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< title > Amplifier Piezoelectric Actuator APA300ML - Test Bench< / title >
< meta name = "author" content = "Dehaeze Thomas" / >
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< 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 = "#org61dfb38" > 1. Model of an Amplified Piezoelectric Actuator and Sensor< / a > < / li >
< li > < a href = "#orga39596d" > 2. Geometrical Measurements< / a >
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< ul >
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< li > < a href = "#orgf18d554" > 2.1. Measurement Setup< / a > < / li >
< li > < a href = "#orgab6a290" > 2.2. Measurement Results< / a > < / li >
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< / ul >
< / li >
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< 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 >
< 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 >
< / ul >
< / li >
< li > < a href = "#org90aaad1" > 6. 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 = "orgca99cce" 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-org61dfb38" class = "outline-2" >
< h2 id = "org61dfb38" > < 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 = "#org2432201" > 2< / a > .
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< / p >
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< div id = "org2432201" 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 = "#orgc142156" > 3< / a > .
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< / p >
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< div id = "orgc142156" 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-orga39596d" class = "outline-2" >
< h2 id = "orga39596d" > < 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 = "orgc8762e5" 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 class = "outline-text-3" id = "text-2-1" >
< div id = "orgec2c3f2" 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 >
< / div >
< / 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 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 >
< table id = "org68cc21a" 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 >
< col class = "org-right" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Flatness [um]< / th >
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< / thead >
< tbody >
< tr >
< td class = "org-right" > 8.9< / td >
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< tr >
< td class = "org-right" > 3.1< / td >
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< tr >
< td class = "org-right" > 9.1< / td >
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< 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 >
< div id = "outline-container-orgc48230a" class = "outline-2" >
< h2 id = "orgc48230a" > < span class = "section-number-2" > 3< / span > Electrical Measurements< / h2 >
< / div >
< div id = "outline-container-org5c918ed" class = "outline-2" >
< h2 id = "org5c918ed" > < span class = "section-number-2" > 4< / span > Test-Bench Description< / h2 >
< div class = "outline-text-2" id = "text-4" >
< div class = "note" id = "org4dcad91" >
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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 = "org7bcb57f" 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 6: < / span > Schematic of the Test Bench< / p >
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< / div >
< / div >
< / div >
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< 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" >
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< / div >
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< 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" >
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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 >
< / div >
< / div >
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< 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" >
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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}
< / div >
< / div >
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< 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" >
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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 = "org19a134a" 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 7: < / 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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< / div >
< / div >
< / div >
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< 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" >
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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-orgd45032c" class = "outline-3" >
< h3 id = "orgd45032c" > < span class = "section-number-3" > 5.5< / span > Piezoelectric Sensor Constant< / h3 >
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From a quasi static excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\):
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\begin{equation}
V_s = g_{V_s/V_a} V_a
\end{equation}
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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.
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Alternatively, the gain can be computed from the dynamical identification and taking the gain at the wanted frequency.
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Using the simscape model, compute the static gain from the actuator force \(F_a\) to the strain of the sensor stack \(dl\):
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\begin{equation}
dl = g_{dl/F_a} F_a
\end{equation}
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Then, the static gain from the sensor stack strain \(dl\) to the general voltage \(V_s\) is:
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\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}
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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.
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< h3 id = "org72919e5" > < span class = "section-number-3" > 5.6< / span > Capacitance Measurement< / h3 >
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Measure the capacitance of the 3 stacks individually using a precise multi-meter.
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< h3 id = "org81e2e82" > < span class = "section-number-3" > 5.7< / span > Dynamical Behavior< / h3 >
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Perform a system identification from \(V_a\) to the measured displacement \(d\) by the interferometer and by the encoder, and to the generated voltage \(V_s\).
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This can be performed using different excitation signals.
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This can also be performed with and without the encoder fixed to the APA.
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< h3 id = "orgcac6823" > < span class = "section-number-3" > 5.8< / span > Compare the results obtained for all 7 APA300ML< / h3 >
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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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< style > . csl-entry { text-indent : -1.5 em ; margin-left : 1.5 em ; } < / style > < h2 class = 'citeproc-org-bib-h2' > Bibliography< / h2 >
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< 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 >
2021-03-01 09:18:16 +01:00
< p class = "date" > Created: 2021-03-01 lun. 09:17< / p >
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