448 lines
14 KiB
HTML
448 lines
14 KiB
HTML
<?xml version="1.0" encoding="utf-8"?>
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<!-- 2020-07-24 ven. 15:48 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Test Bench APA95ML</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Test Bench APA95ML</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgde2ca90">1. Setup</a>
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<ul>
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<li><a href="#orgc62d598">1.1. Parameters</a></li>
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<li><a href="#org128d329">1.2. Filter White Noise</a></li>
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</ul>
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</li>
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<li><a href="#orga229608">2. Run Experiment and Save Data</a>
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<ul>
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<li><a href="#org117998a">2.1. Load Data</a></li>
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<li><a href="#org0aec1ce">2.2. Save Data</a></li>
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</ul>
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</li>
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<li><a href="#orge436fe5">3. Huddle Test</a>
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<ul>
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<li><a href="#orga50e600">3.1. Time Domain Data</a></li>
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<li><a href="#org6637acb">3.2. PSD of Measurement Noise</a></li>
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</ul>
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</li>
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<li><a href="#org1e70b14">4. Transfer Function Estimation using the DAC as the driver</a>
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<ul>
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<li><a href="#org627cdd4">4.1. Time Domain Data</a></li>
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<li><a href="#orgb2e3ad4">4.2. Comparison of the PSD with Huddle Test</a></li>
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<li><a href="#orgd81c13d">4.3. Compute TF estimate and Coherence</a></li>
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<li><a href="#org7b450ca">4.4. Comparison with the FEM model</a></li>
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</ul>
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</li>
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<li><a href="#orgf7b3cee">5. Transfer Function Estimation using the PI Amplifier</a>
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<ul>
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<li><a href="#orgd96ab97">5.1. Comparison of the PSD with Huddle Test</a></li>
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<li><a href="#orgf49c967">5.2. Compute TF estimate and Coherence</a></li>
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<li><a href="#orgeb00ff9">5.3. Comparison with the FEM model</a></li>
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</ul>
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</li>
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<li><a href="#org0baf7a6">6. Transfer function of the PI Amplifier</a>
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<ul>
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<li><a href="#org94a6d47">6.1. Compute TF estimate and Coherence</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="orgfac2673" class="figure">
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<p><img src="figs/setup_picture.png" alt="setup_picture.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the Setup</p>
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</div>
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<div id="orgd8fb946" class="figure">
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<p><img src="figs/setup_zoom.png" alt="setup_zoom.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Zoom on the APA</p>
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</div>
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<div id="outline-container-orgde2ca90" class="outline-2">
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<h2 id="orgde2ca90"><span class="section-number-2">1</span> Setup</h2>
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<div class="outline-text-2" id="text-1">
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</div>
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<div id="outline-container-orgc62d598" class="outline-3">
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<h3 id="orgc62d598"><span class="section-number-3">1.1</span> Parameters</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = 1e-4;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org128d329" class="outline-3">
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<h3 id="org128d329"><span class="section-number-3">1.2</span> Filter White Noise</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="org-src-container">
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<pre class="src src-matlab">Glpf = 1/(1 + s/2/pi/500);
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Gz = c2d(Glpf, Ts, 'tustin');
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</pre>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-orga229608" class="outline-2">
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<h2 id="orga229608"><span class="section-number-2">2</span> Run Experiment and Save Data</h2>
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<div class="outline-text-2" id="text-2">
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</div>
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<div id="outline-container-org117998a" class="outline-3">
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<h3 id="org117998a"><span class="section-number-3">2.1</span> Load Data</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab">data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org0aec1ce" class="outline-3">
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<h3 id="org0aec1ce"><span class="section-number-3">2.2</span> Save Data</h3>
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<div class="outline-text-3" id="text-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab">u = data(:, 1); % Input Voltage [V]
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y = data(:, 2); % Output Displacement [m]
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t = data(:, 3); % Time [s]
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">save('./mat/huddle_test.mat', 't', 'u', 'y', 'Glpf');
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</pre>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-orge436fe5" class="outline-2">
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<h2 id="orge436fe5"><span class="section-number-2">3</span> Huddle Test</h2>
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<div class="outline-text-2" id="text-3">
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</div>
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<div id="outline-container-orga50e600" class="outline-3">
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<h3 id="orga50e600"><span class="section-number-3">3.1</span> Time Domain Data</h3>
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<div class="outline-text-3" id="text-3-1">
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<div id="org9f3cece" class="figure">
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<p><img src="figs/huddle_test_time_domain.png" alt="huddle_test_time_domain.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Measurement of the Mass displacement during Huddle Test</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org6637acb" class="outline-3">
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<h3 id="org6637acb"><span class="section-number-3">3.2</span> PSD of Measurement Noise</h3>
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<div class="outline-text-3" id="text-3-2">
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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win = hanning(ceil(1*Fs));
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">[pxx, f] = pwelch(y(1000:end), win, [], [], Fs);
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</pre>
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</div>
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<div id="org53e3466" class="figure">
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<p><img src="figs/huddle_test_pdf.png" alt="huddle_test_pdf.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the Displacement during Huddle Test</p>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org1e70b14" class="outline-2">
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<h2 id="org1e70b14"><span class="section-number-2">4</span> Transfer Function Estimation using the DAC as the driver</h2>
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<div class="outline-text-2" id="text-4">
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</div>
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<div id="outline-container-org627cdd4" class="outline-3">
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<h3 id="org627cdd4"><span class="section-number-3">4.1</span> Time Domain Data</h3>
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<div class="outline-text-3" id="text-4-1">
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<div id="orga0b06b8" class="figure">
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<p><img src="figs/apa95ml_5kg_10V_time_domain.png" alt="apa95ml_5kg_10V_time_domain.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Time domain signals during the test</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgb2e3ad4" class="outline-3">
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<h3 id="orgb2e3ad4"><span class="section-number-3">4.2</span> Comparison of the PSD with Huddle Test</h3>
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<div class="outline-text-3" id="text-4-2">
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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win = hanning(ceil(1*Fs));
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">[pxx, f] = pwelch(y, win, [], [], Fs);
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[pht, ~] = pwelch(ht.y, win, [], [], Fs);
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</pre>
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</div>
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<div id="org8170f8d" class="figure">
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<p><img src="figs/apa95ml_5kg_10V_pdf_comp_huddle.png" alt="apa95ml_5kg_10V_pdf_comp_huddle.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Comparison of the ASD for the identification test and the huddle test</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgd81c13d" class="outline-3">
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<h3 id="orgd81c13d"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3>
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<div class="outline-text-3" id="text-4-3">
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">win = hann(ceil(1/Ts));
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[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
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[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="orgb44ea20" class="figure">
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<p><img src="figs/apa95ml_5kg_10V_coh.png" alt="apa95ml_5kg_10V_coh.png" />
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</p>
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<p><span class="figure-number">Figure 7: </span>Coherence</p>
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</div>
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<div id="org0f7463c" class="figure">
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<p><img src="figs/apa95ml_5kg_10V_tf.png" alt="apa95ml_5kg_10V_tf.png" />
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</p>
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<p><span class="figure-number">Figure 8: </span>Estimation of the transfer function from input voltage to displacement</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org7b450ca" class="outline-3">
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<h3 id="org7b450ca"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3>
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<div class="outline-text-3" id="text-4-4">
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<div class="org-src-container">
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<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
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</pre>
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</div>
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<div id="orgbdfdc24" class="figure">
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<p><img src="figs/apa95ml_5kg_comp_fem.png" alt="apa95ml_5kg_comp_fem.png" />
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</p>
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<p><span class="figure-number">Figure 9: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
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</div>
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</div>
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</div>
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<div class="outline-text-2" id="text-4">
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<div class="important">
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<p>
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The problem comes from the fact that the piezo is driven directly by the DAC that cannot deliver enought current.
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In the next section, a current amplifier is used.
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</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgf7b3cee" class="outline-2">
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<h2 id="orgf7b3cee"><span class="section-number-2">5</span> Transfer Function Estimation using the PI Amplifier</h2>
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<div class="outline-text-2" id="text-5">
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</div>
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<div id="outline-container-orgd96ab97" class="outline-3">
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<h3 id="orgd96ab97"><span class="section-number-3">5.1</span> Comparison of the PSD with Huddle Test</h3>
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<div class="outline-text-3" id="text-5-1">
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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win = hanning(ceil(1*Fs));
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">[pxx, f] = pwelch(y, win, [], [], Fs);
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[pht, ~] = pwelch(ht.y, win, [], [], Fs);
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</pre>
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</div>
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<div id="orgbc7a9a7" class="figure">
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<p><img src="figs/apa95ml_5kg_PI_pdf_comp_huddle.png" alt="apa95ml_5kg_PI_pdf_comp_huddle.png" />
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</p>
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<p><span class="figure-number">Figure 10: </span>Comparison of the ASD for the identification test and the huddle test</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgf49c967" class="outline-3">
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<h3 id="orgf49c967"><span class="section-number-3">5.2</span> Compute TF estimate and Coherence</h3>
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<div class="outline-text-3" id="text-5-2">
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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</pre>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">win = hann(ceil(1/Ts));
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[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
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[tf_um , ~] = tfestimate(um, -y, win, [], [], 1/Ts);
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[co_est, ~] = mscohere( um, -y, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="org883cf4f" class="figure">
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<p><img src="figs/apa95ml_5kg_PI_coh.png" alt="apa95ml_5kg_PI_coh.png" />
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</p>
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<p><span class="figure-number">Figure 11: </span>Coherence</p>
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</div>
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<div id="orgefbbeeb" class="figure">
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<p><img src="figs/apa95ml_5kg_PI_tf.png" alt="apa95ml_5kg_PI_tf.png" />
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</p>
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<p><span class="figure-number">Figure 12: </span>Estimation of the transfer function from input voltage to displacement</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgeb00ff9" class="outline-3">
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<h3 id="orgeb00ff9"><span class="section-number-3">5.3</span> Comparison with the FEM model</h3>
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<div class="outline-text-3" id="text-5-3">
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<div class="org-src-container">
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<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
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</pre>
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</div>
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<div id="orgfd1fd2d" class="figure">
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<p><img src="figs/apa95ml_5kg_pi_comp_fem.png" alt="apa95ml_5kg_pi_comp_fem.png" />
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</p>
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<p><span class="figure-number">Figure 13: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-org0baf7a6" class="outline-2">
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<h2 id="org0baf7a6"><span class="section-number-2">6</span> Transfer function of the PI Amplifier</h2>
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<div class="outline-text-2" id="text-6">
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</div>
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<div id="outline-container-org94a6d47" class="outline-3">
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<h3 id="org94a6d47"><span class="section-number-3">6.1</span> Compute TF estimate and Coherence</h3>
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<div class="outline-text-3" id="text-6-1">
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<div class="org-src-container">
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<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
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Fs = 1/Ts;
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</pre>
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</div>
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<p>
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The coherence and the transfer function are estimate from the voltage input of the PI amplifier to its voltage inputs.
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</p>
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<p>
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The coherence is very good as expected (Figure <a href="#org12654c2">14</a>).
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</p>
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<p>
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The transfer function show a low pass filter behavior with a lot of phase drop (Figure <a href="#org23ba982">15</a>).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">win = hann(ceil(10/Ts));
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[tf_est, f] = tfestimate(u, um, win, [], [], 1/Ts);
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[co_est, ~] = mscohere( u, um, win, [], [], 1/Ts);
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</pre>
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</div>
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<div id="org12654c2" class="figure">
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<p><img src="figs/PI_E505_coh.png" alt="PI_E505_coh.png" />
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</p>
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<p><span class="figure-number">Figure 14: </span>Coherence</p>
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</div>
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<div id="org23ba982" class="figure">
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<p><img src="figs/PI_E505_tf.png" alt="PI_E505_tf.png" />
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</p>
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<p><span class="figure-number">Figure 15: </span>Estimation of the transfer function from input voltage to displacement</p>
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</div>
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<p>
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The delay can be estimated as follow (in ms):
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">finddelay(u, um)*(1000*Ts)
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</pre>
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</div>
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<pre class="example">
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0.4
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</pre>
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<p>
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This most probably corresponds to a FIR filter.
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</p>
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</div>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-07-24 ven. 15:48</p>
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</div>
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</body>
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</html>
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