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< title > Amplifier Piezoelectric Actuator APA300ML - Test Bench< / title >
< meta name = "author" content = "Dehaeze Thomas" / >
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< / div > < div id = "content" >
< h1 class = "title" > Amplifier Piezoelectric Actuator APA300ML - Test Bench< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org0eb094b" > 1. Model of an Amplified Piezoelectric Actuator and Sensor< / a > < / li >
< li > < a href = "#org6f9ba21" > 2. Geometrical Measurements< / a >
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< ul >
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< li > < a href = "#org8044086" > 2.1. Measurement Setup< / a > < / li >
< li > < a href = "#org4293145" > 2.2. Measurement Results< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org50d4352" > 3. Electrical Measurements< / a > < / li >
< li > < a href = "#orgb8a1481" > 4. Stiffness measurement< / a >
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< ul >
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< li > < a href = "#org21bc9b2" > 4.1. APA test< / a > < / li >
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< / ul >
< / li >
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< 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 >
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< / ul >
< / div >
< / div >
< hr >
< p > This report is also available as a < a href = "./test-bench-apa300ml.pdf" > pdf< / a > .< / p >
< hr >
< p >
The goal of this test bench is to extract all the important parameters of the Amplified Piezoelectric Actuator APA300ML.
< / p >
< p >
This include:
< / p >
< ul class = "org-ul" >
< li > Stroke< / li >
< li > Stiffness< / li >
< li > Hysteresis< / 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 > Dynamical behavior< / li >
< / ul >
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< div id = "org664d1fb" class = "figure" >
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< p > < img src = "figs/apa300ML.png" alt = "apa300ML.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Picture of the APA300ML< / p >
< / div >
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< 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 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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Consider a schematic of the Amplified Piezoelectric Actuator in Figure < a href = "#orgc9df44d" > 2< / a > .
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< / p >
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< div id = "orgc9df44d" class = "figure" >
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< 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 >
< / div >
< p >
A voltage \(V_a\) applied to the actuator stacks will induce an actuator force \(F_a\):
< / p >
\begin{equation}
F_a = g_a \cdot V_a
\end{equation}
< p >
A change of length \(dl\) of the sensor stack will induce a voltage \(V_s\):
< / p >
\begin{equation}
V_s = g_s \cdot dl
\end{equation}
< p >
We wish here to experimental measure \(g_a\) and \(g_s\).
< / p >
< p >
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The block-diagram model of the piezoelectric actuator is then as shown in Figure < a href = "#orgc4bba98" > 3< / a > .
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< / p >
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< div id = "orgc4bba98" class = "figure" >
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< 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 >
< / div >
< / div >
< / div >
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< div id = "outline-container-org6f9ba21" class = "outline-2" >
< h2 id = "org6f9ba21" > < span class = "section-number-2" > 2< / span > Geometrical Measurements< / h2 >
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< div class = "outline-text-2" id = "text-2" >
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< div id = "org939ac64" class = "figure" >
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< 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 >
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< div id = "outline-container-org8044086" class = "outline-3" >
< h3 id = "org8044086" > < span class = "section-number-3" > 2.1< / span > Measurement Setup< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
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< div id = "org43d857b" class = "figure" >
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< 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 >
< / div >
< / div >
< / div >
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< div id = "outline-container-org4293145" class = "outline-3" >
< h3 id = "org4293145" > < span class = "section-number-3" > 2.2< / span > Measurement Results< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
< p >
Height (Z) measurements:
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > apa1 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, < span class = "org-type" > -< / span > 0.5 , 3.5 , 3.5 , 42 , 45.5, 52.5 , 46];
apa2 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, < span class = "org-type" > -< / span > 2.5 , < span class = "org-type" > -< / span > 3 , 0 , < span class = "org-type" > -< / span > 1.5 , 1 , < span class = "org-type" > -< / span > 2 , < span class = "org-type" > -< / span > 4];
apa3 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, < span class = "org-type" > -< / span > 1.5 , 15 , 17.5 , 6.5 , 6.5 , 21 , 23];
apa4 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, 6.5 , 14.5 , 9 , 16 , 22 , 29.5 , 21];
apa5 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, < span class = "org-type" > -< / span > 12.5, 16.5 , 28.5 , < span class = "org-type" > -< / span > 43 , < span class = "org-type" > -< / span > 52 , < span class = "org-type" > -< / span > 22.5, < span class = "org-type" > -< / span > 13.5];
apa6 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, < span class = "org-type" > -< / span > 8 , < span class = "org-type" > -< / span > 2 , 5 , < span class = "org-type" > -< / span > 57.5, < span class = "org-type" > -< / span > 62 , < span class = "org-type" > -< / span > 55.5, < span class = "org-type" > -< / span > 52.5];
apa7 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, 19.5 , < span class = "org-type" > -< / span > 8 , < span class = "org-type" > -< / span > 29.5, 75 , 97.5, 70 , 48];
apa7b = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, 9 , < span class = "org-type" > -< / span > 18.5, < span class = "org-type" > -< / span > 30 , 31 , 46.5, 16.5 , 7.5];
apa = {apa1, apa2, apa3, apa4, apa5, apa6, apa7b};
< / pre >
< / div >
< p >
X/Y Positions of the 8 measurement points:
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > W = 20e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Width [m]< / span >
L = 61e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Length [m]< / span >
d = 1e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Distance from border [m]< / span >
l = 15.5e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % [m]< / span >
pos = [[< span class = "org-type" > -< / span > L< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > d; W< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > d], [< span class = "org-type" > -< / span > L< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > l < span class = "org-type" > -< / span > d; W< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > d], [< span class = "org-type" > -< / span > L< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > l < span class = "org-type" > -< / span > d; < span class = "org-type" > -< / span > W< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > d], [< span class = "org-type" > -< / span > L< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > d; < span class = "org-type" > -< / span > W< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > d], [L< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > l < span class = "org-type" > +< / span > d; W< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > d], [L< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > d; W< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > d], [L< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > d; < span class = "org-type" > -< / span > W< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > d], [L< span class = "org-type" > /< / span > 2 < span class = "org-type" > -< / span > l < span class = "org-type" > +< / span > d; < span class = "org-type" > -< / span > W< span class = "org-type" > /< / span > 2 < span class = "org-type" > +< / span > d]];
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > apa_d = zeros(1, 7);
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > < span class = "org-constant" > i< / span > < / span > = < span class = "org-constant" > 1:7< / span >
fun = @(x)max(abs(([pos; apa{< span class = "org-constant" > i< / span > }]< span class = "org-type" > -< / span > [0;0;x(1)])< span class = "org-type" > '*< / span > ([x(2< span class = "org-type" > :< / span > 3);1]< span class = "org-type" > /< / span > norm([x(2< span class = "org-type" > :< / span > 3);1]))));
x0 = [0;0;0];
[x, min_d] = fminsearch(fun,x0);
apa_d(< span class = "org-constant" > i< / span > ) = min_d;
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< table id = "org2443ab1" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Estimated flatness< / caption >
< colgroup >
< col class = "org-right" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Flatness [um]< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 8.9< / td >
< / tr >
< tr >
< td class = "org-right" > 3.1< / td >
< / tr >
< tr >
< td class = "org-right" > 9.1< / td >
< / tr >
< tr >
< td class = "org-right" > 3.0< / td >
< / tr >
< tr >
< td class = "org-right" > 1.9< / td >
< / tr >
< tr >
< td class = "org-right" > 7.1< / td >
< / tr >
< tr >
< td class = "org-right" > 18.7< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
< / div >
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< 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 = "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 >
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< / div >
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< 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 >
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< 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 >
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< div class = "outline-text-2" id = "text-4" >
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< / 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" > > < / span > 0.1 < span class = "org-type" > & < / span > t < span class = "org-type" > < < / 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" > > < / span > 0.2);
F = F(t < span class = "org-type" > > < / span > 0.2);
t = t(t < span class = "org-type" > > < / 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" > > < / 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 >
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< 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)
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< 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 > )
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< 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" >
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< p >
Here are the documentation of the equipment used for this test bench:
< / p >
< ul class = "org-ul" >
< li > Voltage Amplifier: < a href = "doc/PD200-V7-R1.pdf" > PD200< / a > < / li >
< li > Amplified Piezoelectric Actuator: < a href = "doc/APA300ML.pdf" > APA300ML< / a > < / li >
< li > DAC/ADC: Speedgoat < a href = "doc/IO131-OEM-Datasheet.pdf" > IO313< / a > < / li >
< li > Encoder: < a href = "doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf" > Renishaw Vionic< / a > and used < a href = "doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf" > Ruler< / a > < / li >
< li > Interferometer: < a href = "https://www.attocube.com/en/products/laser-displacement-sensor/displacement-measuring-interferometer" > Attocube IDS3010< / a > < / li >
< / ul >
< / div >
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< div id = "orgfd15602" class = "figure" >
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< p > < img src = "figs/test_bench_apa_alone.png" alt = "test_bench_apa_alone.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 7: < / span > Schematic of the Test Bench< / p >
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< 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" >
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< 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" >
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< p >
Using the PD200 amplifier, output a voltage:
\[ V_a = 65 + 85 \sin(2\pi \cdot t) \]
To have a quasi-static excitation between -20 and 150V.
< / p >
< p >
As the gain of the PD200 amplifier is 20, the DAC output voltage should be:
\[ V_{dac}(t) = 3.25 + 4.25\sin(2\pi \cdot t) \]
< / p >
< p >
Verify that the voltage offset of the PD200 is zero!
< / p >
< p >
Measure the output vertical displacement \(d\) using the interferometer.
< / p >
< p >
Then, plot \(d\) as a function of \(V_a\), and perform a linear regression.
Conclude on the obtained stroke.
< / p >
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< h3 id = "org66ac5bb" > < span class = "section-number-3" > 6.2< / span > Stiffness Measurement< / h3 >
< div class = "outline-text-3" id = "text-6-2" >
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< 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.
< / p >
< p >
As the stiffness will be around \(k \approx 10^6 N/m\), an added mass of \(m \approx 100g\) will induce a static deflection of \(\approx 1\mu m\) which should be large enough for a precise measurement using the interferometer.
< / p >
< p >
Then the obtained stiffness is:
< / p >
\begin{equation}
k = \frac{\delta m g}{\delta d}
\end{equation}
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< h3 id = "orgee2d3e8" > < span class = "section-number-3" > 6.3< / span > Hysteresis measurement< / h3 >
< div class = "outline-text-3" id = "text-6-3" >
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< p >
Supply a quasi static sinusoidal excitation \(V_a\) at different voltages.
< / p >
< p >
The offset should be 65V, and the sin amplitude can range from 1V up to 85V.
< / p >
< p >
For each excitation amplitude, the vertical displacement \(d\) of the mass is measured.
< / p >
< p >
Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
< / p >
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< div id = "org7123135" class = "figure" >
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< p > < img src = "figs/expected_hysteresis.png" alt = "expected_hysteresis.png" / >
< / p >
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< 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 >
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< h3 id = "orge6e89ca" > < span class = "section-number-3" > 6.4< / span > Piezoelectric Actuator Constant< / h3 >
< div class = "outline-text-3" id = "text-6-4" >
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< 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 \(d\).
Perform a linear regression to obtain:
< / p >
\begin{equation}
d = g_{d/V_a} \cdot V_a
\end{equation}
< p >
Using the Simscape model of the APA, it is possible to determine the static gain between the actuator force \(F_a\) to the induced displacement \(d\):
< / p >
\begin{equation}
d = g_{d/F_a} \cdot F_a
\end{equation}
< p >
From the two gains, it is then easy to determine \(g_a\):
< / p >
\begin{equation}
g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \cdot \frac{d}{V_a} = \frac{g_{d/V_a}}{g_{d/F_a}}
\end{equation}
< / div >
< / div >
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< 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" >
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< p >
From a quasi static excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\):
< / p >
\begin{equation}
V_s = g_{V_s/V_a} V_a
\end{equation}
< p >
Note here that there is an high pass filter formed by the piezo capacitor and parallel resistor.
The excitation frequency should then be in between the cut-off frequency of this high pass filter and the first resonance.
< / p >
< p >
Alternatively, the gain can be computed from the dynamical identification and taking the gain at the wanted frequency.
< / p >
< p >
Using the simscape model, compute the static gain from the actuator force \(F_a\) to the strain of the sensor stack \(dl\):
< / p >
\begin{equation}
dl = g_{dl/F_a} F_a
\end{equation}
< p >
Then, the static gain from the sensor stack strain \(dl\) to the general voltage \(V_s\) is:
< / p >
\begin{equation}
g_s = \frac{V_s}{dl} = \frac{V_s}{V_a} \cdot \frac{V_a}{F_a} \cdot \frac{F_a}{dl} = \frac{g_{V_s/V_a}}{g_a \cdot g_{dl/F_a}}
\end{equation}
< p >
Alternatively, we could impose an external force to add strain in the APA that should be equally present in all the 3 stacks and equal to 1/5 of the vertical strain.
This external force can be some weight added, or a piezo in parallel.
< / p >
< / div >
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< h3 id = "org86b3954" > < span class = "section-number-3" > 6.6< / span > Capacitance Measurement< / h3 >
< div class = "outline-text-3" id = "text-6-6" >
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< p >
Measure the capacitance of the 3 stacks individually using a precise multi-meter.
< / p >
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< h3 id = "orgc5205df" > < span class = "section-number-3" > 6.7< / span > Dynamical Behavior< / h3 >
< div class = "outline-text-3" id = "text-6-7" >
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< 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 >
< 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 >
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< h3 id = "org2f73a1b" > < span class = "section-number-3" > 6.8< / span > Compare the results obtained for all 7 APA300ML< / h3 >
< div class = "outline-text-3" id = "text-6-8" >
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< p >
Compare all the obtained parameters for all the test APA.
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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 : -1.5 em ; margin-left : 1.5 em ; } < / style > < h2 class = 'citeproc-org-bib-h2' > Bibliography< / h2 >
< div class = "csl-bib-body" >
< div class = "csl-entry" > < a name = "citeproc_bib_item_1" > < / a > Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” < i > CEAS Space Journal< / i > 10 (2). Springer:157– < / div >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2021-03-15 lun. 11:35< / p >
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