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<title>Test Bench APA95ML</title>
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2020-07-17 11:56:08 +02:00
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2020-07-20 11:27:55 +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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<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="#orgd70d66f">1. Setup</a>
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<ul>
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<li><a href="#org07d3c47">1.1. Parameters</a></li>
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<li><a href="#orgbd4b8f3">1.2. Filter White Noise</a></li>
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</ul>
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</li>
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<li><a href="#orgebffd67">2. Run Experiment and Save Data</a>
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<ul>
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<li><a href="#org9db9f37">2.1. Load Data</a></li>
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<li><a href="#org5b3c786">2.2. Save Data</a></li>
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</ul>
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</li>
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<li><a href="#orge25b163">3. Huddle Test</a>
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<ul>
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<li><a href="#orgbc09977">3.1. Time Domain Data</a></li>
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<li><a href="#org7e6bc47">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="#org0348c7c">4. Transfer Function Estimation using the DAC as the driver</a>
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<ul>
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<li><a href="#orgf0f7314">4.1. Time Domain Data</a></li>
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<li><a href="#orge50aef7">4.2. Comparison of the PSD with Huddle Test</a></li>
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<li><a href="#org870e2ef">4.3. Compute TF estimate and Coherence</a></li>
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<li><a href="#orgb06d21d">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="#org563fed9">5. Transfer Function Estimation using the PI Amplifier</a>
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<ul>
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<li><a href="#org9c121df">5.1. Load Data</a></li>
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<li><a href="#org990c144">5.2. Comparison of the PSD with Huddle Test</a></li>
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<li><a href="#org323b9c5">5.3. Compute TF estimate and Coherence</a></li>
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<li><a href="#org6045724">5.4. Comparison with the FEM model</a></li>
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</ul>
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</li>
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<li><a href="#org5ef5f65">6. Transfer function from force actuator to force sensor</a>
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<ul>
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<li><a href="#org098bbb0">6.1. System Identification</a></li>
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<li><a href="#orge0e4f46">6.2. Integral Force Feedback</a></li>
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</ul>
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</li>
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<li><a href="#org102cc6a">7. IFF Tests</a>
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<ul>
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<li><a href="#org9e16daf">7.1. Load Data</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="org5c42466" 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="orgc98a0fb" 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-orgd70d66f" class="outline-2">
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<h2 id="orgd70d66f"><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-org07d3c47" class="outline-3">
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<h3 id="org07d3c47"><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 id="outline-container-orgbd4b8f3" class="outline-3">
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<h3 id="orgbd4b8f3"><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-orgebffd67" class="outline-2">
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<h2 id="orgebffd67"><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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2020-08-20 23:08:38 +02:00
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<div id="outline-container-org9db9f37" class="outline-3">
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<h3 id="org9db9f37"><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 id="outline-container-org5b3c786" class="outline-3">
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<h3 id="org5b3c786"><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 id="outline-container-orge25b163" class="outline-2">
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<h2 id="orge25b163"><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-orgbc09977" class="outline-3">
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<h3 id="orgbc09977"><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="orgfbf5913" 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-org7e6bc47" class="outline-3">
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<h3 id="org7e6bc47"><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="orgaf72ca6" 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-org0348c7c" class="outline-2">
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<h2 id="org0348c7c"><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 class="important">
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<p>
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Results presented in this sections are wrong as the ADC cannot deliver enought current to the piezoelectric actuator.
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</p>
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</div>
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</div>
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<div id="outline-container-orgf0f7314" class="outline-3">
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<h3 id="orgf0f7314"><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="org60f734d" 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-orge50aef7" class="outline-3">
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<h3 id="orge50aef7"><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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<pre class="src src-matlab">[pxx, f] = pwelch(y, win, [], [], Fs);
|
|
|
|
|
[pht, ~] = pwelch(ht.y, win, [], [], Fs);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="orga45d905" class="figure">
|
2020-07-20 11:27:55 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_10V_pdf_comp_huddle.png" alt="apa95ml_5kg_10V_pdf_comp_huddle.png" />
|
|
|
|
|
</p>
|
2020-07-20 13:17:34 +02:00
|
|
|
<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
|
|
|
</div>
|
2020-07-17 11:56:08 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
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|
|
|
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|
2020-08-20 23:08:38 +02:00
|
|
|
<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>
|
2020-07-20 11:27:55 +02:00
|
|
|
<div class="outline-text-3" id="text-4-3">
|
2020-07-23 09:43:42 +02:00
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
|
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|
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|
Fs = 1/Ts;
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|
|
|
</pre>
|
|
|
|
|
</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
|
|
|
<pre class="src src-matlab">win = hann(ceil(1/Ts));
|
|
|
|
|
|
|
|
|
|
[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
|
|
|
|
|
[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts);
|
2020-07-17 11:56:08 +02:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
2020-07-20 11:27:55 +02:00
|
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|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="org6abff24" class="figure">
|
2020-07-20 11:27:55 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_10V_coh.png" alt="apa95ml_5kg_10V_coh.png" />
|
|
|
|
|
</p>
|
2020-07-20 13:17:34 +02:00
|
|
|
<p><span class="figure-number">Figure 7: </span>Coherence</p>
|
2020-07-20 11:27:55 +02:00
|
|
|
</div>
|
|
|
|
|
|
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|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="org8e6794a" class="figure">
|
2020-07-20 11:27:55 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_10V_tf.png" alt="apa95ml_5kg_10V_tf.png" />
|
|
|
|
|
</p>
|
2020-07-20 13:17:34 +02:00
|
|
|
<p><span class="figure-number">Figure 8: </span>Estimation of the transfer function from input voltage to displacement</p>
|
|
|
|
|
</div>
|
2020-07-20 11:27:55 +02:00
|
|
|
</div>
|
2020-07-17 11:56:08 +02:00
|
|
|
</div>
|
2020-07-20 13:29:36 +02:00
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<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>
|
2020-07-20 13:29:36 +02:00
|
|
|
<div class="outline-text-3" id="text-4-4">
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'Ghm');
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
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|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="org4563de9" 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" />
|
|
|
|
|
</p>
|
|
|
|
|
<p><span class="figure-number">Figure 9: </span>Comparison of the identified transfer function and the one estimated from the FE model</p>
|
|
|
|
|
</div>
|
2020-07-24 11:34:18 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<div class="outline-text-2" id="text-4">
|
|
|
|
|
<div class="important">
|
|
|
|
|
<p>
|
|
|
|
|
The problem comes from the fact that the piezo is driven directly by the DAC that cannot deliver enought current.
|
|
|
|
|
In the next section, a current amplifier is used.
|
|
|
|
|
</p>
|
|
|
|
|
|
2020-07-20 13:29:36 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
2020-07-17 11:56:08 +02:00
|
|
|
</div>
|
2020-07-23 09:43:42 +02:00
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<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>
|
2020-07-23 09:43:42 +02:00
|
|
|
<div class="outline-text-2" id="text-5">
|
|
|
|
|
</div>
|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="outline-container-org9c121df" class="outline-3">
|
|
|
|
|
<h3 id="org9c121df"><span class="section-number-3">5.1</span> Load Data</h3>
|
2020-07-23 09:43:42 +02:00
|
|
|
<div class="outline-text-3" id="text-5-1">
|
|
|
|
|
<div class="org-src-container">
|
2020-08-20 23:08:38 +02:00
|
|
|
<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">
|
2020-07-23 09:43:42 +02:00
|
|
|
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
|
|
|
|
|
Fs = 1/Ts;
|
2020-07-24 13:16:28 +02:00
|
|
|
|
|
|
|
|
win = hanning(ceil(1*Fs));
|
2020-07-24 11:34:18 +02:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
2020-07-24 13:16:28 +02:00
|
|
|
<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 11:34:18 +02:00
|
|
|
|
|
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="orgf6222d7" class="figure">
|
2020-07-24 13:16:28 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_PI_pdf_comp_huddle.png" alt="apa95ml_5kg_PI_pdf_comp_huddle.png" />
|
2020-07-24 11:34:18 +02:00
|
|
|
</p>
|
2020-07-24 13:16:28 +02:00
|
|
|
<p><span class="figure-number">Figure 10: </span>Comparison of the ASD for the identification test and the huddle test</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2020-07-24 11:34:18 +02:00
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<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">
|
2020-07-24 11:34:18 +02:00
|
|
|
<div class="org-src-container">
|
2020-07-24 13:16:28 +02:00
|
|
|
<pre class="src src-matlab">Ts = t(end)/(length(t)-1);
|
|
|
|
|
Fs = 1/Ts;
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
2020-07-24 11:34:18 +02:00
|
|
|
|
2020-07-24 13:16:28 +02:00
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-matlab">win = hann(ceil(1/Ts));
|
|
|
|
|
|
|
|
|
|
[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
|
|
|
|
|
[tf_um , ~] = tfestimate(um, -y, win, [], [], 1/Ts);
|
|
|
|
|
[co_est, ~] = mscohere( um, -y, win, [], [], 1/Ts);
|
2020-07-24 11:34:18 +02:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="org751008e" class="figure">
|
2020-07-24 13:16:28 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_PI_coh.png" alt="apa95ml_5kg_PI_coh.png" />
|
2020-07-24 11:34:18 +02:00
|
|
|
</p>
|
2020-07-24 13:16:28 +02:00
|
|
|
<p><span class="figure-number">Figure 11: </span>Coherence</p>
|
2020-07-24 11:34:18 +02:00
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="orgaed957e" class="figure">
|
2020-07-24 13:16:28 +02:00
|
|
|
<p><img src="figs/apa95ml_5kg_PI_tf.png" alt="apa95ml_5kg_PI_tf.png" />
|
2020-07-24 11:34:18 +02:00
|
|
|
</p>
|
2020-07-24 13:16:28 +02:00
|
|
|
<p><span class="figure-number">Figure 12: </span>Estimation of the transfer function from input voltage to displacement</p>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2020-07-24 11:34:18 +02:00
|
|
|
</div>
|
2020-07-24 13:06:02 +02:00
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<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">
|
2020-07-24 13:06:02 +02:00
|
|
|
<div class="org-src-container">
|
2020-08-20 23:08:38 +02:00
|
|
|
<pre class="src src-matlab">load('mat/fem_model_5kg.mat', 'G');
|
2020-07-24 13:06:02 +02:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
2020-07-24 13:16:28 +02:00
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
<div id="org693de8c" class="figure">
|
2020-07-24 13:16:28 +02:00
|
|
|
<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>
|
2020-07-24 11:34:18 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2020-07-24 13:16:28 +02:00
|
|
|
</div>
|
2020-08-20 23:08:38 +02:00
|
|
|
|
|
|
|
|
<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>
|
2020-07-24 11:34:18 +02:00
|
|
|
<div class="outline-text-2" id="text-6">
|
2020-08-20 23:08:38 +02:00
|
|
|
<p>
|
|
|
|
|
Two measurements are performed:
|
|
|
|
|
</p>
|
|
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li>Speedgoat DAC => Voltage Amplifier (x20) => 1 Piezo Stack => … => 2 Stacks as Force Sensor (parallel) => Speedgoat ADC</li>
|
|
|
|
|
<li>Speedgoat DAC => Voltage Amplifier (x20) => 2 Piezo Stacks (parallel) => … => 1 Stack as Force Sensor => 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>
|
2020-07-24 11:34:18 +02:00
|
|
|
<div class="org-src-container">
|
2020-08-20 23:08:38 +02:00
|
|
|
<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');
|
2020-07-23 09:43:42 +02:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
2020-07-24 13:16:28 +02:00
|
|
|
<p>
|
2020-08-20 23:08:38 +02:00
|
|
|
Let’s use the amplifier gain to obtain the true voltage applied to the actuator stack(s)
|
2020-07-24 13:16:28 +02:00
|
|
|
</p>
|
2020-07-23 09:43:42 +02:00
|
|
|
|
2020-07-24 13:16:28 +02:00
|
|
|
<p>
|
2020-08-20 23:08:38 +02:00
|
|
|
The parameters of the piezoelectric stacks are defined below:
|
2020-07-23 09:43:42 +02:00
|
|
|
</p>
|
2020-08-20 23:08:38 +02:00
|
|
|
<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>
|
2020-07-23 09:43:42 +02:00
|
|
|
|
2020-07-24 13:16:28 +02:00
|
|
|
<p>
|
2020-08-20 23:08:38 +02:00
|
|
|
From the FEM, we construct the transfer function from DAC voltage to ADC voltage.
|
2020-07-24 13:16:28 +02:00
|
|
|
</p>
|
2020-07-23 09:43:42 +02:00
|
|
|
<div class="org-src-container">
|
2020-08-20 23:08:38 +02:00
|
|
|
<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;
|
2020-07-23 09:43:42 +02:00
|
|
|
|
2020-08-20 23:08:38 +02:00
|
|
|
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);
|
2020-07-23 09:43:42 +02:00
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</pre>
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</div>
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2020-08-20 23:08:38 +02:00
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<div id="orge80e7b7" class="figure">
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<p><img src="figs/bode_plot_force_sensor_voltage_comp_fem.png" alt="bode_plot_force_sensor_voltage_comp_fem.png" />
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2020-07-23 09:43:42 +02:00
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</p>
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2020-08-20 23:08:38 +02:00
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<p><span class="figure-number">Figure 14: </span>Comparison of the identified dynamics from voltage output to voltage input and the FEM</p>
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</div>
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</div>
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<div id="outline-container-org098bbb0" class="outline-3">
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<h3 id="org098bbb0"><span class="section-number-3">6.1</span> System Identification</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">w_z = 2*pi*111; % Zeros frequency [rad/s]
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w_p = 2*pi*255; % Pole frequency [rad/s]
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xi_z = 0.05;
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xi_p = 0.015;
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G_inf = 2;
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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);
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</pre>
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2020-07-23 09:43:42 +02:00
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</div>
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2020-08-20 23:08:38 +02:00
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<div id="org76af419" class="figure">
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<p><img src="figs/iff_plant_identification_apa95ml.png" alt="iff_plant_identification_apa95ml.png" />
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2020-07-23 09:43:42 +02:00
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</p>
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2020-08-20 23:08:38 +02:00
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<p><span class="figure-number">Figure 15: </span>Identification of the IFF plant</p>
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</div>
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</div>
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2020-07-23 09:43:42 +02:00
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</div>
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2020-08-20 23:08:38 +02:00
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<div id="outline-container-orge0e4f46" class="outline-3">
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<h3 id="orge0e4f46"><span class="section-number-3">6.2</span> Integral Force Feedback</h3>
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<div class="outline-text-3" id="text-6-2">
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<div id="org114ceb2" class="figure">
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<p><img src="figs/root_locus_iff_apa95ml_identification.png" alt="root_locus_iff_apa95ml_identification.png" />
|
2020-07-24 13:16:28 +02:00
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</p>
|
2020-08-20 23:08:38 +02:00
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<p><span class="figure-number">Figure 16: </span>Root Locus for IFF</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-org102cc6a" class="outline-2">
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<h2 id="org102cc6a"><span class="section-number-2">7</span> IFF Tests</h2>
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<div class="outline-text-2" id="text-7">
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</div>
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<div id="outline-container-org9e16daf" class="outline-3">
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<h3 id="org9e16daf"><span class="section-number-3">7.1</span> Load Data</h3>
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|
<div class="outline-text-3" id="text-7-1">
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2020-07-23 09:43:42 +02:00
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<div class="org-src-container">
|
2020-08-20 23:08:38 +02:00
|
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<pre class="src src-matlab">iff_g10 = load('./mat/apa95ml_iff_g10_res.mat', 'u', 't', 'y', 'v');
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iff_g100 = load('./mat/apa95ml_iff_g100_res.mat', 'u', 't', 'y', 'v');
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iff_of = load('./mat/apa95ml_iff_off_res.mat', 'u', 't', 'y', 'v');
|
2020-07-23 09:43:42 +02:00
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</pre>
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</div>
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|
2020-08-20 23:08:38 +02:00
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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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|
win = hann(ceil(10/Ts));
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[tf_iff_g10, f] = tfestimate(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
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|
[co_iff_g10, ~] = mscohere(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
|
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[tf_iff_g100, f] = tfestimate(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
|
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|
[co_iff_g100, ~] = mscohere(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
|
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|
[tf_iff_of, ~] = tfestimate(iff_of.u, iff_of.y, win, [], [], 1/Ts);
|
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|
|
[co_iff_of, ~] = mscohere(iff_of.u, iff_of.y, win, [], [], 1/Ts);
|
2020-07-24 13:16:28 +02:00
|
|
|
</pre>
|
2020-08-20 23:08:38 +02:00
|
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</div>
|
2020-07-24 15:48:22 +02:00
|
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|
2020-08-20 23:08:38 +02:00
|
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|
<div class="org-src-container">
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|
<pre class="src src-matlab">figure;
|
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|
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|
hold on;
|
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|
|
plot(f, co_iff_of, '-', 'DisplayName', 'g=0')
|
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|
plot(f, co_iff_g10, '-', 'DisplayName', 'g=10')
|
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|
plot(f, co_iff_g100, '-', 'DisplayName', 'g=100')
|
|
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|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
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|
|
ylabel('Coherence'); xlabel('Frequency [Hz]');
|
|
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|
|
hold off;
|
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|
legend();
|
|
|
|
|
xlim([60, 600])
|
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|
</pre>
|
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</div>
|
2020-07-24 15:48:22 +02:00
|
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|
2020-08-20 23:08:38 +02:00
|
|
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|
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|
<div id="org3768cef" class="figure">
|
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|
|
<p><img src="figs/iff_first_test_coherence.png" alt="iff_first_test_coherence.png" />
|
2020-07-24 15:48:22 +02:00
|
|
|
</p>
|
2020-08-20 23:08:38 +02:00
|
|
|
<p><span class="figure-number">Figure 17: </span>Coherence</p>
|
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|
</div>
|
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|
<div class="org-src-container">
|
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|
|
|
<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>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<div id="orgf1ca4d4" class="figure">
|
|
|
|
|
<p><img src="figs/iff_first_test_bode_plot.png" alt="iff_first_test_bode_plot.png" />
|
|
|
|
|
</p>
|
|
|
|
|
<p><span class="figure-number">Figure 18: </span>Bode plot for different values of IFF gain</p>
|
|
|
|
|
</div>
|
2020-07-23 09:43:42 +02:00
|
|
|
</div>
|
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|
</div>
|
|
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|
</div>
|
2020-07-17 11:56:08 +02:00
|
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</div>
|
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|
|
<div id="postamble" class="status">
|
|
|
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
2020-08-20 23:08:38 +02:00
|
|
|
<p class="date">Created: 2020-08-20 jeu. 23:08</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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