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2020-07-17 11:56:08 +02:00
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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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2020-07-20 12:55:13 +02:00
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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="#org2723d81">1. Setup</a>
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<ul>
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<li><a href="#orgfd55c36">1.1. Parameters</a></li>
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<li><a href="#org292fe55">1.2. Filter White Noise</a></li>
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</ul>
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</li>
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<li><a href="#orge27b441">2. Run Experiment and Save Data</a>
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<ul>
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<li><a href="#orgba39bc1">2.1. Load Data</a></li>
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<li><a href="#orga7db326">2.2. Save Data</a></li>
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</ul>
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</li>
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<li><a href="#orgca23311">3. Huddle Test</a>
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<ul>
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<li><a href="#org28c4ff9">3.1. Time Domain Data</a></li>
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<li><a href="#org61d66e9">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="#orgd62d5d5">4. Transfer Function Estimation with \(m=5kg\)</a>
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<ul>
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<li><a href="#orgd195c16">4.1. Time Domain Data</a></li>
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<li><a href="#org008a2d9">4.2. Comparison of the PSD with Huddle Test</a></li>
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<li><a href="#orgb223df5">4.3. Compute TF estimate and Coherence</a></li>
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<li><a href="#orgf0b54fc">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="#org189b278">5. Transfer function of the PI Amplifier</a>
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<ul>
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<li><a href="#org970db83">5.1. Compute TF estimate and Coherence</a></li>
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</ul>
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</li>
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<li><a href="#orgea1748b">6. PI Amplifier</a>
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<ul>
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<li><a href="#org53f7284">6.1. Comparison of the PSD with Huddle Test</a></li>
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<li><a href="#org9081582">6.2. Compute TF estimate and Coherence</a></li>
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<li><a href="#org52ebb83">6.3. Comparison with the FEM model</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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2020-07-20 13:17:34 +02:00
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<div id="org059b319" 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="org64743ab" 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-org2723d81" class="outline-2">
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<h2 id="org2723d81"><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-orgfd55c36" class="outline-3">
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<h3 id="orgfd55c36"><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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2020-07-24 13:06:02 +02:00
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<div id="outline-container-org292fe55" class="outline-3">
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<h3 id="org292fe55"><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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2020-07-24 13:06:02 +02:00
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<div id="outline-container-orge27b441" class="outline-2">
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<h2 id="orge27b441"><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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2020-07-24 13:06:02 +02:00
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<div id="outline-container-orgba39bc1" class="outline-3">
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<h3 id="orgba39bc1"><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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2020-07-24 13:06:02 +02:00
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<div id="outline-container-orga7db326" class="outline-3">
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<h3 id="orga7db326"><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-orgca23311" class="outline-2">
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<h2 id="orgca23311"><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-org28c4ff9" class="outline-3">
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<h3 id="org28c4ff9"><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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2020-07-24 13:06:02 +02:00
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<div id="org8b0837a" 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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2020-07-24 13:06:02 +02:00
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<div id="outline-container-org61d66e9" class="outline-3">
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<h3 id="org61d66e9"><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, win, [], [], Fs);
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</pre>
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</div>
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<div id="orge35cf94" 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-orgd62d5d5" class="outline-2">
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<h2 id="orgd62d5d5"><span class="section-number-2">4</span> Transfer Function Estimation with \(m=5kg\)</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-orgd195c16" class="outline-3">
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<h3 id="orgd195c16"><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="orgb8b0684" 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 id="outline-container-org008a2d9" class="outline-3">
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<h3 id="org008a2d9"><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 id="org3189602" 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>
|
2020-07-20 13:17:34 +02:00
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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>
|
2020-07-20 11:27:55 +02:00
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</div>
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2020-07-17 11:56:08 +02:00
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</div>
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</div>
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2020-07-24 13:06:02 +02:00
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<div id="outline-container-orgb223df5" class="outline-3">
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|
<h3 id="orgb223df5"><span class="section-number-3">4.3</span> Compute TF estimate and Coherence</h3>
|
2020-07-20 11:27:55 +02:00
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|
<div class="outline-text-3" id="text-4-3">
|
2020-07-23 09:43:42 +02:00
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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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2020-07-17 11:56:08 +02:00
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<div class="org-src-container">
|
2020-07-20 11:27:55 +02:00
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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);
|
2020-07-17 11:56:08 +02:00
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</pre>
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</div>
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2020-07-20 11:27:55 +02:00
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2020-07-24 13:06:02 +02:00
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<div id="orgc74f977" class="figure">
|
2020-07-20 11:27:55 +02:00
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<p><img src="figs/apa95ml_5kg_10V_coh.png" alt="apa95ml_5kg_10V_coh.png" />
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</p>
|
2020-07-20 13:17:34 +02:00
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<p><span class="figure-number">Figure 7: </span>Coherence</p>
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2020-07-20 11:27:55 +02:00
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</div>
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2020-07-24 13:06:02 +02:00
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<div id="orgc54bab7" class="figure">
|
2020-07-20 11:27:55 +02:00
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<p><img src="figs/apa95ml_5kg_10V_tf.png" alt="apa95ml_5kg_10V_tf.png" />
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</p>
|
2020-07-20 13:17:34 +02:00
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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>
|
2020-07-20 11:27:55 +02:00
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</div>
|
2020-07-17 11:56:08 +02:00
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</div>
|
2020-07-20 13:29:36 +02:00
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2020-07-24 13:06:02 +02:00
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<div id="outline-container-orgf0b54fc" class="outline-3">
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|
<h3 id="orgf0b54fc"><span class="section-number-3">4.4</span> Comparison with the FEM model</h3>
|
2020-07-20 13:29:36 +02:00
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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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|
2020-07-24 13:06:02 +02:00
|
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|
<div id="orge0b2a40" class="figure">
|
2020-07-20 13:29:36 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_comp_fem.png" alt="apa95ml_5kg_comp_fem.png" />
|
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|
|
|
</p>
|
|
|
|
|
<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>
|
2020-07-24 11:34:18 +02:00
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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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|
2020-07-20 13:29:36 +02:00
|
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|
</div>
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|
</div>
|
2020-07-17 11:56:08 +02:00
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</div>
|
2020-07-23 09:43:42 +02:00
|
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|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="outline-container-org189b278" class="outline-2">
|
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|
|
<h2 id="org189b278"><span class="section-number-2">5</span> Transfer function of the PI Amplifier</h2>
|
2020-07-23 09:43:42 +02:00
|
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|
<div class="outline-text-2" id="text-5">
|
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|
|
</div>
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="outline-container-org970db83" class="outline-3">
|
|
|
|
|
<h3 id="org970db83"><span class="section-number-3">5.1</span> Compute TF estimate and Coherence</h3>
|
2020-07-23 09:43:42 +02:00
|
|
|
<div class="outline-text-3" id="text-5-1">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
|
|
|
|
|
Fs = 1/Ts;
|
2020-07-24 11:34:18 +02:00
|
|
|
</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>
|
2020-07-24 13:06:02 +02:00
|
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|
The coherence is very good as expected (Figure <a href="#org1877c12">10</a>).
|
2020-07-24 11:34:18 +02:00
|
|
|
</p>
|
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|
<p>
|
2020-07-24 13:06:02 +02:00
|
|
|
The transfer function show a low pass filter behavior with a lot of phase drop (Figure <a href="#org76c3cb3">11</a>).
|
2020-07-24 11:34:18 +02:00
|
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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));
|
|
|
|
|
|
|
|
|
|
[tf_est, f] = tfestimate(u, um, win, [], [], 1/Ts);
|
|
|
|
|
[co_est, ~] = mscohere( u, um, win, [], [], 1/Ts);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
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|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="org1877c12" class="figure">
|
2020-07-24 11:34:18 +02:00
|
|
|
<p><img src="figs/PI_E505_coh.png" alt="PI_E505_coh.png" />
|
|
|
|
|
</p>
|
|
|
|
|
<p><span class="figure-number">Figure 10: </span>Coherence</p>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="org76c3cb3" class="figure">
|
2020-07-24 11:34:18 +02:00
|
|
|
<p><img src="figs/PI_E505_tf.png" alt="PI_E505_tf.png" />
|
|
|
|
|
</p>
|
|
|
|
|
<p><span class="figure-number">Figure 11: </span>Estimation of the transfer function from input voltage to displacement</p>
|
|
|
|
|
</div>
|
2020-07-24 13:06:02 +02:00
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
The delay can be estimated as follow:
|
|
|
|
|
</p>
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">finddelay(u, um)*Ts
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<pre class="example">
|
|
|
|
|
0.0004
|
|
|
|
|
</pre>
|
2020-07-24 11:34:18 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="outline-container-orgea1748b" class="outline-2">
|
|
|
|
|
<h2 id="orgea1748b"><span class="section-number-2">6</span> PI Amplifier</h2>
|
2020-07-24 11:34:18 +02:00
|
|
|
<div class="outline-text-2" id="text-6">
|
|
|
|
|
</div>
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="outline-container-org53f7284" class="outline-3">
|
|
|
|
|
<h3 id="org53f7284"><span class="section-number-3">6.1</span> Comparison of the PSD with Huddle Test</h3>
|
2020-07-24 11:34:18 +02:00
|
|
|
<div class="outline-text-3" id="text-6-1">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
|
|
|
|
|
Fs = 1/Ts;
|
2020-07-23 09:43:42 +02:00
|
|
|
|
|
|
|
|
win = hanning(ceil(1*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);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="org1d7bc05" class="figure">
|
2020-07-23 09:43:42 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_PI_pdf_comp_huddle.png" alt="apa95ml_5kg_PI_pdf_comp_huddle.png" />
|
|
|
|
|
</p>
|
2020-07-24 11:34:18 +02:00
|
|
|
<p><span class="figure-number">Figure 12: </span>Comparison of the ASD for the identification test and the huddle test</p>
|
2020-07-23 09:43:42 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="outline-container-org9081582" class="outline-3">
|
|
|
|
|
<h3 id="org9081582"><span class="section-number-3">6.2</span> Compute TF estimate and Coherence</h3>
|
2020-07-24 11:34:18 +02:00
|
|
|
<div class="outline-text-3" id="text-6-2">
|
2020-07-23 09:43:42 +02:00
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
|
|
|
|
|
Fs = 1/Ts;
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">win = hann(ceil(10/Ts));
|
|
|
|
|
|
|
|
|
|
[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
|
|
|
|
|
[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="orge505858" class="figure">
|
2020-07-23 09:43:42 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_PI_coh.png" alt="apa95ml_5kg_PI_coh.png" />
|
|
|
|
|
</p>
|
2020-07-24 11:34:18 +02:00
|
|
|
<p><span class="figure-number">Figure 13: </span>Coherence</p>
|
2020-07-23 09:43:42 +02:00
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="org5754167" class="figure">
|
2020-07-23 09:43:42 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_PI_tf.png" alt="apa95ml_5kg_PI_tf.png" />
|
|
|
|
|
</p>
|
2020-07-24 11:34:18 +02:00
|
|
|
<p><span class="figure-number">Figure 14: </span>Estimation of the transfer function from input voltage to displacement</p>
|
2020-07-23 09:43:42 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="outline-container-org52ebb83" class="outline-3">
|
|
|
|
|
<h3 id="org52ebb83"><span class="section-number-3">6.3</span> Comparison with the FEM model</h3>
|
2020-07-24 11:34:18 +02:00
|
|
|
<div class="outline-text-3" id="text-6-3">
|
2020-07-23 09:43:42 +02:00
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-07-24 13:06:02 +02:00
|
|
|
<div id="orge0e655f" class="figure">
|
2020-07-23 09:43:42 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_pi_comp_fem.png" alt="apa95ml_5kg_pi_comp_fem.png" />
|
|
|
|
|
</p>
|
2020-07-24 11:34:18 +02:00
|
|
|
<p><span class="figure-number">Figure 15: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
|
2020-07-23 09:43:42 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2020-07-17 11:56:08 +02:00
|
|
|
</div>
|
|
|
|
|
<div id="postamble" class="status">
|
|
|
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
2020-07-24 13:06:02 +02:00
|
|
|
<p class="date">Created: 2020-07-24 ven. 13:06</p>
|
2020-07-17 11:56:08 +02:00
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</div>
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</body>
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</html>
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