains</a></li>
<li><a href="#org1241f3d">7.2. Second test with many Gains</a></li>
<li><a href="#orgd2939f8">7.1. First tests with few gains</a></li>
<li><a href="#org7987703">7.2. Second test with many Gains</a></li>
</ul>
</li>
</ul>
@ -78,90 +78,90 @@
</div>
<div id="org0b2119e" class="figure">
<div id="orgf074020" 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="org0256fb0" class="figure">
<div id="org3fc88d7" 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-org6c2cfcc" class="outline-2">
<h2 id="org6c2cfcc"><span class="section-number-2">1</span> Setup</h2>
<div id="outline-container-orgdcc1f5c" class="outline-2">
<h2 id="orgdcc1f5c"><span class="section-number-2">1</span> Setup</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org9e42c6d" class="outline-3">
<h3 id="org9e42c6d"><span class="section-number-3">1.1</span> Parameters</h3>
<div id="outline-container-orgf7defdc" class="outline-3">
<h3 id="orgf7defdc"><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;
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
</pre>
</div>
</div>
</div>
<div id="outline-container-org8bb3ebf" class="outline-3">
<h3 id="org8bb3ebf"><span class="section-number-3">1.2</span> Filter White Noise</h3>
<div id="outline-container-org6e2beab" class="outline-3">
<h3 id="org6e2beab"><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);
<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, 'tustin');
Gz = c2d(Glpf, Ts, <span class="org-string">'tustin'</span>);
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org229c57e" class="outline-2">
<h2 id="org229c57e"><span class="section-number-2">2</span> Run Experiment and Save Data</h2>
<div id="outline-container-org6fb223c" class="outline-2">
<h2 id="org6fb223c"><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-org79522ee" class="outline-3">
<h3 id="org79522ee"><span class="section-number-3">2.1</span> Load Data</h3>
<div id="outline-container-orge108931" class="outline-3">
<h3 id="orge108931"><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;
<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-org050454c" class="outline-3">
<h3 id="org050454c"><span class="section-number-3">2.2</span> Save Data</h3>
<div id="outline-container-org4c370ec" class="outline-3">
<h3 id="org4c370ec"><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]
y = data(:, 2); % Output Displacement [m]
t = data(:, 3); % Time [s]
<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('./mat/huddle_test.mat', 't', 'u', 'y', 'Glpf');
<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-org178348e" class="outline-2">
<h2 id="org178348e"><span class="section-number-2">3</span> Huddle Test</h2>
<div id="outline-container-org78464fb" class="outline-2">
<h2 id="org78464fb"><span class="section-number-2">3</span> Huddle Test</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-org7eb915d" class="outline-3">
<h3 id="org7eb915d"><span class="section-number-3">3.1</span> Time Domain Data</h3>
<div id="outline-container-org1d3dde0" class="outline-3">
<h3 id="org1d3dde0"><span class="section-number-3">3.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-3-1">
<div id="orgedb79ed" class="figure">
<div id="orgc626b0d" 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>
@ -169,24 +169,24 @@ t = data(:, 3); % Time [s]
</div>
</div>
<div id="outline-container-org959048f" class="outline-3">
<h3 id="org959048f"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3>
<div id="outline-container-org01c740a" class="outline-3">
<h3 id="org01c740a"><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);
Fs = 1/Ts;
<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;
win = hanning(ceil(1*Fs));
win = hanning(ceil(1<span class="org-type">*</span>Fs));
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">[pxx, f] = pwelch(y(1000:end), win, [], [], Fs);
<pre class="src src-matlab">[pxx, f] = pwelch(y(1000<span class="org-type">:</span>end), win, [], [], Fs);
</pre>
</div>
<div id="org4ad69f0" class="figure">
<div id="orgca5cf6e" 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>
@ -195,10 +195,10 @@ win = hanning(ceil(1*Fs));
</div>
</div>
<div id="outline-container-org4742221" class="outline-2">
<h2 id="org4742221"><span class="section-number-2">4</span> Transfer Function Estimation using the DAC as the driver</h2>
<div id="outline-container-orgf4b384a" class="outline-2">
<h2 id="orgf4b384a"><span class="section-number-2">4</span> Transfer Function Estimation using the DAC as the driver</h2>
<div class="outline-text-2" id="text-4">
<div class="important">
<div class="important" id="org6ea9dc1">
<p>
Results presented in this sections are wrong as the ADC cannot deliver enought current to the piezoelectric actuator.
</p>
@ -206,11 +206,11 @@ Results presented in this sections are wrong as the ADC cannot deliver enought c
</div>
</div>
<div id="outline-container-org3d81de2" class="outline-3">
<h3 id="org3d81de2"><span class="section-number-3">4.1</span> Time Domain Data</h3>
<div id="outline-container-orgc3e175d" class="outline-3">
<h3 id="orgc3e175d"><span class="section-number-3">4.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-4-1">
<div id="orgdf6c7aa" class="figure">
<div id="org45e7018" 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>
@ -218,25 +218,25 @@ Results presented in this sections are wrong as the ADC cannot deliver enought c
</div>
</div>
<div id="outline-container-org39e0140" class="outline-3">
<h3 id="org39e0140"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3>
<div id="outline-container-orge6e7a4a" class="outline-3">
<h3 id="orge6e7a4a"><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);
Fs = 1/Ts;
<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;
win = hanning(ceil(1*Fs));
win = hanning(ceil(1<span class="org-type">*</span>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);
[pht, <span class="org-type">~</span>] = pwelch(ht.y, win, [], [], Fs);
</pre>
</div>
<div id="org6c52ffe" class="figure">
<div id="org2f464a0" 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>
@ -244,32 +244,32 @@ win = hanning(ceil(1*Fs));
</div>
</div>
<div id="outline-container-org8b00bfb" class="outline-3">
<h3 id="org8b00bfb"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3>
<div id="outline-container-org4fe238a" class="outline-3">
<h3 id="org4fe238a"><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">Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
<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;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(1/Ts));
<pre class="src src-matlab">win = hann(ceil(1<span class="org-type">/</span>Ts));
[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts);
[tf_est, f] = tfestimate(u, <span class="org-type">-</span>y, win, [], [], 1<span class="org-type">/</span>Ts);
[co_est, <span class="org-type">~</span>] = mscohere( u, <span class="org-type">-</span>y, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
<div id="org8bed71a" class="figure">
<div id="org81de8a0" 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="org80b2e97" class="figure">
<div id="org297b2fb" 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>
@ -277,16 +277,16 @@ Fs = 1/Ts;
</div>
</div>
<div id="outline-container-orgbf49872" class="outline-3">
<h3 id="orgbf49872"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3>
<div id="outline-container-orgdfa1999" class="outline-3">
<h3 id="orgdfa1999"><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 class="src src-matlab">load(<span class="org-string">'mat/fem_model_5kg.mat'</span>, <span class="org-string">'Ghm'</span>);
</pre>
</div>
<div id="orgc255f7f" class="figure">
<div id="org4247213" 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>
@ -295,7 +295,7 @@ Fs = 1/Ts;
</div>
<div class="outline-text-2" id="text-4">
<div class="important">
<div class="important" id="orgf487d60">
<p>
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.
@ -305,50 +305,50 @@ In the next section, a current amplifier is used.
</div>
</div>
<div id="outline-container-orga133ef0" class="outline-2">
<h2 id="orga133ef0"><span class="section-number-2">5</span> Transfer Function Estimation using the PI Amplifier</h2>
<div id="outline-container-org3a522d2" class="outline-2">
<h2 id="org3a522d2"><span class="section-number-2">5</span> Transfer Function Estimation using the PI Amplifier</h2>
<div class="outline-text-2" id="text-5">
</div>
<div id="outline-container-orgb86aac7" class="outline-3">
<h3 id="orgb86aac7"><span class="section-number-3">5.1</span> Load Data</h3>
<div id="outline-container-org37ebc58" class="outline-3">
<h3 id="org37ebc58"><span class="section-number-3">5.1</span> Load Data</h3>
<div class="outline-text-3" id="text-5-1">
<div class="org-src-container">
<pre class="src src-matlab">ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um', 'y');
<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>
</div>
<div class="org-src-container">
<pre class="src src-matlab">u = 10*(u - mean(u)); % Input Voltage of Piezo [V]
um = 10*(um - mean(um)); % Monitor [V]
y = y - mean(y); % Mass displacement [m]
<pre class="src src-matlab">u = 10<span class="org-type">*</span>(u <span class="org-type">-</span> mean(u)); <span class="org-comment">% Input Voltage of Piezo [V]</span>
um = 10<span class="org-type">*</span>(um <span class="org-type">-</span> mean(um)); <span class="org-comment">% Monitor [V]</span>
y = y <span class="org-type">-</span> mean(y); <span class="org-comment">% Mass displacement [m]</span>
ht.u = 10*(ht.u - mean(ht.u));
ht.y = ht.y - mean(ht.y);
ht.u = 10<span class="org-type">*</span>(ht.u <span class="org-type">-</span> mean(ht.u));
ht.y = ht.y <span class="org-type">-</span> mean(ht.y);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf221216" class="outline-3">
<h3 id="orgf221216"><span class="section-number-3">5.2</span> Comparison of the PSD with Huddle Test</h3>
<div id="outline-container-org96481d0" class="outline-3">
<h3 id="org96481d0"><span class="section-number-3">5.2</span> Comparison of the PSD with Huddle Test</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 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;
win = hanning(ceil(1*Fs));
win = hanning(ceil(1<span class="org-type">*</span>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);
[pht, <span class="org-type">~</span>] = pwelch(ht.y, win, [], [], Fs);
</pre>
</div>
<div id="orgc3cf37d" class="figure">
<div id="orgdd13db1" 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>
@ -356,33 +356,33 @@ win = hanning(ceil(1*Fs));
</div>
</div>
<div id="outline-container-orgeb0ef60" class="outline-3">
<h3 id="orgeb0ef60"><span class="section-number-3">5.3</span> Compute TF estimate and Coherence</h3>
<div id="outline-container-org0d0f5af" class="outline-3">
<h3 id="org0d0f5af"><span class="section-number-3">5.3</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-5-3">
<div class="org-src-container">
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
<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;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">win = hann(ceil(1/Ts));
<pre class="src src-matlab">win = hann(ceil(1<span class="org-type">/</span>Ts));
[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
[tf_um , ~] = tfestimate(um, -y, win, [], [], 1/Ts);
[co_est, ~] = mscohere( um, -y, win, [], [], 1/Ts);
[tf_est, f] = tfestimate(u, <span class="org-type">-</span>y, win, [], [], 1<span class="org-type">/</span>Ts);
[tf_um , <span class="org-type">~</span>] = tfestimate(um, <span class="org-type">-</span>y, win, [], [], 1<span class="org-type">/</span>Ts);
[co_est, <span class="org-type">~</span>] = mscohere( um, <span class="org-type">-</span>y, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
<div id="orgbf0faa3" class="figure">
<div id="orga4ba98f" 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="org408425b" class="figure">
<div id="org565db50" 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>
@ -390,16 +390,16 @@ Fs = 1/Ts;
</div>
</div>
<div id="outline-container-orgc786d54" class="outline-3">
<h3 id="orgc786d54"><span class="section-number-3">5.4</span> Comparison with the FEM model</h3>
<div id="outline-container-org3e6bc68" class="outline-3">
<h3 id="org3e6bc68"><span class="section-number-3">5.4</span> Comparison with the FEM model</h3>
<div class="outline-text-3" id="text-5-4">
<div class="org-src-container">
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'G');
<pre class="src src-matlab">load(<span class="org-string">'mat/fem_model_5kg.mat'</span>, <span class="org-string">'G'</span>);
</pre>
</div>
<div id="org5c02e5d" class="figure">
<div id="org9580a6b" 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>
@ -408,8 +408,8 @@ Fs = 1/Ts;
</div>
</div>
<div id="outline-container-org7363765" class="outline-2">
<h2 id="org7363765"><span class="section-number-2">6</span> Transfer function from force actuator to force sensor</h2>
<div id="outline-container-org97bbea0" class="outline-2">
<h2 id="org97bbea0"><span class="section-number-2">6</span> Transfer function from force actuator to force sensor</h2>
<div class="outline-text-2" id="text-6">
<p>
Two measurements are performed:
@ -426,9 +426,9 @@ 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('mat/apa95ml_5kg_1a_2s.mat', 't', 'u', 'y', 'v');
aa_s = load('mat/apa95ml_5kg_2a_1s.mat', 't', 'u', 'y', 'v');
load('mat/G_force_sensor_5kg.mat', 'G');
<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>
</div>
<p>
@ -439,11 +439,11 @@ Let&rsquo;s use the amplifier gain to obtain the true voltage applied to the act
The parameters of the piezoelectric stacks are defined below:
</p>
<div class="org-src-container">
<pre class="src src-matlab">d33 = 3e-10; % Strain constant [m/V]
n = 80; % Number of layers per stack
eT = 1.6e-8; % Permittivity under constant stress [F/m]
sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N]
ka = 235e6; % Stack stiffness [N/m]
<pre class="src src-matlab">d33 = 3e<span class="org-type">-</span>10; <span class="org-comment">% Strain constant [m/V]</span>
n = 80; <span class="org-comment">% Number of layers per stack</span>
eT = 1.6e<span class="org-type">-</span>8; <span class="org-comment">% Permittivity under constant stress [F/m]</span>
sD = 2e<span class="org-type">-</span>11; <span class="org-comment">% Elastic compliance under constant electric displacement [m2/N]</span>
ka = 235e6; <span class="org-comment">% Stack stiffness [N/m]</span>
</pre>
</div>
@ -451,51 +451,51 @@ ka = 235e6; % Stack stiffness [N/m]
From the FEM, we construct the transfer function from DAC voltage to ADC voltage.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Gfem_aa_s = exp(-s/1e4)*20*(2*d33*n*ka)*(G(3,1)+G(3,2))*d33/(eT*sD*n);
Gfem_a_ss = exp(-s/1e4)*20*( d33*n*ka)*(G(3,1)+G(2,1))*d33/(eT*sD*n);
<pre class="src src-matlab">Gfem_aa_s = exp(<span class="org-type">-</span>s<span class="org-type">/</span>1e4)<span class="org-type">*</span>20<span class="org-type">*</span>(2<span class="org-type">*</span>d33<span class="org-type">*</span>n<span class="org-type">*</span>ka)<span class="org-type">*</span>(G(3,1)<span class="org-type">+</span>G(3,2))<span class="org-type">*</span>d33<span class="org-type">/</span>(eT<span class="org-type">*</span>sD<span class="org-type">*</span>n);
Gfem_a_ss = exp(<span class="org-type">-</span>s<span class="org-type">/</span>1e4)<span class="org-type">*</span>20<span class="org-type">*</span>( d33<span class="org-type">*</span>n<span class="org-type">*</span>ka)<span class="org-type">*</span>(G(3,1)<span class="org-type">+</span>G(2,1))<span class="org-type">*</span>d33<span class="org-type">/</span>(eT<span class="org-type">*</span>sD<span class="org-type">*</span>n);
</pre>
</div>
<p>
The transfer function from input voltage to output voltage are computed and shown in Figure <a href="#org819df41">14</a>.
The transfer function from input voltage to output voltage are computed and shown in Figure <a href="#org23238ab">14</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">Ts = a_ss.t(end)/(length(a_ss.t)-1);
Fs = 1/Ts;
<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);
Fs = 1<span class="org-type">/</span>Ts;
win = hann(ceil(10/Ts));
win = hann(ceil(10<span class="org-type">/</span>Ts));
[tf_a_ss, f] = tfestimate(a_ss.u, a_ss.v, win, [], [], 1/Ts);
[coh_a_ss, ~] = mscohere( a_ss.u, a_ss.v, win, [], [], 1/Ts);
[tf_a_ss, f] = tfestimate(a_ss.u, a_ss.v, win, [], [], 1<span class="org-type">/</span>Ts);
[coh_a_ss, <span class="org-type">~</span>] = mscohere( a_ss.u, a_ss.v, win, [], [], 1<span class="org-type">/</span>Ts);
[tf_aa_s, f] = tfestimate(aa_s.u, aa_s.v, win, [], [], 1/Ts);
[coh_aa_s, ~] = mscohere( aa_s.u, aa_s.v, win, [], [], 1/Ts);
[tf_aa_s, f] = tfestimate(aa_s.u, aa_s.v, win, [], [], 1<span class="org-type">/</span>Ts);
[coh_aa_s, <span class="org-type">~</span>] = mscohere( aa_s.u, aa_s.v, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
<div id="org819df41" class="figure">
<div id="org23238ab" 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 14: </span>Comparison of the identified dynamics from voltage output to voltage input and the FEM</p>
</div>
</div>
<div id="outline-container-org5ad8bf1" class="outline-3">
<h3 id="org5ad8bf1"><span class="section-number-3">6.1</span> System Identification</h3>
<div id="outline-container-org89a469b" class="outline-3">
<h3 id="org89a469b"><span class="section-number-3">6.1</span> System Identification</h3>
<div class="outline-text-3" id="text-6-1">
<div class="org-src-container">
<pre class="src src-matlab">w_z = 2*pi*111; % Zeros frequency [rad/s]
w_p = 2*pi*255; % Pole frequency [rad/s]
<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>
xi_z = 0.05;
xi_p = 0.015;
G_inf = 2;
Gi = G_inf*(s^2 - 2*xi_z*w_z*s + w_z^2)/(s^2 + 2*xi_p*w_p*s + w_p^2);
Gi = G_inf<span class="org-type">*</span>(s<span class="org-type">^</span>2 <span class="org-type">-</span> 2<span class="org-type">*</span>xi_z<span class="org-type">*</span>w_z<span class="org-type">*</span>s <span class="org-type">+</span> w_z<span class="org-type">^</span>2)<span class="org-type">/</span>(s<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span class="org-type">*</span>xi_p<span class="org-type">*</span>w_p<span class="org-type">*</span>s <span class="org-type">+</span> w_p<span class="org-type">^</span>2);
</pre>
</div>
<div id="orgc283618" class="figure">
<div id="org506d2b4" class="figure">
<p><img src="figs/iff_plant_identification_apa95ml.png" alt="iff_plant_identification_apa95ml.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Identification of the IFF plant</p>
@ -504,11 +504,11 @@ Gi = G_inf*(s^2 - 2*xi_z*w_z*s + w_z^2)/(s^2 + 2*xi_p*w_p*s + w_p^2);
</div>
<div id="outline-container-orgf1d7d77" class="outline-3">
<h3 id="orgf1d7d77"><span class="section-number-3">6.2</span> Integral Force Feedback</h3>
<div id="outline-container-org5101bab" class="outline-3">
<h3 id="org5101bab"><span class="section-number-3">6.2</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-6-2">
<div id="org6524816" class="figure">
<div id="orga196955" 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 16: </span>Root Locus for IFF</p>
@ -517,37 +517,37 @@ Gi = G_inf*(s^2 - 2*xi_z*w_z*s + w_z^2)/(s^2 + 2*xi_p*w_p*s + w_p^2);
</div>
</div>
<div id="outline-container-orgabc1447" class="outline-2">
<h2 id="orgabc1447"><span class="section-number-2">7</span> IFF Tests</h2>
<div id="outline-container-orgea75537" class="outline-2">
<h2 id="orgea75537"><span class="section-number-2">7</span> IFF Tests</h2>
<div class="outline-text-2" id="text-7">
</div>
<div id="outline-container-org8a1d06a" class="outline-3">
<h3 id="org8a1d06a"><span class="section-number-3">7.1</span> First tests with few gains</h3>
<div id="outline-container-orgd2939f8" class="outline-3">
<h3 id="orgd2939f8"><span class="section-number-3">7.1</span> First tests with few gains</h3>
<div class="outline-text-3" id="text-7-1">
<div class="org-src-container">
<pre class="src src-matlab">iff_g10 = load('./mat/apa95ml_iff_g10_res.mat', 'u', 't', 'y', 'v');
iff_g100 = load('./mat/apa95ml_iff_g100_res.mat', 'u', 't', 'y', 'v');
iff_of = load('./mat/apa95ml_iff_off_res.mat', 'u', 't', 'y', 'v');
<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>
</div>
<div class="org-src-container">
<pre class="src src-matlab">Ts = 1e-4;
win = hann(ceil(10/Ts));
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
win = hann(ceil(10<span class="org-type">/</span>Ts));
[tf_iff_g10, f] = tfestimate(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
[co_iff_g10, ~] = mscohere(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
[tf_iff_g10, f] = tfestimate(iff_g10.u, iff_g10.y, win, [], [], 1<span class="org-type">/</span>Ts);
[co_iff_g10, <span class="org-type">~</span>] = mscohere(iff_g10.u, iff_g10.y, win, [], [], 1<span class="org-type">/</span>Ts);
[tf_iff_g100, f] = tfestimate(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
[co_iff_g100, ~] = mscohere(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
[tf_iff_g100, f] = tfestimate(iff_g100.u, iff_g100.y, win, [], [], 1<span class="org-type">/</span>Ts);
[co_iff_g100, <span class="org-type">~</span>] = mscohere(iff_g100.u, iff_g100.y, win, [], [], 1<span class="org-type">/</span>Ts);
[tf_iff_of, ~] = tfestimate(iff_of.u, iff_of.y, win, [], [], 1/Ts);
[co_iff_of, ~] = mscohere(iff_of.u, iff_of.y, win, [], [], 1/Ts);
[tf_iff_of, <span class="org-type">~</span>] = tfestimate(iff_of.u, iff_of.y, win, [], [], 1<span class="org-type">/</span>Ts);
[co_iff_of, <span class="org-type">~</span>] = mscohere(iff_of.u, iff_of.y, win, [], [], 1<span class="org-type">/</span>Ts);
</pre>
</div>
<div id="orgbc64698" class="figure">
<div id="org6ca73df" class="figure">
<p><img src="figs/iff_first_test_coherence.png" alt="iff_first_test_coherence.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Coherence</p>
@ -555,7 +555,7 @@ win = hann(ceil(10/Ts));
<div id="org16a4139" class="figure">
<div id="orgb430e51" 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 18: </span>Bode plot for different values of IFF gain</p>
@ -563,17 +563,17 @@ win = hann(ceil(10/Ts));
</div>
</div>
<div id="outline-container-org1241f3d" class="outline-3">
<h3 id="org1241f3d"><span class="section-number-3">7.2</span> Second test with many Gains</h3>
<div id="outline-container-org7987703" class="outline-3">
<h3 id="org7987703"><span class="section-number-3">7.2</span> Second test with many Gains</h3>
<div class="outline-text-3" id="text-7-2">
<div class="org-src-container">
<pre class="src src-matlab">load('./mat/apa95ml_iff_test.mat', 'results');
<pre class="src src-matlab">load(<span class="org-string">'./mat/apa95ml_iff_test.mat'</span>, <span class="org-string">'results'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">Ts = 1e-4;
win = hann(ceil(10/Ts));
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4;
win = hann(ceil(10<span class="org-type">/</span>Ts));
</pre>
</div>
@ -582,18 +582,18 @@ win = hann(ceil(10/Ts));
co_iff = {zeros(1, length(results))};
g_iff = [0, 1, 5, 10, 50, 100];
for i=1:length(results)
[tf_est, f] = tfestimate(results{i}.u, results{i}.y, win, [], [], 1/Ts);
[co_est, ~] = mscohere(results{i}.u, results{i}.y, win, [], [], 1/Ts);
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span>=<span class="org-constant">1:length(results)</span>
[tf_est, f] = tfestimate(results{<span class="org-constant">i</span>}.u, results{<span class="org-constant">i</span>}.y, win, [], [], 1<span class="org-type">/</span>Ts);
[co_est, <span class="org-type">~</span>] = mscohere(results{<span class="org-constant">i</span>}.u, results{<span class="org-constant">i</span>}.y, win, [], [], 1<span class="org-type">/</span>Ts);
tf_iff(i) = {tf_est};
co_iff(i) = {co_est};
end
tf_iff(<span class="org-constant">i</span>) = {tf_est};
co_iff(<span class="org-constant">i</span>) = {co_est};
<span class="org-keyword">end</span>
</pre>
</div>
<div id="orgcc7302c" class="figure">
<div id="orgb6055a9" class="figure">
<p><img src="figs/iff_results_bode_plots.png" alt="iff_results_bode_plots.png" />
</p>
</div>
@ -601,27 +601,27 @@ end
<div class="org-src-container">
<pre class="src src-matlab">G_id = {zeros(1,length(results))};
f_start = 70; % [Hz]
f_end = 500; % [Hz]
f_start = 70; <span class="org-comment">% [Hz]</span>
f_end = 500; <span class="org-comment">% [Hz]</span>
for i = 1:length(results)
tf_id = tf_iff{i}(sum(f&lt;f_start):length(f)-sum(f&gt;f_end));
f_id = f(sum(f&lt;f_start):length(f)-sum(f&gt;f_end));
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(results)</span>
tf_id = tf_iff{<span class="org-constant">i</span>}(sum(f<span class="org-type">&lt;</span>f_start)<span class="org-type">:</span>length(f)<span class="org-type">-</span>sum(f<span class="org-type">&gt;</span>f_end));
f_id = f(sum(f<span class="org-type">&lt;</span>f_start)<span class="org-type">:</span>length(f)<span class="org-type">-</span>sum(f<span class="org-type">&gt;</span>f_end));
gfr = idfrd(tf_id, 2*pi*f_id, Ts);
G_id(i) = {procest(gfr,'P2UDZ')};
end
gfr = idfrd(tf_id, 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f_id, Ts);
G_id(<span class="org-constant">i</span>) = {procest(gfr,<span class="org-string">'P2UDZ'</span>)};
<span class="org-keyword">end</span>
</pre>
</div>
<div id="org435aaa6" class="figure">
<div id="orgf5bb2b0" class="figure">
<p><img src="figs/iff_results_bode_plots_identification.png" alt="iff_results_bode_plots_identification.png" />
</p>
</div>
<div id="org9db1293" class="figure">
<div id="org4ef9435" class="figure">
<p><img src="figs/iff_results_root_locus.png" alt="iff_results_root_locus.png" />
</p>
</div>
@ -631,7 +631,7 @@ end
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-08-21 ven. 15:26</p>
<p class="date">Created: 2020-11-03 mar. 10:11</p>
</div>
</body>
</html>

2
index.org
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@ -680,7 +680,7 @@ The transfer function from input voltage to output voltage are computed and show
plot(real(pole(Gi)), imag(pole(Gi)), 'kx');
plot(real(tzero(Gi)), imag(tzero(Gi)), 'ko');
for i = 1:length(gains)
cl_poles = pole(feedback(Gi, (gains(i)/s)));
cl_poles = pole(feedback(Gi, (gains(i)/(s + 2*2*pi)*s/(s + 0.5*2*pi))));
plot(real(cl_poles), imag(cl_poles), 'k.');
end
ylim([0, 1800]);

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