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Thomas Dehaeze 2021-03-15 13:34:01 +01:00
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2021-03-01 lun. 09:17 -->
<!-- 2021-03-15 lun. 11:35 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title>
<meta name="author" content="Dehaeze Thomas" />
@ -39,28 +39,33 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org61dfb38">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
<li><a href="#orga39596d">2. Geometrical Measurements</a>
<li><a href="#org0eb094b">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
<li><a href="#org6f9ba21">2. Geometrical Measurements</a>
<ul>
<li><a href="#orgf18d554">2.1. Measurement Setup</a></li>
<li><a href="#orgab6a290">2.2. Measurement Results</a></li>
<li><a href="#org8044086">2.1. Measurement Setup</a></li>
<li><a href="#org4293145">2.2. Measurement Results</a></li>
</ul>
</li>
<li><a href="#orgc48230a">3. Electrical Measurements</a></li>
<li><a href="#org5c918ed">4. Test-Bench Description</a></li>
<li><a href="#org8d4b8e2">5. Measurement Procedure</a>
<li><a href="#org50d4352">3. Electrical Measurements</a></li>
<li><a href="#orgb8a1481">4. Stiffness measurement</a>
<ul>
<li><a href="#org5d94aa9">5.1. Stroke Measurement</a></li>
<li><a href="#org3c05855">5.2. Stiffness Measurement</a></li>
<li><a href="#orgf42db98">5.3. Hysteresis measurement</a></li>
<li><a href="#orgf14c8a5">5.4. Piezoelectric Actuator Constant</a></li>
<li><a href="#orgd45032c">5.5. Piezoelectric Sensor Constant</a></li>
<li><a href="#org72919e5">5.6. Capacitance Measurement</a></li>
<li><a href="#org81e2e82">5.7. Dynamical Behavior</a></li>
<li><a href="#orgcac6823">5.8. Compare the results obtained for all 7 APA300ML</a></li>
<li><a href="#org21bc9b2">4.1. APA test</a></li>
</ul>
</li>
<li><a href="#org90aaad1">6. Measurement Results</a></li>
<li><a href="#orgb3154e0">5. Test-Bench Description</a></li>
<li><a href="#orgac581ad">6. Measurement Procedure</a>
<ul>
<li><a href="#orge00396f">6.1. Stroke Measurement</a></li>
<li><a href="#org66ac5bb">6.2. Stiffness Measurement</a></li>
<li><a href="#orgee2d3e8">6.3. Hysteresis measurement</a></li>
<li><a href="#orge6e89ca">6.4. Piezoelectric Actuator Constant</a></li>
<li><a href="#orge970d07">6.5. Piezoelectric Sensor Constant</a></li>
<li><a href="#org86b3954">6.6. Capacitance Measurement</a></li>
<li><a href="#orgc5205df">6.7. Dynamical Behavior</a></li>
<li><a href="#org2f73a1b">6.8. Compare the results obtained for all 7 APA300ML</a></li>
</ul>
</li>
<li><a href="#org175e8d0">7. Measurement Results</a></li>
</ul>
</div>
</div>
@ -85,21 +90,21 @@ This include:
</ul>
<div id="orgca99cce" class="figure">
<div id="org664d1fb" class="figure">
<p><img src="figs/apa300ML.png" alt="apa300ML.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the APA300ML</p>
</div>
<div id="outline-container-org61dfb38" class="outline-2">
<h2 id="org61dfb38"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
<div id="outline-container-org0eb094b" class="outline-2">
<h2 id="org0eb094b"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
<div class="outline-text-2" id="text-1">
<p>
Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#org2432201">2</a>.
Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#orgc9df44d">2</a>.
</p>
<div id="org2432201" class="figure">
<div id="orgc9df44d" class="figure">
<p><img src="figs/apa_model_schematic.png" alt="apa_model_schematic.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Amplified Piezoelectric Actuator Schematic</p>
@ -124,11 +129,11 @@ We wish here to experimental measure \(g_a\) and \(g_s\).
</p>
<p>
The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#orgc142156">3</a>.
The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#orgc4bba98">3</a>.
</p>
<div id="orgc142156" class="figure">
<div id="orgc4bba98" class="figure">
<p><img src="figs/apa-model-simscape-schematic.png" alt="apa-model-simscape-schematic.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Model of the APA with Simscape/Simulink</p>
@ -136,22 +141,22 @@ The block-diagram model of the piezoelectric actuator is then as shown in Figure
</div>
</div>
<div id="outline-container-orga39596d" class="outline-2">
<h2 id="orga39596d"><span class="section-number-2">2</span> Geometrical Measurements</h2>
<div id="outline-container-org6f9ba21" class="outline-2">
<h2 id="org6f9ba21"><span class="section-number-2">2</span> Geometrical Measurements</h2>
<div class="outline-text-2" id="text-2">
<div id="orgc8762e5" class="figure">
<div id="org939ac64" class="figure">
<p><img src="figs/IMG_20210224_143500.jpg" alt="IMG_20210224_143500.jpg" />
</p>
<p><span class="figure-number">Figure 4: </span>Received APA</p>
</div>
</div>
<div id="outline-container-orgf18d554" class="outline-3">
<h3 id="orgf18d554"><span class="section-number-3">2.1</span> Measurement Setup</h3>
<div id="outline-container-org8044086" class="outline-3">
<h3 id="org8044086"><span class="section-number-3">2.1</span> Measurement Setup</h3>
<div class="outline-text-3" id="text-2-1">
<div id="orgec2c3f2" class="figure">
<div id="org43d857b" class="figure">
<p><img src="figs/IMG_20210224_143809.jpg" alt="IMG_20210224_143809.jpg" />
</p>
<p><span class="figure-number">Figure 5: </span>Measurement Setup</p>
@ -159,8 +164,8 @@ The block-diagram model of the piezoelectric actuator is then as shown in Figure
</div>
</div>
<div id="outline-container-orgab6a290" class="outline-3">
<h3 id="orgab6a290"><span class="section-number-3">2.2</span> Measurement Results</h3>
<div id="outline-container-org4293145" class="outline-3">
<h3 id="org4293145"><span class="section-number-3">2.2</span> Measurement Results</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Height (Z) measurements:
@ -202,7 +207,7 @@ pos = [[<span class="org-type">-</span>L<span class="org-type">/</span>2 <span c
</pre>
</div>
<table id="org68cc21a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org2443ab1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Estimated flatness</caption>
<colgroup>
@ -247,15 +252,173 @@ pos = [[<span class="org-type">-</span>L<span class="org-type">/</span>2 <span c
</div>
</div>
<div id="outline-container-orgc48230a" class="outline-2">
<h2 id="orgc48230a"><span class="section-number-2">3</span> Electrical Measurements</h2>
<div id="outline-container-org50d4352" class="outline-2">
<h2 id="org50d4352"><span class="section-number-2">3</span> Electrical Measurements</h2>
<div class="outline-text-2" id="text-3">
<div class="note" id="org262a984">
<p>
The capacitance of the stacks is measure with the <a href="https://www.gwinstek.com/en-global/products/detail/LCR-800">LCR-800 Meter</a> (<a href="doc/DS_LCR-800_Series_V2_E.pdf">doc</a>)
</p>
</div>
<div id="outline-container-org5c918ed" class="outline-2">
<h2 id="org5c918ed"><span class="section-number-2">4</span> Test-Bench Description</h2>
<div id="orgdaa55e5" class="figure">
<p><img src="figs/IMG_20210312_120337.jpg" alt="IMG_20210312_120337.jpg" />
</p>
<p><span class="figure-number">Figure 6: </span>LCR Meter used for the measurements</p>
</div>
<p>
The excitation frequency is set to be 1kHz.
</p>
<table id="org9d7793d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Capacitance measured with the LCR meter. The excitation signal is a sinus at 1kHz</caption>
<colgroup>
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right"><b>APA Number</b></th>
<th scope="col" class="org-right"><b>Sensor Stack</b></th>
<th scope="col" class="org-right"><b>Actuator Stacks</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-right">5.10</td>
<td class="org-right">10.03</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-right">4.99</td>
<td class="org-right">9.85</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-right">1.72</td>
<td class="org-right">5.18</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-right">4.94</td>
<td class="org-right">9.82</td>
</tr>
<tr>
<td class="org-right">5</td>
<td class="org-right">4.90</td>
<td class="org-right">9.66</td>
</tr>
<tr>
<td class="org-right">6</td>
<td class="org-right">4.99</td>
<td class="org-right">9.91</td>
</tr>
<tr>
<td class="org-right">7</td>
<td class="org-right">4.85</td>
<td class="org-right">9.85</td>
</tr>
</tbody>
</table>
<div class="warning" id="org5042148">
<p>
There is clearly a problem with APA300ML number 3
</p>
</div>
</div>
</div>
<div id="outline-container-orgb8a1481" class="outline-2">
<h2 id="orgb8a1481"><span class="section-number-2">4</span> Stiffness measurement</h2>
<div class="outline-text-2" id="text-4">
<div class="note" id="org4dcad91">
</div>
<div id="outline-container-org21bc9b2" class="outline-3">
<h3 id="org21bc9b2"><span class="section-number-3">4.1</span> APA test</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'meas_stiff_apa_1_x.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'F'</span>, <span class="org-string">'d'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
plot(t, F)
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Automatic Zero of the force</span></span>
F = F <span class="org-type">-</span> mean(F(t <span class="org-type">&gt;</span> 0.1 <span class="org-type">&amp;</span> t <span class="org-type">&lt;</span> 0.3));
<span class="org-matlab-cellbreak"><span class="org-comment">%% Start measurement at t = 0.2 s</span></span>
d = d(t <span class="org-type">&gt;</span> 0.2);
F = F(t <span class="org-type">&gt;</span> 0.2);
t = t(t <span class="org-type">&gt;</span> 0.2); t = t <span class="org-type">-</span> t(1);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">i_l_start = find(F <span class="org-type">&gt;</span> 0.3, 1, <span class="org-string">'first'</span>);
[<span class="org-type">~</span>, i_l_stop] = max(F);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">F_l = F(i_l_start<span class="org-type">:</span>i_l_stop);
d_l = d(i_l_start<span class="org-type">:</span>i_l_stop);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">fit_l = polyfit(F_l, d_l, 1);
<span class="org-comment">% %% Reset displacement based on fit</span>
<span class="org-comment">% d = d - fit_l(2);</span>
<span class="org-comment">% fit_s(2) = fit_s(2) - fit_l(2);</span>
<span class="org-comment">% fit_l(2) = 0;</span>
<span class="org-comment">% %% Estimated Stroke</span>
<span class="org-comment">% F_max = fit_s(2)/(fit_l(1) - fit_s(1));</span>
<span class="org-comment">% d_max = fit_l(1)*F_max;</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">h<span class="org-type">^</span>2<span class="org-type">/</span>fit_l(1)
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(F,d,<span class="org-string">'k'</span>)
plot(F_l, d_l)
plot(F_l, F_l<span class="org-type">*</span>fit_l(1) <span class="org-type">+</span> fit_l(2), <span class="org-string">'--'</span>)
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orgb3154e0" class="outline-2">
<h2 id="orgb3154e0"><span class="section-number-2">5</span> Test-Bench Description</h2>
<div class="outline-text-2" id="text-5">
<div class="note" id="orgc87eff8">
<p>
Here are the documentation of the equipment used for this test bench:
</p>
@ -270,21 +433,21 @@ Here are the documentation of the equipment used for this test bench:
</div>
<div id="org7bcb57f" class="figure">
<div id="orgfd15602" class="figure">
<p><img src="figs/test_bench_apa_alone.png" alt="test_bench_apa_alone.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Schematic of the Test Bench</p>
<p><span class="figure-number">Figure 7: </span>Schematic of the Test Bench</p>
</div>
</div>
</div>
<div id="outline-container-org8d4b8e2" class="outline-2">
<h2 id="org8d4b8e2"><span class="section-number-2">5</span> Measurement Procedure</h2>
<div class="outline-text-2" id="text-5">
<div id="outline-container-orgac581ad" class="outline-2">
<h2 id="orgac581ad"><span class="section-number-2">6</span> Measurement Procedure</h2>
<div class="outline-text-2" id="text-6">
</div>
<div id="outline-container-org5d94aa9" class="outline-3">
<h3 id="org5d94aa9"><span class="section-number-3">5.1</span> Stroke Measurement</h3>
<div class="outline-text-3" id="text-5-1">
<div id="outline-container-orge00396f" class="outline-3">
<h3 id="orge00396f"><span class="section-number-3">6.1</span> Stroke Measurement</h3>
<div class="outline-text-3" id="text-6-1">
<p>
Using the PD200 amplifier, output a voltage:
\[ V_a = 65 + 85 \sin(2\pi \cdot t) \]
@ -311,9 +474,9 @@ Conclude on the obtained stroke.
</div>
</div>
<div id="outline-container-org3c05855" class="outline-3">
<h3 id="org3c05855"><span class="section-number-3">5.2</span> Stiffness Measurement</h3>
<div class="outline-text-3" id="text-5-2">
<div id="outline-container-org66ac5bb" class="outline-3">
<h3 id="org66ac5bb"><span class="section-number-3">6.2</span> Stiffness Measurement</h3>
<div class="outline-text-3" id="text-6-2">
<p>
Add some (known) weight \(\delta m g\) on the suspended mass and measure the deflection \(\delta d\).
This can be tested when the piezoelectric stacks are open-circuit.
@ -332,9 +495,9 @@ Then the obtained stiffness is:
</div>
</div>
<div id="outline-container-orgf42db98" class="outline-3">
<h3 id="orgf42db98"><span class="section-number-3">5.3</span> Hysteresis measurement</h3>
<div class="outline-text-3" id="text-5-3">
<div id="outline-container-orgee2d3e8" class="outline-3">
<h3 id="orgee2d3e8"><span class="section-number-3">6.3</span> Hysteresis measurement</h3>
<div class="outline-text-3" id="text-6-3">
<p>
Supply a quasi static sinusoidal excitation \(V_a\) at different voltages.
</p>
@ -352,17 +515,17 @@ Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
</p>
<div id="org19a134a" class="figure">
<div id="org7123135" class="figure">
<p><img src="figs/expected_hysteresis.png" alt="expected_hysteresis.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Expected Hysteresis (<a class='org-ref-reference' href="#poel10_explor_activ_hard_mount_vibrat">poel10_explor_activ_hard_mount_vibrat</a>)</p>
<p><span class="figure-number">Figure 8: </span>Expected Hysteresis (<a class='org-ref-reference' href="#poel10_explor_activ_hard_mount_vibrat">poel10_explor_activ_hard_mount_vibrat</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orgf14c8a5" class="outline-3">
<h3 id="orgf14c8a5"><span class="section-number-3">5.4</span> Piezoelectric Actuator Constant</h3>
<div class="outline-text-3" id="text-5-4">
<div id="outline-container-orge6e89ca" class="outline-3">
<h3 id="orge6e89ca"><span class="section-number-3">6.4</span> Piezoelectric Actuator Constant</h3>
<div class="outline-text-3" id="text-6-4">
<p>
Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage \(V_a\) to the induced displacement \(d\).
Use a quasi static (1Hz) excitation signal \(V_a\) on the piezoelectric stack and measure the vertical displacement \(d\).
@ -388,9 +551,9 @@ From the two gains, it is then easy to determine \(g_a\):
</div>
</div>
<div id="outline-container-orgd45032c" class="outline-3">
<h3 id="orgd45032c"><span class="section-number-3">5.5</span> Piezoelectric Sensor Constant</h3>
<div class="outline-text-3" id="text-5-5">
<div id="outline-container-orge970d07" class="outline-3">
<h3 id="orge970d07"><span class="section-number-3">6.5</span> Piezoelectric Sensor Constant</h3>
<div class="outline-text-3" id="text-6-5">
<p>
From a quasi static excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\):
</p>
@ -428,18 +591,18 @@ This external force can be some weight added, or a piezo in parallel.
</div>
</div>
<div id="outline-container-org72919e5" class="outline-3">
<h3 id="org72919e5"><span class="section-number-3">5.6</span> Capacitance Measurement</h3>
<div class="outline-text-3" id="text-5-6">
<div id="outline-container-org86b3954" class="outline-3">
<h3 id="org86b3954"><span class="section-number-3">6.6</span> Capacitance Measurement</h3>
<div class="outline-text-3" id="text-6-6">
<p>
Measure the capacitance of the 3 stacks individually using a precise multi-meter.
</p>
</div>
</div>
<div id="outline-container-org81e2e82" class="outline-3">
<h3 id="org81e2e82"><span class="section-number-3">5.7</span> Dynamical Behavior</h3>
<div class="outline-text-3" id="text-5-7">
<div id="outline-container-orgc5205df" class="outline-3">
<h3 id="orgc5205df"><span class="section-number-3">6.7</span> Dynamical Behavior</h3>
<div class="outline-text-3" id="text-6-7">
<p>
Perform a system identification from \(V_a\) to the measured displacement \(d\) by the interferometer and by the encoder, and to the generated voltage \(V_s\).
</p>
@ -454,9 +617,9 @@ This can also be performed with and without the encoder fixed to the APA.
</div>
</div>
<div id="outline-container-orgcac6823" class="outline-3">
<h3 id="orgcac6823"><span class="section-number-3">5.8</span> Compare the results obtained for all 7 APA300ML</h3>
<div class="outline-text-3" id="text-5-8">
<div id="outline-container-org2f73a1b" class="outline-3">
<h3 id="org2f73a1b"><span class="section-number-3">6.8</span> Compare the results obtained for all 7 APA300ML</h3>
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<p>
Compare all the obtained parameters for all the test APA.
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@ -464,8 +627,8 @@ Compare all the obtained parameters for all the test APA.
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<h2 id="org90aaad1"><span class="section-number-2">6</span> Measurement Results</h2>
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<h2 id="org175e8d0"><span class="section-number-2">7</span> Measurement Results</h2>
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
@ -475,7 +638,7 @@ Compare all the obtained parameters for all the test APA.
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<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-03-01 lun. 09:17</p>
<p class="date">Created: 2021-03-15 lun. 11:35</p>
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test-bench-apa300ml.org
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@ -193,7 +193,90 @@ data2orgtable(1e6*apa_d', {}, {'Flatness [um]'}, ' %.1f ');
* Electrical Measurements
#+begin_note
The capacitance of the stacks is measure with the [[https://www.gwinstek.com/en-global/products/detail/LCR-800][LCR-800 Meter]] ([[file:doc/DS_LCR-800_Series_V2_E.pdf][doc]])
#+end_note
#+name: fig:LCR_meter
#+caption: LCR Meter used for the measurements
#+attr_latex: :width 0.9\linewidth
[[file:figs/IMG_20210312_120337.jpg]]
The excitation frequency is set to be 1kHz.
#+name: tab:apa300ml_capacitance
#+caption: Capacitance measured with the LCR meter. The excitation signal is a sinus at 1kHz
#+attr_latex: :environment tabularx :width 0.6\linewidth :align lcc
#+attr_latex: :center t :booktabs t :float t
| *APA Number* | *Sensor Stack* | *Actuator Stacks* |
|--------------+----------------+-------------------|
| 1 | 5.10 | 10.03 |
| 2 | 4.99 | 9.85 |
| 3 | 1.72 | 5.18 |
| 4 | 4.94 | 9.82 |
| 5 | 4.90 | 9.66 |
| 6 | 4.99 | 9.91 |
| 7 | 4.85 | 9.85 |
#+begin_warning
There is clearly a problem with APA300ML number 3
#+end_warning
* Stiffness measurement
** APA test
#+begin_src matlab
load('meas_stiff_apa_1_x.mat', 't', 'F', 'd');
#+end_src
#+begin_src matlab
figure;
plot(t, F)
#+end_src
#+begin_src matlab
%% Automatic Zero of the force
F = F - mean(F(t > 0.1 & t < 0.3));
%% Start measurement at t = 0.2 s
d = d(t > 0.2);
F = F(t > 0.2);
t = t(t > 0.2); t = t - t(1);
#+end_src
#+begin_src matlab
i_l_start = find(F > 0.3, 1, 'first');
[~, i_l_stop] = max(F);
#+end_src
#+begin_src matlab
F_l = F(i_l_start:i_l_stop);
d_l = d(i_l_start:i_l_stop);
#+end_src
#+begin_src matlab
fit_l = polyfit(F_l, d_l, 1);
% %% Reset displacement based on fit
% d = d - fit_l(2);
% fit_s(2) = fit_s(2) - fit_l(2);
% fit_l(2) = 0;
% %% Estimated Stroke
% F_max = fit_s(2)/(fit_l(1) - fit_s(1));
% d_max = fit_l(1)*F_max;
#+end_src
#+begin_src matlab
h^2/fit_l(1)
#+end_src
#+begin_src matlab
figure;
hold on;
plot(F,d,'k')
plot(F_l, d_l)
plot(F_l, F_l*fit_l(1) + fit_l(2), '--')
#+end_src
* Test-Bench Description
#+begin_note

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