Update analysis
This commit is contained in:
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matlab/STEPS/full_APA300ML_K.CSV
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matlab/STEPS/full_APA300ML_K.CSV
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36
matlab/STEPS/full_APA300ML_M.CSV
Normal file
36
matlab/STEPS/full_APA300ML_M.CSV
Normal file
@@ -0,0 +1,36 @@
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||||
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|
||||
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|
||||
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|
||||
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|
||||
-9.2804884781376160e-10,-9.9176308427033486e-06,-2.2030882961226875e-08,-1.2794363402458843e-07,4.8637277703907580e-10,-9.1808942751358736e-08,7.1669501117728774e-09,9.9466907193319597e-06,-1.7264584136738321e-09,-1.2858507492534756e-07,1.0746858886167557e-10,9.1847805211491326e-08,-2.5636867082473507e-08,1.2132194952007389e-10,6.9883018200074241e-09,-2.9680455181253399e-08,-1.3443466396538433e-10,2.5763832486765300e-11,9.0434715350633260e-12,6.6832417733352129e-11,2.1093863558312420e-11,4.2663118169011185e-08,9.5342702851480413e-14,-2.6428344165305951e-13,-2.8124976762155787e-08,9.0946404389049521e-09,-2.0813984774814473e-10,1.1134104737899188e-06,-2.6770657790971538e-10,-9.1549075245360975e-11,-2.2746595471083301e-07,-5.5440105502280843e-07,1.0644559644311949e-07,-1.2727795977359786e-07,-4.0087268452467515e-04,-1.3726013554048109e-05
|
||||
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|
||||
1.7828026365384081e-08,-2.4491820723842003e-07,4.8077311716313397e-10,2.6012824175730070e-08,-3.5780709150316614e-10,5.6432011340062909e-08,-1.3160457495372054e-10,-2.5969121980411849e-07,7.8416166288207537e-10,-2.5779443973740474e-08,-1.0073277922273370e-11,5.6366196180689756e-08,1.1643532467258393e-08,-2.6744192499979445e-07,-8.9211460899106898e-10,2.8100830753871640e-11,6.8744841896691323e-11,2.7627234437565930e-10,-7.3851264192454854e-12,-1.1936193963848113e-05,-5.5858578368626676e-12,2.6830981552151709e-14,1.6602468379509925e-13,-5.3653882225437740e-08,-3.9956704099087598e-08,6.9200247432634862e-05,1.5643254887016203e-08,-9.1549075245360975e-11,-2.0276161487202595e-10,9.5752606365202938e-07,8.1652766316775640e-08,1.8338734344352090e-07,-2.3414727196993738e-08,2.9607839458613745e-09,5.8192164593301554e-06,-1.5917184658560470e-04
|
||||
1.2443642889233273e-02,-2.2643886423869724e-05,7.3014689962518399e-03,-4.3414578938503394e-07,-4.2555343598068418e-04,-1.7218986433125755e-06,-2.3889520659404521e-02,6.7836178728686985e-06,1.4203654857645194e-02,-1.3285138021445834e-07,-8.4160580990647028e-04,-2.5096760682066648e-07,-3.5216199283537994e-03,-2.2534462134192864e-05,-1.8241686655288705e-02,1.4434270917625216e-08,5.3628479941231250e-05,9.8683889189486147e-08,4.9438528515937297e-15,8.5337456866444873e-15,-2.0386174888479484e-15,-2.3773042040314455e-17,1.3647281594365435e-18,2.4728530947840425e-17,5.1400833644824669e-03,4.3233606789047737e-05,4.7274882017703149e-02,-2.2746595471083301e-07,-1.2094497818069785e-04,8.1652766316775640e-08,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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||||
-1.2665814760891294e-02,1.4929863741048841e-06,2.8550602200522721e-02,2.5774124427060330e-08,3.4451743146389919e-04,8.9412622862594666e-07,1.1517387162601905e-02,-7.0450284360939704e-07,2.6324082796649471e-02,-1.8717415093643504e-08,3.1514819424967918e-04,2.1621817296699036e-07,1.6906857532482836e-03,1.9265376581661267e-05,5.3358689150398465e-02,-9.2523181038276382e-08,2.7846239084985009e-04,-4.1434277942299052e-08,-4.1357329724553186e-15,-9.0495997073290111e-15,1.7237953511911040e-15,2.2928517333650290e-17,-2.4518395459434443e-18,-2.6752289572637881e-17,-9.6814722815906265e-04,-2.0760469627625316e-05,2.4542545638085618e-02,1.0644559644311949e-07,-1.6185862173618542e-04,-2.3414727196993738e-08,0.0000000000000000e+00,0.0000000000000000e+00,1.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00,0.0000000000000000e+00
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||||
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||||
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||||
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|
||||
|
61
matlab/STEPS/full_APA300ML_out_nodes_3D.txt
Normal file
61
matlab/STEPS/full_APA300ML_out_nodes_3D.txt
Normal file
@@ -0,0 +1,61 @@
|
||||
|
||||
LIST ALL SELECTED NODES. DSYS= 0
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Mechanical Enterprise
|
||||
|
||||
00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188
|
||||
|
||||
Unknown
|
||||
|
||||
|
||||
|
||||
NODE X Y Z THXY THYZ THZX
|
||||
1 0.0000 0.0000 0.28000E-001 0.00 0.00 0.00
|
||||
1228810 0.0000 0.0000 -0.28000E-001 0.00 0.00 0.00
|
||||
1228811 -0.30000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
1228812 0.10000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
1228813 0.30000E-001 0.0000 0.0000 0.00 0.00 0.00
|
||||
|
||||
LIST MASTERS ON ALL SELECTED NODES.
|
||||
CURRENT DOF SET= UX UY UZ ROTX ROTY ROTZ
|
||||
|
||||
*** ANSYS - ENGINEERING ANALYSIS SYSTEM RELEASE 2020 R2 20.2 ***
|
||||
DISTRIBUTED ANSYS Mechanical Enterprise
|
||||
|
||||
00208316 VERSION=WINDOWS x64 10:10:05 MAR 26, 2021 CP= 2.188
|
||||
|
||||
Unknown
|
||||
|
||||
|
||||
NODE LABEL SUPPORT
|
||||
1 UX
|
||||
1 UY
|
||||
1 UZ
|
||||
1 ROTX
|
||||
1 ROTY
|
||||
1 ROTZ
|
||||
1228810 UX
|
||||
1228810 UY
|
||||
1228810 UZ
|
||||
1228810 ROTX
|
||||
1228810 ROTY
|
||||
1228810 ROTZ
|
||||
1228811 UX
|
||||
1228811 UY
|
||||
1228811 UZ
|
||||
1228811 ROTX
|
||||
1228811 ROTY
|
||||
1228811 ROTZ
|
||||
1228812 UX
|
||||
1228812 UY
|
||||
1228812 UZ
|
||||
1228812 ROTX
|
||||
1228812 ROTY
|
||||
1228812 ROTZ
|
||||
1228813 UX
|
||||
1228813 UY
|
||||
1228813 UZ
|
||||
1228813 ROTX
|
||||
1228813 ROTY
|
||||
1228813 ROTZ
|
||||
@@ -61,7 +61,7 @@ for i = 1:7
|
||||
apa_d(i) = min_d;
|
||||
end
|
||||
|
||||
% Stroke Measurement
|
||||
% Stroke and Hysteresis Measurement
|
||||
% <<sec:test_apa_stroke_measurements>>
|
||||
|
||||
% The goal is here to verify that the stroke of the APA300ML is as specified in the datasheet.
|
||||
@@ -111,177 +111,99 @@ xlabel('Voltage [V]'); ylabel('Displacement [$\mu m$]')
|
||||
legend('location', 'southwest', 'FontSize', 8)
|
||||
xlim([-20, 150]); ylim([-250, 0]);
|
||||
|
||||
% X-Bending Mode
|
||||
% Flexible Mode Measurement
|
||||
% SCHEDULED: <2024-03-27 Wed>
|
||||
% <<sec:test_apa_spurious_resonances>>
|
||||
|
||||
% The vibrometer is setup to measure the X-bending motion is shown in Figure ref:fig:test_apa_meas_setup_X_bending.
|
||||
% The APA is excited with an instrumented hammer having a solid metallic tip.
|
||||
% The impact point is on the back-side of the APA aligned with the top measurement point.
|
||||
% In this section, the flexible modes of the APA300ML are investigated both experimentally and using a Finite Element Model.
|
||||
|
||||
% #+name: fig:test_apa_meas_setup_X_bending
|
||||
% #+caption: X-Bending measurement setup
|
||||
% #+attr_latex: :width 0.7\linewidth
|
||||
% To experimentally estimate these modes, the APA is fixed on one end (see Figure ref:fig:test_apa_meas_setup_torsion).
|
||||
% A Laser Doppler Vibrometer[fn:6] is used to measure the difference of motion between two "red" points (i.e. the torsion of the APA along the vertical direction) and an instrumented hammer[fn:7] is used to excite the flexible modes.
|
||||
% Using this setup, the transfer function from the injected force to the measured rotation can be computed in different conditions and the frequency and mode shapes of the flexible modes can be estimated.
|
||||
|
||||
% The flexible modes for the same condition (i.e. one mechanical interface of the APA300ML fixed) are estimated using a finite element software and the results are shown in Figure ref:fig:test_apa_mode_shapes.
|
||||
|
||||
% #+name: fig:test_apa_mode_shapes
|
||||
% #+caption: Spurious resonances - Change this with the updated FEM analysis of the APA300ML
|
||||
% #+attr_latex: :width 0.9\linewidth
|
||||
% [[file:figs/test_apa_mode_shapes.png]]
|
||||
|
||||
% #+name: fig:test_apa_meas_setup_torsion
|
||||
% #+caption: Measurement setup with a Laser Doppler Vibrometer and one instrumental hammer. Here the $Z$ torsion is measured.
|
||||
% #+attr_latex: :width 0.6\linewidth
|
||||
% [[file:figs/test_apa_meas_setup_torsion.jpg]]
|
||||
|
||||
% Two other similar measurements are performed to measured the bending of the APA around the $X$ direction and around the $Y$ direction (see Figure ref:fig:test_apa_meas_setup_modes).
|
||||
|
||||
% #+name: fig:test_apa_meas_setup_modes
|
||||
% #+caption: Experimental setup to measured flexible modes of the APA300ML. For the bending in the $X$ direction, the impact point is located at the back of the top measurement point. For the bending in the $Y$ direction, the impact point is located on the back surface of the top interface (on the back of the 2 measurements points).
|
||||
% #+begin_figure
|
||||
% #+attr_latex: :caption \subcaption{\label{fig:test_apa_meas_setup_X_bending}$X$ bending}
|
||||
% #+attr_latex: :options {0.49\textwidth}
|
||||
% #+begin_subfigure
|
||||
% #+attr_latex: :width 0.95\linewidth
|
||||
% [[file:figs/test_apa_meas_setup_X_bending.jpg]]
|
||||
% #+end_subfigure
|
||||
% #+attr_latex: :caption \subcaption{\label{fig:test_apa_meas_setup_Y_bending}$Y$ Bending}
|
||||
% #+attr_latex: :options {0.49\textwidth}
|
||||
% #+begin_subfigure
|
||||
% #+attr_latex: :width 0.95\linewidth
|
||||
% [[file:figs/test_apa_meas_setup_Y_bending.jpg]]
|
||||
% #+end_subfigure
|
||||
% #+end_figure
|
||||
|
||||
% The data is loaded.
|
||||
|
||||
%% Load Data
|
||||
%% X-Bending Identification
|
||||
% Load Data
|
||||
bending_X = load('apa300ml_bending_X_top.mat');
|
||||
|
||||
|
||||
|
||||
% The configuration (Sampling time and windows) for =tfestimate= is done:
|
||||
|
||||
%% Spectral Analysis setup
|
||||
% Spectral Analysis setup
|
||||
Ts = bending_X.Track1_X_Resolution; % Sampling Time [s]
|
||||
Nfft = floor(1/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
|
||||
|
||||
|
||||
% The transfer function from the input force to the output "rotation" (difference between the two measured distances).
|
||||
|
||||
%% Compute the transfer function from applied force to measured rotation
|
||||
% Compute the transfer function from applied force to measured rotation
|
||||
[G_bending_X, f] = tfestimate(bending_X.Track1, bending_X.Track2, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
|
||||
|
||||
% The result is shown in Figure ref:fig:test_apa_meas_freq_bending_x.
|
||||
|
||||
% The can clearly observe a nice peak at 280Hz, and then peaks at the odd "harmonics" (third "harmonic" at 840Hz, and fifth "harmonic" at 1400Hz).
|
||||
|
||||
%% Plot the transfer function
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_bending_X), 'k-');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 2e-1]);
|
||||
text(280, 5.5e-2,{'280Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(840, 2.0e-3,{'840Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(1400, 7.0e-3,{'1400Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
|
||||
% Y-Bending Mode
|
||||
|
||||
% The setup to measure the Y-bending is shown in Figure ref:fig:test_apa_meas_setup_Y_bending.
|
||||
|
||||
% The impact point of the instrumented hammer is located on the back surface of the top interface (on the back of the 2 measurements points).
|
||||
|
||||
% #+name: fig:test_apa_meas_setup_Y_bending
|
||||
% #+caption: Y-Bending measurement setup
|
||||
% #+attr_latex: :width 0.7\linewidth
|
||||
% [[file:figs/test_apa_meas_setup_Y_bending.jpg]]
|
||||
|
||||
% The data is loaded, and the transfer function from the force to the measured rotation is computed.
|
||||
|
||||
%% Load Data
|
||||
%% Y-Bending identification
|
||||
% Load Data
|
||||
bending_Y = load('apa300ml_bending_Y_top.mat');
|
||||
|
||||
%% Compute the transfer function
|
||||
% Compute the transfer function
|
||||
[G_bending_Y, ~] = tfestimate(bending_Y.Track1, bending_Y.Track2, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
%% Z-Torsion identification
|
||||
% Load data
|
||||
torsion = load('apa300ml_torsion_top.mat');
|
||||
|
||||
% Compute transfer function
|
||||
[G_torsion_top, ~] = tfestimate(torsion.Track1, torsion.Track2, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
% The results are shown in Figure ref:fig:test_apa_meas_freq_bending_y.
|
||||
% The main resonance is at 412Hz, and we also see the third "harmonic" at 1220Hz.
|
||||
|
||||
|
||||
%% Plot the transfer function
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_bending_Y), 'k-');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 3e-2])
|
||||
text(412, 1.5e-2,{'412Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(1218, 1.5e-2,{'1220Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
|
||||
% Z-Torsion Mode
|
||||
|
||||
% Finally, we measure the Z-torsion resonance as shown in Figure ref:fig:test_apa_meas_setup_torsion_bis.
|
||||
|
||||
% The excitation is shown on the other side of the APA, on the side to excite the torsion motion.
|
||||
|
||||
% #+name: fig:test_apa_meas_setup_torsion_bis
|
||||
% #+caption: Z-Torsion measurement setup
|
||||
% #+attr_latex: :width 0.7\linewidth
|
||||
% [[file:figs/test_apa_meas_setup_torsion_bis.jpg]]
|
||||
|
||||
% The data is loaded, and the transfer function computed.
|
||||
|
||||
%% Load Data
|
||||
% Load Data
|
||||
torsion = load('apa300ml_torsion_left.mat');
|
||||
|
||||
%% Compute transfer function
|
||||
% Compute transfer function
|
||||
[G_torsion, ~] = tfestimate(torsion.Track1, torsion.Track2, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
|
||||
|
||||
% The results are shown in Figure ref:fig:test_apa_meas_freq_torsion_z.
|
||||
% We observe a first peak at 267Hz, which corresponds to the X-bending mode that was measured at 280Hz.
|
||||
% And then a second peak at 415Hz, which corresponds to the X-bending mode that was measured at 412Hz.
|
||||
% A third mode at 800Hz could correspond to this torsion mode.
|
||||
% The three measured frequency response functions are shown in Figure ref:fig:test_apa_meas_freq_compare.
|
||||
% - a clear $x$ bending mode at $280\,\text{Hz}$
|
||||
% - a clear $y$ bending mode at $412\,\text{Hz}$
|
||||
% - for the $z$ torsion test, the $y$ bending mode is also excited and observed, and we may see a mode at $800\,\text{Hz}$
|
||||
|
||||
|
||||
%% Plot the transfer function
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_torsion), 'k-');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 2e-2])
|
||||
text(415, 4.3e-3,{'415Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(267, 8e-4,{'267Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
plot(f, abs(G_bending_X), 'DisplayName', '$X$ bending');
|
||||
plot(f, abs(G_bending_Y), 'DisplayName', '$Y$ bending');
|
||||
plot(f, abs(G_torsion), 'DisplayName', '$Z$ torsion');
|
||||
text(280, 5.5e-2,{'280Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(412, 1.5e-2,{'412Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(800, 6e-4,{'800Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
|
||||
|
||||
|
||||
% #+name: fig:test_apa_meas_freq_torsion_z
|
||||
% #+caption: Obtained FRF for the Z-torsion
|
||||
% #+RESULTS:
|
||||
% [[file:figs/test_apa_meas_freq_torsion_z.png]]
|
||||
|
||||
% In order to verify that, the APA is excited on the top part such that the torsion mode should not be excited.
|
||||
|
||||
%% Load data
|
||||
torsion = load('apa300ml_torsion_top.mat');
|
||||
|
||||
%% Compute transfer function
|
||||
[G_torsion_top, ~] = tfestimate(torsion.Track1, torsion.Track2, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
|
||||
|
||||
% The two FRF are compared in Figure ref:fig:test_apa_meas_freq_torsion_z_comp.
|
||||
% It is clear that the first two modes does not correspond to the torsional mode.
|
||||
% Maybe the resonance at 800Hz, or even higher resonances. It is difficult to conclude here.
|
||||
|
||||
%% Plot the two transfer functions
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_torsion), 'k-', 'DisplayName', 'Left excitation');
|
||||
plot(f, abs(G_torsion_top), '-', 'DisplayName', 'Top excitation');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 2e-2])
|
||||
text(415, 4.3e-3,{'415Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(267, 8e-4,{'267Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
text(800, 2e-3,{'800Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
legend('location', 'northwest');
|
||||
|
||||
% Compare
|
||||
% The three measurements are shown in Figure ref:fig:test_apa_meas_freq_compare.
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_torsion), 'DisplayName', 'Torsion');
|
||||
plot(f, abs(G_bending_X), 'DisplayName', 'Bending - X');
|
||||
plot(f, abs(G_bending_Y), 'DisplayName', 'Bending - Y');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 1e-1]);
|
||||
legend('location', 'southeast');
|
||||
xlim([50, 2e3]); ylim([5e-5, 2e-1]);
|
||||
legend('location', 'northeast', 'FontSize', 8)
|
||||
|
||||
@@ -119,7 +119,7 @@ xlabel('Time [s]'); ylabel('Displacement $d_e$ [$\mu$m]');
|
||||
% | 6 | 1.7 | 1.92 |
|
||||
% | 8 | 1.73 | 1.98 |
|
||||
|
||||
% The stiffness can also be computed using equation eqref:eq:test_apa_res_freq by knowing the main vertical resonance frequency $\omega_z \approx 94\,\text{Hz}$ (estimated by the dynamical measurements shown in section ref:ssec:test_apa_meas_frf_disp) and the suspended mass $m_{\text{sus}} = 5.7\,\text{kg}$.
|
||||
% The stiffness can also be computed using equation eqref:eq:test_apa_res_freq by knowing the main vertical resonance frequency $\omega_z \approx 95\,\text{Hz}$ (estimated by the dynamical measurements shown in section ref:ssec:test_apa_meas_dynamics) and the suspended mass $m_{\text{sus}} = 5.7\,\text{kg}$.
|
||||
|
||||
% \begin{equation} \label{eq:test_apa_res_freq}
|
||||
% \omega_z = \sqrt{\frac{k}{m_{\text{sus}}}}
|
||||
@@ -204,7 +204,7 @@ save('mat/meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
|
||||
% - A "stiffness line" indicating a static gain equal to $\approx -17\,\mu m/V$.
|
||||
% The minus sign comes from the fact that an increase in voltage stretches the piezoelectric stack that then reduces the height of the APA
|
||||
% - A lightly damped resonance at $95\,\text{Hz}$
|
||||
% - A "mass line" up to $\approx 800\,\text{Hz}$, above which some resonances appear
|
||||
% - A "mass line" up to $\approx 800\,\text{Hz}$, above which some resonances appear. These additional resonances might be coming from the limited stiffness of the encoder support or from the limited compliance of the APA support.
|
||||
|
||||
|
||||
%% Plot the FRF from u to de
|
||||
@@ -305,17 +305,17 @@ xlim([10, 2e3]);
|
||||
|
||||
|
||||
%% Load the data
|
||||
wi_k = load('frf_data_1_sweep_lf_with_R.mat', 't', 'Vs', 'Va'); % With the resistor
|
||||
wo_k = load('frf_data_1_sweep_lf.mat', 't', 'Vs', 'Va'); % Without the resistor
|
||||
wi_k = load('frf_data_1_sweep_lf_with_R.mat', 't', 'Vs', 'u'); % With the resistor
|
||||
wo_k = load('frf_data_1_sweep_lf.mat', 't', 'Vs', 'u'); % Without the resistor
|
||||
|
||||
%% Large Hanning window for good low frequency estimate
|
||||
Nfft = floor(50/Ts);
|
||||
win = hanning(Nfft);
|
||||
Noverlap = floor(Nfft/2);
|
||||
|
||||
%% Compute the transfer functions from Va to Vs
|
||||
[frf_wo_k, f] = tfestimate(wo_k.Va, wo_k.Vs, win, Noverlap, Nfft, 1/Ts);
|
||||
[frf_wi_k, ~] = tfestimate(wi_k.Va, wi_k.Vs, win, Noverlap, Nfft, 1/Ts);
|
||||
%% Compute the transfer functions from u to Vs
|
||||
[frf_wo_k, f] = tfestimate(wo_k.u, wo_k.Vs, win, Noverlap, Nfft, 1/Ts);
|
||||
[frf_wi_k, ~] = tfestimate(wi_k.u, wi_k.Vs, win, Noverlap, Nfft, 1/Ts);
|
||||
|
||||
%% Model for the high pass filter
|
||||
C = 5.1e-6; % Sensor Stack capacitance [F]
|
||||
|
||||
177
matlab/test_apa_3_model_2dof.m
Normal file
177
matlab/test_apa_3_model_2dof.m
Normal file
@@ -0,0 +1,177 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./src/'); % Path for scripts
|
||||
addpath('./mat/'); % Path for data
|
||||
|
||||
addpath('./STEPS/'); % Path for Simscape Model
|
||||
|
||||
%% Linearization options
|
||||
opts = linearizeOptions;
|
||||
opts.SampleTime = 0;
|
||||
|
||||
%% Open Simscape Model
|
||||
mdl = 'test_apa_simscape'; % Name of the Simulink File
|
||||
open(mdl); % Open Simscape Model
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Input/Output definition of the Model
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/u'], 1, 'openinput'); io_i = io_i + 1; % DAC Voltage
|
||||
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
|
||||
io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder
|
||||
|
||||
% Tuning of the APA model
|
||||
% <<ssec:test_apa_2dof_model_tuning>>
|
||||
|
||||
% 9 parameters ($m$, $k_1$, $c_1$, $k_e$, $c_e$, $k_a$, $c_a$, $g_s$ and $g_a$) have to be tuned such that the dynamics of the model (Figure ref:fig:test_apa_2dof_model_simscape) well represents the identified dynamics in Section ref:sec:test_apa_dynamics.
|
||||
|
||||
% #+name: fig:test_apa_2dof_model_simscape
|
||||
% #+caption: Schematic of the two degrees of freedom model of the APA300ML with input $V_a$ and outputs $d_e$ and $V_s$
|
||||
% [[file:figs/test_apa_2dof_model_simscape.png]]
|
||||
|
||||
|
||||
%% Stiffness values for the 2DoF APA model
|
||||
k1 = 0.38e6; % Estimated Shell Stiffness [N/m]
|
||||
|
||||
w0 = 2*pi*95; % Resonance frequency [rad/s]
|
||||
m = 5.7; % Suspended mass [kg]
|
||||
ktot = m*(w0)^2; % Total Axial Stiffness to have to wanted resonance frequency [N/m]
|
||||
|
||||
ka = 1.5*(ktot-k1); % Stiffness of the (two) actuator stacks [N/m]
|
||||
ke = 2*ka; % Stiffness of the Sensor stack [N/m]
|
||||
|
||||
%% Damping values for the 2DoF APA model
|
||||
c1 = 20; % Damping for the Shell [N/(m/s)]
|
||||
ca = 100; % Damping of the actuators stacks [N/(m/s)]
|
||||
ce = 2*ca; % Damping of the sensor stack [N/(m/s)]
|
||||
|
||||
%% Estimation ot the sensor and actuator gains
|
||||
% Initialize the structure with unitary sensor and actuator "gains"
|
||||
n_hexapod = struct();
|
||||
n_hexapod.actuator = initializeAPA(...
|
||||
'type', '2dof', ...
|
||||
'k', k1, ...
|
||||
'ka', ka, ...
|
||||
'ke', ke, ...
|
||||
'c', c1, ...
|
||||
'ca', ca, ...
|
||||
'ce', ce, ...
|
||||
'Ga', 1, ... % Actuator constant [N/V]
|
||||
'Gs', 1 ... % Sensor constant [V/m]
|
||||
);
|
||||
|
||||
c_granite = 0; % Do not take into account damping added by the air bearing
|
||||
|
||||
% Run the linearization
|
||||
G_norm = linearize(mdl, io, 0.0, opts);
|
||||
G_norm.InputName = {'u'};
|
||||
G_norm.OutputName = {'Vs', 'de'};
|
||||
|
||||
% Load Identification Data to estimate the two gains
|
||||
load('meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
|
||||
|
||||
% Estimation ot the Actuator Gain
|
||||
fa = 10; % Frequency where the two FRF should match [Hz]
|
||||
[~, i_f] = min(abs(f - fa));
|
||||
ga = -abs(enc_frf(i_f,1))./abs(evalfr(G_norm('de', 'u'), 1i*2*pi*fa));
|
||||
|
||||
% Estimation ot the Sensor Gain
|
||||
fs = 600; % Frequency where the two FRF should match [Hz]
|
||||
[~, i_f] = min(abs(f - fs))
|
||||
gs = -abs(iff_frf(i_f,1))./abs(evalfr(G_norm('Vs', 'u'), 1i*2*pi*fs))/ga;
|
||||
|
||||
% Obtained Dynamics
|
||||
% <<ssec:test_apa_2dof_model_result>>
|
||||
|
||||
% The dynamics of the 2DoF APA300ML model is now extracted using optimized parameters (listed in Table ref:tab:test_apa_2dof_parameters) from the Simscape model.
|
||||
% It is compared with the experimental data in Figure ref:fig:test_apa_2dof_comp_frf.
|
||||
|
||||
% A good match can be observed between the model and the experimental data, both for the encoder and for the force sensor.
|
||||
% This indicates that this model represents well the axial dynamics of the APA300ML.
|
||||
|
||||
|
||||
%% 2DoF APA300ML with optimized parameters
|
||||
n_hexapod = struct();
|
||||
n_hexapod.actuator = initializeAPA(...
|
||||
'type', '2dof', ...
|
||||
'k', k1, ...
|
||||
'ka', ka, ...
|
||||
'ke', ke, ...
|
||||
'c', c1, ...
|
||||
'ca', ca, ...
|
||||
'ce', ce, ...
|
||||
'Ga', ga, ...
|
||||
'Gs', gs ...
|
||||
);
|
||||
|
||||
%% Identification of the APA300ML with optimized parameters
|
||||
G_2dof = exp(-s*Ts)*linearize(mdl, io, 0.0, opts);
|
||||
G_2dof.InputName = {'u'};
|
||||
G_2dof.OutputName = {'Vs', 'de'};
|
||||
|
||||
%% Comparison of the measured FRF and the optimized 2DoF model of the APA300ML
|
||||
freqs = 5*logspace(0, 3, 1000);
|
||||
figure;
|
||||
tiledlayout(3, 2, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(enc_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2], 'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_2dof('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '2DoF Model')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-8, 1e-3]);
|
||||
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
|
||||
ax1b = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(iff_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
|
||||
for i = 2:length(apa_nums)
|
||||
plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2], 'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_2dof('Vs', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '2DoF Model')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-2, 1e2]);
|
||||
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
ax2b = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_2dof('Vs', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2,ax1b,ax2b],'x');
|
||||
xlim([10, 2e3]);
|
||||
202
matlab/test_apa_4_model_flexible.m
Normal file
202
matlab/test_apa_4_model_flexible.m
Normal file
@@ -0,0 +1,202 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
%% Path for functions, data and scripts
|
||||
addpath('./src/'); % Path for scripts
|
||||
addpath('./mat/'); % Path for data
|
||||
|
||||
addpath('./STEPS/'); % Path for Simscape Model
|
||||
|
||||
%% Linearization options
|
||||
opts = linearizeOptions;
|
||||
opts.SampleTime = 0;
|
||||
|
||||
%% Open Simscape Model
|
||||
mdl = 'test_apa_simscape'; % Name of the Simulink File
|
||||
open(mdl); % Open Simscape Model
|
||||
|
||||
%% Colors for the figures
|
||||
colors = colororder;
|
||||
|
||||
%% Input/Output definition of the Model
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/u'], 1, 'openinput'); io_i = io_i + 1; % DAC Voltage
|
||||
io(io_i) = linio([mdl, '/Vs'], 1, 'openoutput'); io_i = io_i + 1; % Sensor Voltage
|
||||
io(io_i) = linio([mdl, '/de'], 1, 'openoutput'); io_i = io_i + 1; % Encoder
|
||||
|
||||
% Identification of the Actuator and Sensor constants
|
||||
% <<ssec:test_apa_flexible_ga_gs>>
|
||||
|
||||
% Once the APA300ML /super element/ is included in the Simscape model, the transfer function from $F_a$ to $d_L$ and $d_e$ can be identified.
|
||||
% The gains $g_a$ and $g_s$ can then be tuned such that the gain of the transfer functions are matching the identified ones.
|
||||
|
||||
% By doing so, $g_s = 4.9\,V/\mu m$ and $g_a = 23.2\,N/V$ are obtained.
|
||||
|
||||
|
||||
%% Identification of the actuator and sensor "constants"
|
||||
% Initialize the APA as a flexible body with unity "constants"
|
||||
n_hexapod.actuator = initializeAPA(...
|
||||
'type', 'flexible', ...
|
||||
'ga', 1, ...
|
||||
'gs', 1);
|
||||
|
||||
c_granite = 100; % Rought estimation of the damping added by the air bearing
|
||||
|
||||
% Identify the dynamics
|
||||
G_norm = linearize(mdl, io, 0.0, opts);
|
||||
G_norm.InputName = {'u'};
|
||||
G_norm.OutputName = {'Vs', 'de'};
|
||||
|
||||
% Load Identification Data to estimate the two gains
|
||||
load('meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
|
||||
|
||||
% Actuator Constant in [N/V]
|
||||
ga = -mean(abs(enc_frf(f>10 & f<20)))./dcgain(G_norm('de', 'u'));
|
||||
|
||||
% Sensor Constant in [V/m]
|
||||
gs = -mean(abs(iff_frf(f>400 & f<500)))./(ga*abs(squeeze(freqresp(G_norm('Vs', 'u'), 1e3, 'Hz'))));
|
||||
|
||||
|
||||
|
||||
|
||||
% To make sure these "gains" are physically valid, it is possible to estimate them from physical properties of the piezoelectric stack material.
|
||||
|
||||
% From [[cite:&fleming14_desig_model_contr_nanop_system p. 123]], the relation between relative displacement $d_L$ of the sensor stack and generated voltage $V_s$ is given by eqref:eq:test_apa_piezo_strain_to_voltage and from [[cite:&fleming10_integ_strain_force_feedb_high]] the relation between the force $F_a$ and the applied voltage $V_a$ is given by eqref:eq:test_apa_piezo_voltage_to_force.
|
||||
|
||||
% \begin{subequations}
|
||||
% \begin{align}
|
||||
% V_s &= \underbrace{\frac{d_{33}}{\epsilon^T s^D n}}_{g_s} d_L \label{eq:test_apa_piezo_strain_to_voltage} \\
|
||||
% F_a &= \underbrace{d_{33} n k_a}_{g_a} \cdot V_a, \quad k_a = \frac{c^{E} A}{L} \label{eq:test_apa_piezo_voltage_to_force}
|
||||
% \end{align}
|
||||
% \end{subequations}
|
||||
|
||||
% Parameters used in equations eqref:eq:test_apa_piezo_strain_to_voltage and eqref:eq:test_apa_piezo_voltage_to_force are described in Table ref:tab:test_apa_piezo_properties.
|
||||
|
||||
% Unfortunately, the manufacturer of the stack was not willing to share the piezoelectric material properties of the stack used in the APA300ML.
|
||||
% However, based on available properties of the APA300ML stacks in the data-sheet, the soft Lead Zirconate Titanate "THP5H" from Thorlabs seemed to match quite well the observed properties.
|
||||
% The properties of this "THP5H" material used to compute $g_a$ and $g_s$ are listed in Table ref:tab:test_apa_piezo_properties.
|
||||
|
||||
% From these parameters, $g_s = 5.1\,V/\mu m$ and $g_a = 26\,N/V$ were obtained which are very close to the identified constants using the experimentally identified transfer functions.
|
||||
|
||||
% #+name: tab:test_apa_piezo_properties
|
||||
% #+caption: Piezoelectric properties used for the estimation of the sensor and actuators "gains"
|
||||
% #+attr_latex: :environment tabularx :width 1\linewidth :align ccX
|
||||
% #+attr_latex: :center t :booktabs t
|
||||
% | *Parameter* | *Value* | *Description* |
|
||||
% |----------------+----------------------------+--------------------------------------------------------------|
|
||||
% | $d_{33}$ | $680 \cdot 10^{-12}\,m/V$ | Piezoelectric constant |
|
||||
% | $\epsilon^{T}$ | $4.0 \cdot 10^{-8}\,F/m$ | Permittivity under constant stress |
|
||||
% | $s^{D}$ | $21 \cdot 10^{-12}\,m^2/N$ | Elastic compliance understand constant electric displacement |
|
||||
% | $c^{E}$ | $48 \cdot 10^{9}\,N/m^2$ | Young's modulus of elasticity |
|
||||
% | $L$ | $20\,mm$ per stack | Length of the stack |
|
||||
% | $A$ | $10^{-4}\,m^2$ | Area of the piezoelectric stack |
|
||||
% | $n$ | $160$ per stack | Number of layers in the piezoelectric stack |
|
||||
|
||||
|
||||
%% Estimate "Sensor Constant" - (THP5H)
|
||||
d33 = 680e-12; % Strain constant [m/V]
|
||||
n = 160; % Number of layers per stack
|
||||
eT = 4500*8.854e-12; % Permittivity under constant stress [F/m]
|
||||
sD = 21e-12; % Compliance under constant electric displacement [m2/N]
|
||||
|
||||
gs = d33/(eT*sD*n); % Sensor Constant [V/m]
|
||||
|
||||
%% Estimate "Actuator Constant" - (THP5H)
|
||||
d33 = 680e-12; % Strain constant [m/V]
|
||||
n = 320; % Number of layers
|
||||
|
||||
cE = 1/sD; % Youngs modulus [N/m^2]
|
||||
A = (10e-3)^2; % Area of the stacks [m^2]
|
||||
L = 40e-3; % Length of the two stacks [m]
|
||||
ka = cE*A/L; % Stiffness of the two stacks [N/m]
|
||||
|
||||
ga = d33*n*ka; % Actuator Constant [N/V]
|
||||
|
||||
% Comparison of the obtained dynamics
|
||||
|
||||
% The obtained dynamics using the /super element/ with the tuned "sensor gain" and "actuator gain" are compared with the experimentally identified frequency response functions in Figure ref:fig:test_apa_super_element_comp_frf.
|
||||
|
||||
% A good match between the model and the experimental results is observed.
|
||||
% - the /super element/
|
||||
|
||||
% This model represents fairly
|
||||
|
||||
% The flexible model is a bit "soft" as compared with the experimental results.
|
||||
|
||||
% This method can be used to model piezoelectric stack actuators as well as amplified piezoelectric stack actuators.
|
||||
|
||||
|
||||
%% Idenfify the dynamics of the Simscape model with correct actuator and sensor "constants"
|
||||
% Initialize the APA
|
||||
n_hexapod.actuator = initializeAPA(...
|
||||
'type', 'flexible', ...
|
||||
'ga', 23.2, ... % Actuator gain [N/V]
|
||||
'gs', -4.9e6); % Sensor gain [V/m]
|
||||
|
||||
% Identify with updated constants
|
||||
G_flex = exp(-Ts*s)*linearize(mdl, io, 0.0, opts);
|
||||
G_flex.InputName = {'u'};
|
||||
G_flex.OutputName = {'Vs', 'de'};
|
||||
|
||||
%% Comparison of the measured FRF and the "Flexible" model of the APA300ML
|
||||
freqs = 5*logspace(0, 3, 1000);
|
||||
figure;
|
||||
tiledlayout(3, 2, 'TileSpacing', 'Compact', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(enc_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, abs(enc_frf(:, i)), 'color', [0,0,0,0.2], 'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '"Flexible" Model')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-8, 1e-3]);
|
||||
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
|
||||
ax1b = nexttile([2,1]);
|
||||
hold on;
|
||||
plot(f, abs(iff_frf(:, 1)), 'color', [0,0,0,0.2], 'DisplayName', 'Identified');
|
||||
for i = 2:length(apa_nums)
|
||||
plot(f, abs(iff_frf(:, i)), 'color', [0,0,0,0.2], 'HandleVisibility', 'off');
|
||||
end
|
||||
plot(freqs, abs(squeeze(freqresp(G_flex('Vs', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:), 'DisplayName', '"Flexible" Model')
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-2, 1e2]);
|
||||
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(enc_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('de', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
ax2b = nexttile;
|
||||
hold on;
|
||||
for i = 1:length(apa_nums)
|
||||
plot(f, 180/pi*angle(iff_frf(:, i)), 'color', [0,0,0,0.2]);
|
||||
end
|
||||
plot(freqs, 180/pi*angle(squeeze(freqresp(G_flex('Vs', 'u'), freqs, 'Hz'))), '--', 'color', colors(2,:))
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360); ylim([-180, 180]);
|
||||
|
||||
linkaxes([ax1,ax2,ax1b,ax2b],'x');
|
||||
xlim([10, 2e3]);
|
||||
Binary file not shown.
Reference in New Issue
Block a user