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figs/bode_plot_force_sensor_voltage_comp_fem.pdf
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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>
<!-- 2020-08-20 jeu. 23:08 -->
<!-- 2020-07-24 ven. 15:48 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Test Bench APA95ML</title>
<meta name="generator" content="Org mode" />
@ -27,49 +27,42 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgd70d66f">1. Setup</a>
<li><a href="#orgde2ca90">1. Setup</a>
<ul>
<li><a href="#org07d3c47">1.1. Parameters</a></li>
<li><a href="#orgbd4b8f3">1.2. Filter White Noise</a></li>
<li><a href="#orgc62d598">1.1. Parameters</a></li>
<li><a href="#org128d329">1.2. Filter White Noise</a></li>
</ul>
</li>
<li><a href="#orgebffd67">2. Run Experiment and Save Data</a>
<li><a href="#orga229608">2. Run Experiment and Save Data</a>
<ul>
<li><a href="#org9db9f37">2.1. Load Data</a></li>
<li><a href="#org5b3c786">2.2. Save Data</a></li>
<li><a href="#org117998a">2.1. Load Data</a></li>
<li><a href="#org0aec1ce">2.2. Save Data</a></li>
</ul>
</li>
<li><a href="#orge25b163">3. Huddle Test</a>
<li><a href="#orge436fe5">3. Huddle Test</a>
<ul>
<li><a href="#orgbc09977">3.1. Time Domain Data</a></li>
<li><a href="#org7e6bc47">3.2. PSD of Measurement Noise</a></li>
<li><a href="#orga50e600">3.1. Time Domain Data</a></li>
<li><a href="#org6637acb">3.2. PSD of Measurement Noise</a></li>
</ul>
</li>
<li><a href="#org0348c7c">4. Transfer Function Estimation using the DAC as the driver</a>
<li><a href="#org1e70b14">4. Transfer Function Estimation using the DAC as the driver</a>
<ul>
<li><a href="#orgf0f7314">4.1. Time Domain Data</a></li>
<li><a href="#orge50aef7">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#org870e2ef">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#orgb06d21d">4.4. Comparison with the FEM model</a></li>
<li><a href="#org627cdd4">4.1. Time Domain Data</a></li>
<li><a href="#orgb2e3ad4">4.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgd81c13d">4.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org7b450ca">4.4. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#org563fed9">5. Transfer Function Estimation using the PI Amplifier</a>
<li><a href="#orgf7b3cee">5. Transfer Function Estimation using the PI Amplifier</a>
<ul>
<li><a href="#org9c121df">5.1. Load Data</a></li>
<li><a href="#org990c144">5.2. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#org323b9c5">5.3. Compute TF estimate and Coherence</a></li>
<li><a href="#org6045724">5.4. Comparison with the FEM model</a></li>
<li><a href="#orgd96ab97">5.1. Comparison of the PSD with Huddle Test</a></li>
<li><a href="#orgf49c967">5.2. Compute TF estimate and Coherence</a></li>
<li><a href="#orgeb00ff9">5.3. Comparison with the FEM model</a></li>
</ul>
</li>
<li><a href="#org5ef5f65">6. Transfer function from force actuator to force sensor</a>
<li><a href="#org0baf7a6">6. Transfer function of the PI Amplifier</a>
<ul>
<li><a href="#org098bbb0">6.1. System Identification</a></li>
<li><a href="#orge0e4f46">6.2. Integral Force Feedback</a></li>
</ul>
</li>
<li><a href="#org102cc6a">7. IFF Tests</a>
<ul>
<li><a href="#org9e16daf">7.1. Load Data</a></li>
<li><a href="#org94a6d47">6.1. Compute TF estimate and Coherence</a></li>
</ul>
</li>
</ul>
@ -77,26 +70,26 @@
</div>
<div id="org5c42466" class="figure">
<div id="orgfac2673" 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="orgc98a0fb" class="figure">
<div id="orgd8fb946" 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-orgd70d66f" class="outline-2">
<h2 id="orgd70d66f"><span class="section-number-2">1</span> Setup</h2>
<div id="outline-container-orgde2ca90" class="outline-2">
<h2 id="orgde2ca90"><span class="section-number-2">1</span> Setup</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org07d3c47" class="outline-3">
<h3 id="org07d3c47"><span class="section-number-3">1.1</span> Parameters</h3>
<div id="outline-container-orgc62d598" class="outline-3">
<h3 id="orgc62d598"><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;
@ -105,8 +98,8 @@
</div>
</div>
<div id="outline-container-orgbd4b8f3" class="outline-3">
<h3 id="orgbd4b8f3"><span class="section-number-3">1.2</span> Filter White Noise</h3>
<div id="outline-container-org128d329" class="outline-3">
<h3 id="org128d329"><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);
@ -118,13 +111,13 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div>
</div>
<div id="outline-container-orgebffd67" class="outline-2">
<h2 id="orgebffd67"><span class="section-number-2">2</span> Run Experiment and Save Data</h2>
<div id="outline-container-orga229608" class="outline-2">
<h2 id="orga229608"><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-org9db9f37" class="outline-3">
<h3 id="org9db9f37"><span class="section-number-3">2.1</span> Load Data</h3>
<div id="outline-container-org117998a" class="outline-3">
<h3 id="org117998a"><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;
@ -133,8 +126,8 @@ Gz = c2d(Glpf, Ts, 'tustin');
</div>
</div>
<div id="outline-container-org5b3c786" class="outline-3">
<h3 id="org5b3c786"><span class="section-number-3">2.2</span> Save Data</h3>
<div id="outline-container-org0aec1ce" class="outline-3">
<h3 id="org0aec1ce"><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]
@ -151,16 +144,16 @@ t = data(:, 3); % Time [s]
</div>
</div>
<div id="outline-container-orge25b163" class="outline-2">
<h2 id="orge25b163"><span class="section-number-2">3</span> Huddle Test</h2>
<div id="outline-container-orge436fe5" class="outline-2">
<h2 id="orge436fe5"><span class="section-number-2">3</span> Huddle Test</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-orgbc09977" class="outline-3">
<h3 id="orgbc09977"><span class="section-number-3">3.1</span> Time Domain Data</h3>
<div id="outline-container-orga50e600" class="outline-3">
<h3 id="orga50e600"><span class="section-number-3">3.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-3-1">
<div id="orgfbf5913" class="figure">
<div id="org9f3cece" 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>
@ -168,8 +161,8 @@ t = data(:, 3); % Time [s]
</div>
</div>
<div id="outline-container-org7e6bc47" class="outline-3">
<h3 id="org7e6bc47"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3>
<div id="outline-container-org6637acb" class="outline-3">
<h3 id="org6637acb"><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);
@ -185,7 +178,7 @@ win = hanning(ceil(1*Fs));
</div>
<div id="orgaf72ca6" class="figure">
<div id="org53e3466" 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>
@ -194,22 +187,16 @@ win = hanning(ceil(1*Fs));
</div>
</div>
<div id="outline-container-org0348c7c" class="outline-2">
<h2 id="org0348c7c"><span class="section-number-2">4</span> Transfer Function Estimation using the DAC as the driver</h2>
<div id="outline-container-org1e70b14" class="outline-2">
<h2 id="org1e70b14"><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">
<p>
Results presented in this sections are wrong as the ADC cannot deliver enought current to the piezoelectric actuator.
</p>
</div>
</div>
<div id="outline-container-orgf0f7314" class="outline-3">
<h3 id="orgf0f7314"><span class="section-number-3">4.1</span> Time Domain Data</h3>
<div id="outline-container-org627cdd4" class="outline-3">
<h3 id="org627cdd4"><span class="section-number-3">4.1</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-4-1">
<div id="org60f734d" class="figure">
<div id="orga0b06b8" 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>
@ -217,8 +204,8 @@ Results presented in this sections are wrong as the ADC cannot deliver enought c
</div>
</div>
<div id="outline-container-orge50aef7" class="outline-3">
<h3 id="orge50aef7"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3>
<div id="outline-container-orgb2e3ad4" class="outline-3">
<h3 id="orgb2e3ad4"><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);
@ -235,7 +222,7 @@ win = hanning(ceil(1*Fs));
</div>
<div id="orga45d905" class="figure">
<div id="org8170f8d" 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>
@ -243,8 +230,8 @@ win = hanning(ceil(1*Fs));
</div>
</div>
<div id="outline-container-org870e2ef" class="outline-3">
<h3 id="org870e2ef"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3>
<div id="outline-container-orgd81c13d" class="outline-3">
<h3 id="orgd81c13d"><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);
@ -261,14 +248,14 @@ Fs = 1/Ts;
</div>
<div id="org6abff24" class="figure">
<div id="orgb44ea20" 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="org8e6794a" class="figure">
<div id="org0f7463c" 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>
@ -276,8 +263,8 @@ Fs = 1/Ts;
</div>
</div>
<div id="outline-container-orgb06d21d" class="outline-3">
<h3 id="orgb06d21d"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3>
<div id="outline-container-org7b450ca" class="outline-3">
<h3 id="org7b450ca"><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');
@ -285,7 +272,7 @@ Fs = 1/Ts;
</div>
<div id="org4563de9" class="figure">
<div id="orgbdfdc24" 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>
@ -304,35 +291,14 @@ In the next section, a current amplifier is used.
</div>
</div>
<div id="outline-container-org563fed9" class="outline-2">
<h2 id="org563fed9"><span class="section-number-2">5</span> Transfer Function Estimation using the PI Amplifier</h2>
<div id="outline-container-orgf7b3cee" class="outline-2">
<h2 id="orgf7b3cee"><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-org9c121df" class="outline-3">
<h3 id="org9c121df"><span class="section-number-3">5.1</span> Load Data</h3>
<div id="outline-container-orgd96ab97" class="outline-3">
<h3 id="orgd96ab97"><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">ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um', 'y');
</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]
ht.u = 10*(ht.u - mean(ht.u));
ht.y = ht.y - mean(ht.y);
</pre>
</div>
</div>
</div>
<div id="outline-container-org990c144" class="outline-3">
<h3 id="org990c144"><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;
@ -347,7 +313,7 @@ win = hanning(ceil(1*Fs));
</div>
<div id="orgf6222d7" class="figure">
<div id="orgbc7a9a7" 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>
@ -355,9 +321,9 @@ win = hanning(ceil(1*Fs));
</div>
</div>
<div id="outline-container-org323b9c5" class="outline-3">
<h3 id="org323b9c5"><span class="section-number-3">5.3</span> Compute TF estimate and Coherence</h3>
<div class="outline-text-3" id="text-5-3">
<div id="outline-container-orgf49c967" class="outline-3">
<h3 id="orgf49c967"><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;
@ -374,14 +340,14 @@ Fs = 1/Ts;
</div>
<div id="org751008e" class="figure">
<div id="org883cf4f" 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="orgaed957e" class="figure">
<div id="orgefbbeeb" 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>
@ -389,16 +355,16 @@ Fs = 1/Ts;
</div>
</div>
<div id="outline-container-org6045724" class="outline-3">
<h3 id="org6045724"><span class="section-number-3">5.4</span> Comparison with the FEM model</h3>
<div class="outline-text-3" id="text-5-4">
<div id="outline-container-orgeb00ff9" class="outline-3">
<h3 id="orgeb00ff9"><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', 'G');
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
</pre>
</div>
<div id="org693de8c" class="figure">
<div id="orgfd1fd2d" 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>
@ -406,207 +372,76 @@ Fs = 1/Ts;
</div>
</div>
</div>
<div id="outline-container-org5ef5f65" class="outline-2">
<h2 id="org5ef5f65"><span class="section-number-2">6</span> Transfer function from force actuator to force sensor</h2>
<div id="outline-container-org0baf7a6" class="outline-2">
<h2 id="org0baf7a6"><span class="section-number-2">6</span> Transfer function of the PI Amplifier</h2>
<div class="outline-text-2" id="text-6">
<p>
Two measurements are performed:
</p>
<ul class="org-ul">
<li>Speedgoat DAC =&gt; Voltage Amplifier (x20) =&gt; 1 Piezo Stack =&gt; &#x2026; =&gt; 2 Stacks as Force Sensor (parallel) =&gt; Speedgoat ADC</li>
<li>Speedgoat DAC =&gt; Voltage Amplifier (x20) =&gt; 2 Piezo Stacks (parallel) =&gt; &#x2026; =&gt; 1 Stack as Force Sensor =&gt; Speedgoat ADC</li>
</ul>
<p>
The obtained dynamics from force actuator to force sensor are compare with the FEM model.
</p>
<p>
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>
</div>
<p>
Let&rsquo;s use the amplifier gain to obtain the true voltage applied to the actuator stack(s)
</p>
<p>
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>
</div>
<p>
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>
</div>
<p>
The transfer function from input voltage to output voltage are computed and shown in Figure <a href="#orge80e7b7">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;
win = hann(ceil(10/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_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);
</pre>
</div>
<div id="orge80e7b7" 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-org098bbb0" class="outline-3">
<h3 id="org098bbb0"><span class="section-number-3">6.1</span> System Identification</h3>
<div id="outline-container-org94a6d47" class="outline-3">
<h3 id="org94a6d47"><span class="section-number-3">6.1</span> Compute TF estimate and Coherence</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]
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);
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
</pre>
</div>
<div id="org76af419" class="figure">
<p><img src="figs/iff_plant_identification_apa95ml.png" alt="iff_plant_identification_apa95ml.png" />
<p>
The coherence and the transfer function are estimate from the voltage input of the PI amplifier to its voltage inputs.
</p>
<p><span class="figure-number">Figure 15: </span>Identification of the IFF plant</p>
</div>
</div>
</div>
<div id="outline-container-orge0e4f46" class="outline-3">
<h3 id="orge0e4f46"><span class="section-number-3">6.2</span> Integral Force Feedback</h3>
<div class="outline-text-3" id="text-6-2">
<div id="org114ceb2" class="figure">
<p><img src="figs/root_locus_iff_apa95ml_identification.png" alt="root_locus_iff_apa95ml_identification.png" />
<p>
The coherence is very good as expected (Figure <a href="#org12654c2">14</a>).
</p>
<p><span class="figure-number">Figure 16: </span>Root Locus for IFF</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org102cc6a" class="outline-2">
<h2 id="org102cc6a"><span class="section-number-2">7</span> IFF Tests</h2>
<div class="outline-text-2" id="text-7">
</div>
<div id="outline-container-org9e16daf" class="outline-3">
<h3 id="org9e16daf"><span class="section-number-3">7.1</span> Load Data</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>
</div>
<p>
The transfer function show a low pass filter behavior with a lot of phase drop (Figure <a href="#org23ba982">15</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">Ts = 1e-4;
win = hann(ceil(10/Ts));
<pre class="src src-matlab">win = hann(ceil(10/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_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_of, ~] = tfestimate(iff_of.u, iff_of.y, win, [], [], 1/Ts);
[co_iff_of, ~] = mscohere(iff_of.u, iff_of.y, win, [], [], 1/Ts);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">figure;
hold on;
plot(f, co_iff_of, '-', 'DisplayName', 'g=0')
plot(f, co_iff_g10, '-', 'DisplayName', 'g=10')
plot(f, co_iff_g100, '-', 'DisplayName', 'g=100')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Coherence'); xlabel('Frequency [Hz]');
hold off;
legend();
xlim([60, 600])
[tf_est, f] = tfestimate(u, um, win, [], [], 1/Ts);
[co_est, ~] = mscohere( u, um, win, [], [], 1/Ts);
</pre>
</div>
<div id="org3768cef" class="figure">
<p><img src="figs/iff_first_test_coherence.png" alt="iff_first_test_coherence.png" />
<div id="org12654c2" class="figure">
<p><img src="figs/PI_E505_coh.png" alt="PI_E505_coh.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Coherence</p>
<p><span class="figure-number">Figure 14: </span>Coherence</p>
</div>
<div id="org23ba982" class="figure">
<p><img src="figs/PI_E505_tf.png" alt="PI_E505_tf.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Estimation of the transfer function from input voltage to displacement</p>
</div>
<p>
The delay can be estimated as follow (in ms):
</p>
<div class="org-src-container">
<pre class="src src-matlab">figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(tf_iff_of), '-', 'DisplayName', 'g=0')
plot(f, abs(tf_iff_g10), '-', 'DisplayName', 'g=10')
plot(f, abs(tf_iff_g100), '-', 'DisplayName', 'g=100')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
legend();
ax2 = subplot(2, 1, 2);
hold on;
plot(f, 180/pi*angle(-tf_iff_of), '-')
plot(f, 180/pi*angle(-tf_iff_g10), '-')
plot(f, 180/pi*angle(-tf_iff_g100), '-')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
linkaxes([ax1,ax2], 'x');
xlim([60, 600]);
<pre class="src src-matlab">finddelay(u, um)*(1000*Ts)
</pre>
</div>
<pre class="example">
0.4
</pre>
<div id="orgf1ca4d4" class="figure">
<p><img src="figs/iff_first_test_bode_plot.png" alt="iff_first_test_bode_plot.png" />
<p>
This most probably corresponds to a FIR filter.
</p>
<p><span class="figure-number">Figure 18: </span>Bode plot for different values of IFF gain</p>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-08-20 jeu. 23:08</p>
<p class="date">Created: 2020-07-24 ven. 15:48</p>
</div>
</body>
</html>

294
index.org
View File

@ -166,11 +166,6 @@
:header-args:matlab+: :comments org :mkdirp yes
:END:
** Introduction :ignore:
#+begin_important
Results presented in this sections are wrong as the ADC cannot deliver enought current to the piezoelectric actuator.
#+end_important
** 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>>
@ -358,18 +353,18 @@ In the next section, a current amplifier is used.
<<matlab-init>>
#+end_src
** Load Data
** Load Data :noexport:
#+begin_src matlab
ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um', 'y');
#+end_src
#+begin_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]
u = u - mean(u);
um = um - mean(um);
y = y - mean(y);
ht.u = 10*(ht.u - mean(ht.u));
ht.u = ht.u - mean(ht.u);
ht.y = ht.y - mean(ht.y);
#+end_src
@ -448,7 +443,7 @@ In the next section, a current amplifier is used.
plot(f, abs(tf_est), 'DisplayName', 'Input Voltage')
plot(f, abs(tf_um), 'DisplayName', 'Monitor Voltage')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude [m/V]'); xlabel('Frequency [Hz]');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
legend('location', 'southwest')
@ -477,7 +472,7 @@ In the next section, a current amplifier is used.
** Comparison with the FEM model
#+begin_src matlab
load('mat/fem_model_5kg.mat', 'G');
load('mat/fem_model_5kg.mat', 'Ghm');
#+end_src
#+begin_src matlab :exports none
@ -485,17 +480,17 @@ In the next section, a current amplifier is used.
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(tf_um), 'DisplayName', 'Identification')
plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))), 'DisplayName', 'FEM')
plot(f, 1/10*170/1400*abs(tf_um), 'DisplayName', 'Identification')
plot(freqs, abs(squeeze(freqresp(Ghm, freqs, 'Hz'))), 'DisplayName', 'FEM')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude [m/V]'); xlabel('Frequency [Hz]');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
legend('location', 'northeast')
hold off;
ax2 = subplot(2, 1, 2);
hold on;
plot(f, 180/pi*unwrap(angle(tf_um)))
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G, freqs, 'Hz')))))
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Ghm, freqs, 'Hz')))))
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
@ -514,192 +509,7 @@ In the next section, a current amplifier is used.
#+caption: Comparison of the identified transfer function and the one estimated from the FE model
#+RESULTS:
[[file:figs/apa95ml_5kg_pi_comp_fem.png]]
* Transfer function from force actuator to force sensor
** Introduction :ignore:
Two measurements are performed:
- Speedgoat DAC => Voltage Amplifier (x20) => 1 Piezo Stack => ... => 2 Stacks as Force Sensor (parallel) => Speedgoat ADC
- Speedgoat DAC => Voltage Amplifier (x20) => 2 Piezo Stacks (parallel) => ... => 1 Stack as Force Sensor => Speedgoat ADC
The obtained dynamics from force actuator to force sensor are compare with the FEM model.
** 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 :ignore:
The data are loaded:
#+begin_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');
#+end_src
** Adjust gain :ignore:
Let's use the amplifier gain to obtain the true voltage applied to the actuator stack(s)
The parameters of the piezoelectric stacks are defined below:
#+begin_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]
#+end_src
From the FEM, we construct the transfer function from DAC voltage to ADC voltage.
#+begin_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);
#+end_src
** Compute TF estimate and Coherence :ignore:
The transfer function from input voltage to output voltage are computed and shown in Figure [[fig:bode_plot_force_sensor_voltage_comp_fem]].
#+begin_src matlab
Ts = a_ss.t(end)/(length(a_ss.t)-1);
Fs = 1/Ts;
win = hann(ceil(10/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_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);
#+end_src
#+begin_src matlab :exports none
freqs = logspace(1, 4, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
set(gca,'ColorOrderIndex',1)
plot(f, abs(tf_aa_s), '-')
set(gca,'ColorOrderIndex',1)
plot(freqs, abs(squeeze(freqresp(Gfem_aa_s, freqs, 'Hz'))), '--')
set(gca,'ColorOrderIndex',2)
plot(f, abs(tf_a_ss), '-')
set(gca,'ColorOrderIndex',2)
plot(freqs, abs(squeeze(freqresp(Gfem_a_ss, freqs, 'Hz'))), '--')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
ylim([1e-2, 1e2]);
ax2 = subplot(2, 1, 2);
hold on;
set(gca,'ColorOrderIndex',1)
plot(f, 180/pi*angle(tf_aa_s), '-', 'DisplayName', '2 Act - 1 Sen')
set(gca,'ColorOrderIndex',1)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gfem_aa_s, freqs, 'Hz'))), '--', 'DisplayName', '2 Act - 1 Sen, - FEM')
set(gca,'ColorOrderIndex',2)
plot(f, 180/pi*angle(tf_a_ss), '-', 'DisplayName', '1 Act - 2 Sen')
set(gca,'ColorOrderIndex',2)
plot(freqs, 180/pi*angle(squeeze(freqresp(Gfem_a_ss, freqs, 'Hz'))), '--', 'DisplayName', '1 Act - 2 Sen, - FEM')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
ylim([-180, 180]);
yticks(-180:90:180);
legend('location', 'northeast')
linkaxes([ax1,ax2], 'x');
xlim([10, 5e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/bode_plot_force_sensor_voltage_comp_fem.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:bode_plot_force_sensor_voltage_comp_fem
#+caption: Comparison of the identified dynamics from voltage output to voltage input and the FEM
#+RESULTS:
[[file:figs/bode_plot_force_sensor_voltage_comp_fem.png]]
** System Identification
#+begin_src matlab
w_z = 2*pi*111; % Zeros frequency [rad/s]
w_p = 2*pi*255; % Pole frequency [rad/s]
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);
#+end_src
#+begin_src matlab :exports none
freqs = logspace(1, 4, 1000);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(tf_aa_s), '-')
plot(freqs, abs(squeeze(freqresp(Gi, freqs, 'Hz'))), '--')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
ylim([1e-2, 1e2]);
ax2 = subplot(2, 1, 2);
hold on;
plot(f, 180/pi*angle(tf_aa_s), '-', 'DisplayName', '2 Act - 1 Sen')
plot(freqs, 180/pi*angle(squeeze(freqresp(Gi, freqs, 'Hz'))), '--', 'DisplayName', '2 Act - 1 Sen, - FEM')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
ylim([-180, 180]);
yticks(-180:90:180);
legend('location', 'northeast')
linkaxes([ax1,ax2], 'x');
xlim([10, 5e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/iff_plant_identification_apa95ml.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:iff_plant_identification_apa95ml
#+caption: Identification of the IFF plant
#+RESULTS:
[[file:figs/iff_plant_identification_apa95ml.png]]
** Integral Force Feedback
#+begin_src matlab :exports none
gains = logspace(0, 5, 1000);
figure;
hold on;
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)));
plot(real(cl_poles), imag(cl_poles), 'k.');
end
ylim([0, 1800]);
xlim([-1600,200]);
xlabel('Real Part')
ylabel('Imaginary Part')
axis square
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/root_locus_iff_apa95ml_identification.pdf', 'width', 'wide', 'height', 'tall');
#+end_src
#+name: fig:root_locus_iff_apa95ml_identification
#+caption: Root Locus for IFF
#+RESULTS:
[[file:figs/root_locus_iff_apa95ml_identification.png]]
* IFF Tests
* Transfer function of the 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>>
@ -709,81 +519,87 @@ The transfer function from input voltage to output voltage are computed and show
<<matlab-init>>
#+end_src
** Load Data
** Load Data :noexport:
#+begin_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');
load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um');
#+end_src
** Compute TF estimate and Coherence
#+begin_src matlab
Ts = t(end)/(length(t)-1);
Fs = 1/Ts;
#+end_src
The coherence and the transfer function are estimate from the voltage input of the PI amplifier to its voltage inputs.
The coherence is very good as expected (Figure [[fig:PI_E505_coh]]).
The transfer function show a low pass filter behavior with a lot of phase drop (Figure [[fig:PI_E505_tf]]).
#+begin_src matlab
Ts = 1e-4;
win = hann(ceil(10/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_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_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_est, f] = tfestimate(u, um, win, [], [], 1/Ts);
[co_est, ~] = mscohere( u, um, win, [], [], 1/Ts);
#+end_src
#+begin_src matlab
#+begin_src matlab :exports none
figure;
hold on;
plot(f, co_iff_of, '-', 'DisplayName', 'g=0')
plot(f, co_iff_g10, '-', 'DisplayName', 'g=10')
plot(f, co_iff_g100, '-', 'DisplayName', 'g=100')
plot(f, co_est, 'k-')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Coherence'); xlabel('Frequency [Hz]');
hold off;
legend();
xlim([60, 600])
xlim([10, 5e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/iff_first_test_coherence.pdf', 'width', 'wide', 'height', 'normal');
exportFig('figs/PI_E505_coh.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:iff_first_test_coherence
#+name: fig:PI_E505_coh
#+caption: Coherence
#+RESULTS:
[[file:figs/iff_first_test_coherence.png]]
[[file:figs/PI_E505_coh.png]]
#+begin_src matlab
#+begin_src matlab :exports none
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(tf_iff_of), '-', 'DisplayName', 'g=0')
plot(f, abs(tf_iff_g10), '-', 'DisplayName', 'g=10')
plot(f, abs(tf_iff_g100), '-', 'DisplayName', 'g=100')
plot(f, abs(tf_est), 'k-')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
legend();
ax2 = subplot(2, 1, 2);
hold on;
plot(f, 180/pi*angle(-tf_iff_of), '-')
plot(f, 180/pi*angle(-tf_iff_g10), '-')
plot(f, 180/pi*angle(-tf_iff_g100), '-')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
plot(f, 180/pi*angle(tf_est), 'k-')
set(gca, 'Xscale', 'lin'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
ylim([-180, 180]);
yticks(-180:90:180);
linkaxes([ax1,ax2], 'x');
xlim([60, 600]);
xlim([10, 5e3]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/iff_first_test_bode_plot.pdf', 'width', 'full', 'height', 'full');
exportFig('figs/PI_E505_tf.pdf', 'width', 'full', 'height', 'full');
#+end_src
#+name: fig:iff_first_test_bode_plot
#+caption: Bode plot for different values of IFF gain
#+name: fig:PI_E505_tf
#+caption: Estimation of the transfer function from input voltage to displacement
#+RESULTS:
[[file:figs/iff_first_test_bode_plot.png]]
[[file:figs/PI_E505_tf.png]]
The delay can be estimated as follow (in ms):
#+begin_src matlab :results replace value
finddelay(u, um)*(1000*Ts)
#+end_src
#+RESULTS:
: 0.4
This most probably corresponds to a FIR filter.