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Add block diagram of piezo model

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Thomas Dehaeze 2020-12-17 14:55:18 +01:00
parent 882486d8c6
commit d978cd0570
5 changed files with 349 additions and 40 deletions
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-12-16 mer. 11:07 --> <!-- 2020-12-17 jeu. 14:55 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title> <title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -30,18 +30,21 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org1313e99">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li> <li><a href="#org678b530">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
<li><a href="#org3c114e3">2. Test-Bench Description</a></li> <li><a href="#orgb60d741">2. Test-Bench Description</a></li>
<li><a href="#orgeef8a7b">3. Measurement Procedure</a> <li><a href="#orgf881aa5">3. Measurement Procedure</a>
<ul> <ul>
<li><a href="#orgf5f4de4">3.1. Stroke Measurement</a></li> <li><a href="#orgd3519e0">3.1. Stroke Measurement</a></li>
<li><a href="#orgc6a7f40">3.2. Stiffness Measurement</a></li> <li><a href="#org6844a7e">3.2. Stiffness Measurement</a></li>
<li><a href="#orgf924c27">3.3. Hysteresis measurement</a></li> <li><a href="#org9b16fa0">3.3. Hysteresis measurement</a></li>
<li><a href="#org8dd84d4">3.4. Piezoelectric Actuator Constant</a></li> <li><a href="#orgbfe1da1">3.4. Piezoelectric Actuator Constant</a></li>
<li><a href="#org133086b">3.5. Piezoelectric Sensor Constant</a></li> <li><a href="#orgb1792b1">3.5. Piezoelectric Sensor Constant</a></li>
<li><a href="#org6d5e309">3.6. Capacitance Measurement</a></li> <li><a href="#orgd76cbb5">3.6. Capacitance Measurement</a></li>
<li><a href="#orgbfe739f">3.7. Dynamical Behavior</a></li>
<li><a href="#org007452b">3.8. Compare the results obtained for all 7 APA300ML</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org7bda022">4. Measurement Results</a></li>
</ul> </ul>
</div> </div>
</div> </div>
@ -59,15 +62,23 @@ This include:
<li>Hysteresis</li> <li>Hysteresis</li>
<li>Gain from the applied voltage \(V_a\) to the generated Force \(F_a\)</li> <li>Gain from the applied voltage \(V_a\) to the generated Force \(F_a\)</li>
<li>Gain from the sensor stack strain \(\delta L\) to the generated voltage \(V_s\)</li> <li>Gain from the sensor stack strain \(\delta L\) to the generated voltage \(V_s\)</li>
<li>Dynamical behavior</li>
</ul> </ul>
<div id="outline-container-org1313e99" class="outline-2"> <div id="outline-container-org678b530" class="outline-2">
<h2 id="org1313e99"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2> <h2 id="org678b530"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#org5dd279e">1</a>. Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#orgf04d73b">1</a>.
</p> </p>
<div id="orgf04d73b" class="figure">
<p><img src="figs/apa_model_schematic.png" alt="apa_model_schematic.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Amplified Piezoelectric Actuator Schematic</p>
</div>
<p> <p>
A voltage \(V_a\) applied to the actuator stacks will induce an actuator force \(F_a\): A voltage \(V_a\) applied to the actuator stacks will induce an actuator force \(F_a\):
</p> </p>
@ -86,19 +97,23 @@ A change of length \(dl\) of the sensor stack will induce a voltage \(V_s\):
We wish here to experimental measure \(g_a\) and \(g_s\). We wish here to experimental measure \(g_a\) and \(g_s\).
</p> </p>
<p>
<div id="org5dd279e" class="figure"> The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#org7ba9352">2</a>.
<p><img src="figs/apa_model_schematic.png" alt="apa_model_schematic.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Amplified Piezoelectric Actuator Schematic</p>
<div id="org7ba9352" class="figure">
<p><img src="figs/apa-model-simscape-schematic.png" alt="apa-model-simscape-schematic.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Model of the APA with Simscape/Simulink</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org3c114e3" class="outline-2"> <div id="outline-container-orgb60d741" class="outline-2">
<h2 id="org3c114e3"><span class="section-number-2">2</span> Test-Bench Description</h2> <h2 id="orgb60d741"><span class="section-number-2">2</span> Test-Bench Description</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<div class="note" id="org84f08a9"> <div class="note" id="org12ee0dc">
<p> <p>
Here are the documentation of the equipment used for this test bench: Here are the documentation of the equipment used for this test bench:
</p> </p>
@ -113,20 +128,20 @@ Here are the documentation of the equipment used for this test bench:
</div> </div>
<div id="org9ba13fa" class="figure"> <div id="orgfaaa568" class="figure">
<p><img src="figs/test_bench_apa_alone.png" alt="test_bench_apa_alone.png" /> <p><img src="figs/test_bench_apa_alone.png" alt="test_bench_apa_alone.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Schematic of the Test Bench</p> <p><span class="figure-number">Figure 3: </span>Schematic of the Test Bench</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgeef8a7b" class="outline-2"> <div id="outline-container-orgf881aa5" class="outline-2">
<h2 id="orgeef8a7b"><span class="section-number-2">3</span> Measurement Procedure</h2> <h2 id="orgf881aa5"><span class="section-number-2">3</span> Measurement Procedure</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
</div> </div>
<div id="outline-container-orgf5f4de4" class="outline-3"> <div id="outline-container-orgd3519e0" class="outline-3">
<h3 id="orgf5f4de4"><span class="section-number-3">3.1</span> Stroke Measurement</h3> <h3 id="orgd3519e0"><span class="section-number-3">3.1</span> Stroke Measurement</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
Using the PD200 amplifier, output a voltage: Using the PD200 amplifier, output a voltage:
@ -154,8 +169,8 @@ Conclude on the obtained stroke.
</div> </div>
</div> </div>
<div id="outline-container-orgc6a7f40" class="outline-3"> <div id="outline-container-org6844a7e" class="outline-3">
<h3 id="orgc6a7f40"><span class="section-number-3">3.2</span> Stiffness Measurement</h3> <h3 id="org6844a7e"><span class="section-number-3">3.2</span> Stiffness Measurement</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
Add some (known) weight \(\delta m g\) on the suspended mass and measure the deflection \(\delta d\). Add some (known) weight \(\delta m g\) on the suspended mass and measure the deflection \(\delta d\).
@ -175,8 +190,8 @@ Then the obtained stiffness is:
</div> </div>
</div> </div>
<div id="outline-container-orgf924c27" class="outline-3"> <div id="outline-container-org9b16fa0" class="outline-3">
<h3 id="orgf924c27"><span class="section-number-3">3.3</span> Hysteresis measurement</h3> <h3 id="org9b16fa0"><span class="section-number-3">3.3</span> Hysteresis measurement</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
Supply a quasi static sinusoidal excitation \(V_a\) at different voltages. Supply a quasi static sinusoidal excitation \(V_a\) at different voltages.
@ -196,8 +211,8 @@ Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
</div> </div>
</div> </div>
<div id="outline-container-org8dd84d4" class="outline-3"> <div id="outline-container-orgbfe1da1" class="outline-3">
<h3 id="org8dd84d4"><span class="section-number-3">3.4</span> Piezoelectric Actuator Constant</h3> <h3 id="orgbfe1da1"><span class="section-number-3">3.4</span> Piezoelectric Actuator Constant</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<p> <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 \(d\). Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage \(V_a\) to the induced displacement \(d\).
@ -224,8 +239,8 @@ From the two gains, it is then easy to determine \(g_a\):
</div> </div>
</div> </div>
<div id="outline-container-org133086b" class="outline-3"> <div id="outline-container-orgb1792b1" class="outline-3">
<h3 id="org133086b"><span class="section-number-3">3.5</span> Piezoelectric Sensor Constant</h3> <h3 id="orgb1792b1"><span class="section-number-3">3.5</span> Piezoelectric Sensor Constant</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<p> <p>
From a quasi static (1Hz) excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\): From a quasi static (1Hz) excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\):
@ -255,19 +270,49 @@ This external force can be some weight added, or a piezo in parallel.
</div> </div>
</div> </div>
<div id="outline-container-org6d5e309" class="outline-3"> <div id="outline-container-orgd76cbb5" class="outline-3">
<h3 id="org6d5e309"><span class="section-number-3">3.6</span> Capacitance Measurement</h3> <h3 id="orgd76cbb5"><span class="section-number-3">3.6</span> Capacitance Measurement</h3>
<div class="outline-text-3" id="text-3-6"> <div class="outline-text-3" id="text-3-6">
<p> <p>
Measure the capacitance of the 3 stacks individually using a precise multi-meter. Measure the capacitance of the 3 stacks individually using a precise multi-meter.
</p> </p>
</div> </div>
</div> </div>
<div id="outline-container-orgbfe739f" class="outline-3">
<h3 id="orgbfe739f"><span class="section-number-3">3.7</span> Dynamical Behavior</h3>
<div class="outline-text-3" id="text-3-7">
<p>
Perform a system identification from \(V_a\) to the measured displacement \(d\) by the interferometer and by the encoder, and to the general voltage \(V_s\).
</p>
<p>
This can be performed using different excitation signals.
</p>
<p>
This can also be performed with and without the encoder fixed to the APA.
</p>
</div>
</div>
<div id="outline-container-org007452b" class="outline-3">
<h3 id="org007452b"><span class="section-number-3">3.8</span> Compare the results obtained for all 7 APA300ML</h3>
<div class="outline-text-3" id="text-3-8">
<p>
Compare all the obtained parameters for all the test APA.
</p>
</div>
</div>
</div>
<div id="outline-container-org7bda022" class="outline-2">
<h2 id="org7bda022"><span class="section-number-2">4</span> Measurement Results</h2>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-12-16 mer. 11:07</p> <p class="date">Created: 2020-12-17 jeu. 14:55</p>
</div> </div>
</body> </body>
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@ -50,11 +50,16 @@ This include:
- Hysteresis - Hysteresis
- Gain from the applied voltage $V_a$ to the generated Force $F_a$ - Gain from the applied voltage $V_a$ to the generated Force $F_a$
- Gain from the sensor stack strain $\delta L$ to the generated voltage $V_s$ - Gain from the sensor stack strain $\delta L$ to the generated voltage $V_s$
- Dynamical behavior
* Model of an Amplified Piezoelectric Actuator and Sensor * Model of an Amplified Piezoelectric Actuator and Sensor
Consider a schematic of the Amplified Piezoelectric Actuator in Figure [[fig:apa_model_schematic]]. Consider a schematic of the Amplified Piezoelectric Actuator in Figure [[fig:apa_model_schematic]].
#+name: fig:apa_model_schematic
#+caption: Amplified Piezoelectric Actuator Schematic
[[file:figs/apa_model_schematic.png]]
A voltage $V_a$ applied to the actuator stacks will induce an actuator force $F_a$: A voltage $V_a$ applied to the actuator stacks will induce an actuator force $F_a$:
\begin{equation} \begin{equation}
F_a = g_a \cdot V_a F_a = g_a \cdot V_a
@ -67,9 +72,25 @@ A change of length $dl$ of the sensor stack will induce a voltage $V_s$:
We wish here to experimental measure $g_a$ and $g_s$. We wish here to experimental measure $g_a$ and $g_s$.
#+name: fig:apa_model_schematic The block-diagram model of the piezoelectric actuator is then as shown in Figure [[fig:apa-model-simscape-schematic]].
#+caption: Amplified Piezoelectric Actuator Schematic
[[file:figs/apa_model_schematic.png]] #+begin_src latex :file apa-model-simscape-schematic.pdf
\begin{tikzpicture}
\node[block={2.0cm}{2.0cm}, align=center] (model) at (0,0){Simscape\\Model};
\node[block, left=1.0 of model] (ga){$g_a(s)$};
\node[block, right=1.0 of model] (gs){$g_s(s)$};
\draw[<-] (ga.west) -- node[midway, above]{$V_a$} node[midway, below]{$[V]$} ++(-1.0, 0);
\draw[->] (ga.east) --node[midway, above]{$F_a$} node[midway, below]{$[N]$} (model.west);
\draw[->] (model.east) --node[midway, above]{$dl$} node[midway, below]{$[m]$} (gs.west);
\draw[->] (gs.east) -- node[midway, above]{$V_s$} node[midway, below]{$[V]$} ++(1.0, 0);
\end{tikzpicture}
#+end_src
#+name: fig:apa-model-simscape-schematic
#+caption: Model of the APA with Simscape/Simulink
#+RESULTS:
[[file:figs/apa-model-simscape-schematic.png]]
* Test-Bench Description * Test-Bench Description
@ -87,6 +108,8 @@ Here are the documentation of the equipment used for this test bench:
[[file:figs/test_bench_apa_alone.png]] [[file:figs/test_bench_apa_alone.png]]
* Measurement Procedure * Measurement Procedure
** Introduction :ignore:
** Stroke Measurement ** Stroke Measurement
Using the PD200 amplifier, output a voltage: Using the PD200 amplifier, output a voltage:
@ -167,3 +190,17 @@ This external force can be some weight added, or a piezo in parallel.
** Capacitance Measurement ** Capacitance Measurement
Measure the capacitance of the 3 stacks individually using a precise multi-meter. Measure the capacitance of the 3 stacks individually using a precise multi-meter.
** Dynamical Behavior
Perform a system identification from $V_a$ to the measured displacement $d$ by the interferometer and by the encoder, and to the general voltage $V_s$.
This can be performed using different excitation signals.
This can also be performed with and without the encoder fixed to the APA.
** Compare the results obtained for all 7 APA300ML
Compare all the obtained parameters for all the test APA.
* Measurement Results