Figure 1: Picture of the Setup
+
-
Figure 2: Zoom on the APA
-
1 Setup
+
+
-
1 Setup
-
1.1 Parameters
+
+
-
1.1 Parameters
Ts = 1e-4; @@ -98,8 +105,8 @@
-
1.2 Filter White Noise
+
+
-
1.2 Filter White Noise
Glpf = 1/(1 + s/2/pi/500); @@ -111,13 +118,13 @@ Gz = c2d(Glpf, Ts, 'tustin');
-
2 Run Experiment and Save Data
+
+
-
2 Run Experiment and Save Data
-
2.1 Load Data
+
+
-
2.1 Load Data
data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data;
@@ -126,8 +133,8 @@ Gz = c2d(Glpf, Ts, 'tustin');
-
2.2 Save Data
+
+
-
2.2 Save Data
u = data(:, 1); % Input Voltage [V] @@ -144,16 +151,16 @@ t = data(:, 3); % Time [s]
-
3 Huddle Test
+
+
-
3 Huddle Test
-
3.1 Time Domain Data
+
+
3.1 Time Domain Data
-
+
-
Figure 3: Measurement of the Mass displacement during Huddle Test
@@ -161,8 +168,8 @@ t = data(:, 3); % Time [s]
-
3.2 PSD of Measurement Noise
+
+
-
3.2 PSD of Measurement Noise
Ts = t(end)/(length(t)-1); @@ -178,7 +185,7 @@ win = hanning(ceil(1*Fs));
+
-
Figure 4: Amplitude Spectral Density of the Displacement during Huddle Test
@@ -187,16 +194,22 @@ win = hanning(ceil(1*Fs));
-
4 Transfer Function Estimation using the DAC as the driver
+
+
4 Transfer Function Estimation using the DAC as the driver
+
-
+
+Results presented in this sections are wrong as the ADC cannot deliver enought current to the piezoelectric actuator. +
+ +
-
4.1 Time Domain Data
+
+
4.1 Time Domain Data
-
+
-
Figure 5: Time domain signals during the test
@@ -204,8 +217,8 @@ win = hanning(ceil(1*Fs));
-
4.2 Comparison of the PSD with Huddle Test
+
+
-
4.2 Comparison of the PSD with Huddle Test
Ts = t(end)/(length(t)-1); @@ -222,7 +235,7 @@ win = hanning(ceil(1*Fs));
+
-
Figure 6: Comparison of the ASD for the identification test and the huddle test
@@ -230,8 +243,8 @@ win = hanning(ceil(1*Fs));
-
4.3 Compute TF estimate and Coherence
+
+
-
4.3 Compute TF estimate and Coherence
Ts = t(end)/(length(t)-1); @@ -248,14 +261,14 @@ Fs = 1/Ts;
+
-
Figure 7: Coherence
+
-
Figure 8: Estimation of the transfer function from input voltage to displacement
@@ -263,8 +276,8 @@ Fs = 1/Ts;
-
4.4 Comparison with the FEM model
+
+
-
4.4 Comparison with the FEM model
load('mat/fem_model_5kg.mat', 'Ghm');
@@ -272,7 +285,7 @@ Fs = 1/Ts;
+
-
Figure 9: Comparison of the identified transfer function and the one estimated from the FE model
@@ -291,14 +304,35 @@ In the next section, a current amplifier is used.
-
5 Transfer Function Estimation using the PI Amplifier
+
+
-
5 Transfer Function Estimation using the PI Amplifier
-
5.1 Comparison of the PSD with Huddle Test
+
+
+
+
+5.1 Load Data
+
+
+ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
+load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um', 'y');
+
+
+
+u = 10*(u - mean(u)); % Input Voltage of Piezo [V] +um = 10*(um - mean(um)); % Monitor [V] +y = y - mean(y); % Mass displacement [m] + +ht.u = 10*(ht.u - mean(ht.u)); +ht.y = ht.y - mean(ht.y); ++
+
5.2 Comparison of the PSD with Huddle Test
+
+
-
Ts = t(end)/(length(t)-1); Fs = 1/Ts; @@ -313,7 +347,7 @@ win = hanning(ceil(1*Fs));
+
-
Figure 10: Comparison of the ASD for the identification test and the huddle test
@@ -321,9 +355,9 @@ win = hanning(ceil(1*Fs));
-
5.2 Compute TF estimate and Coherence
-
+
+
-
5.3 Compute TF estimate and Coherence
+Ts = t(end)/(length(t)-1); Fs = 1/Ts; @@ -340,14 +374,14 @@ Fs = 1/Ts;
+
-
Figure 11: Coherence
+
-
Figure 12: Estimation of the transfer function from input voltage to displacement
@@ -355,16 +389,16 @@ Fs = 1/Ts;
-
5.3 Comparison with the FEM model
-
+
+
-
5.4 Comparison with the FEM model
+
-
-load('mat/fem_model_5kg.mat', 'Ghm');
+load('mat/fem_model_5kg.mat', 'G');
+
Figure 13: Comparison of the identified transfer function and the one estimated from the FE model
@@ -372,76 +406,207 @@ Fs = 1/Ts;
->
@@ -353,18 +358,18 @@ In the next section, a current amplifier is used.
<>
#+end_src
-** Load Data :noexport:
+** Load Data
#+begin_src matlab
ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um', 'y');
#+end_src
#+begin_src matlab
- u = u - mean(u);
- um = um - mean(um);
- y = y - mean(y);
+ u = 10*(u - mean(u)); % Input Voltage of Piezo [V]
+ um = 10*(um - mean(um)); % Monitor [V]
+ y = y - mean(y); % Mass displacement [m]
- ht.u = ht.u - mean(ht.u);
+ ht.u = 10*(ht.u - mean(ht.u));
ht.y = ht.y - mean(ht.y);
#+end_src
@@ -443,7 +448,7 @@ In the next section, a current amplifier is used.
plot(f, abs(tf_est), 'DisplayName', 'Input Voltage')
plot(f, abs(tf_um), 'DisplayName', 'Monitor Voltage')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
- ylabel('Amplitude'); xlabel('Frequency [Hz]');
+ ylabel('Amplitude [m/V]'); xlabel('Frequency [Hz]');
hold off;
legend('location', 'southwest')
@@ -472,7 +477,7 @@ In the next section, a current amplifier is used.
** Comparison with the FEM model
#+begin_src matlab
- load('mat/fem_model_5kg.mat', 'Ghm');
+ load('mat/fem_model_5kg.mat', 'G');
#+end_src
#+begin_src matlab :exports none
@@ -480,17 +485,17 @@ In the next section, a current amplifier is used.
figure;
ax1 = subplot(2, 1, 1);
hold on;
- plot(f, 1/10*170/1400*abs(tf_um), 'DisplayName', 'Identification')
- plot(freqs, abs(squeeze(freqresp(Ghm, freqs, 'Hz'))), 'DisplayName', 'FEM')
+ plot(f, abs(tf_um), 'DisplayName', 'Identification')
+ plot(freqs, abs(squeeze(freqresp(G, freqs, 'Hz'))), 'DisplayName', 'FEM')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
- ylabel('Amplitude'); xlabel('Frequency [Hz]');
+ ylabel('Amplitude [m/V]'); xlabel('Frequency [Hz]');
legend('location', 'northeast')
hold off;
ax2 = subplot(2, 1, 2);
hold on;
plot(f, 180/pi*unwrap(angle(tf_um)))
- plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Ghm, freqs, 'Hz')))))
+ plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(G, freqs, 'Hz')))))
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
@@ -509,7 +514,192 @@ In the next section, a current amplifier is used.
#+caption: Comparison of the identified transfer function and the one estimated from the FE model
#+RESULTS:
[[file:figs/apa95ml_5kg_pi_comp_fem.png]]
-* Transfer function of the PI Amplifier
+
+* Transfer function from force actuator to force sensor
+** Introduction :ignore:
+Two measurements are performed:
+- Speedgoat DAC => Voltage Amplifier (x20) => 1 Piezo Stack => ... => 2 Stacks as Force Sensor (parallel) => Speedgoat ADC
+- Speedgoat DAC => Voltage Amplifier (x20) => 2 Piezo Stacks (parallel) => ... => 1 Stack as Force Sensor => Speedgoat ADC
+
+The obtained dynamics from force actuator to force sensor are compare with the FEM model.
+
+** Matlab Init :noexport:ignore:
+#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
+ <>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+ <>
+#+end_src
+
+** Load Data :ignore:
+The data are loaded:
+#+begin_src matlab
+ a_ss = load('mat/apa95ml_5kg_1a_2s.mat', 't', 'u', 'y', 'v');
+ aa_s = load('mat/apa95ml_5kg_2a_1s.mat', 't', 'u', 'y', 'v');
+ load('mat/G_force_sensor_5kg.mat', 'G');
+#+end_src
+
+** Adjust gain :ignore:
+Let's use the amplifier gain to obtain the true voltage applied to the actuator stack(s)
+
+The parameters of the piezoelectric stacks are defined below:
+#+begin_src matlab
+ d33 = 3e-10; % Strain constant [m/V]
+ n = 80; % Number of layers per stack
+ eT = 1.6e-8; % Permittivity under constant stress [F/m]
+ sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N]
+ ka = 235e6; % Stack stiffness [N/m]
+#+end_src
+
+From the FEM, we construct the transfer function from DAC voltage to ADC voltage.
+#+begin_src matlab
+ Gfem_aa_s = exp(-s/1e4)*20*(2*d33*n*ka)*(G(3,1)+G(3,2))*d33/(eT*sD*n);
+ Gfem_a_ss = exp(-s/1e4)*20*( d33*n*ka)*(G(3,1)+G(2,1))*d33/(eT*sD*n);
+#+end_src
+
+** Compute TF estimate and Coherence :ignore:
+The transfer function from input voltage to output voltage are computed and shown in Figure [[fig:bode_plot_force_sensor_voltage_comp_fem]].
+#+begin_src matlab
+ Ts = a_ss.t(end)/(length(a_ss.t)-1);
+ Fs = 1/Ts;
+
+ win = hann(ceil(10/Ts));
+
+ [tf_a_ss, f] = tfestimate(a_ss.u, a_ss.v, win, [], [], 1/Ts);
+ [coh_a_ss, ~] = mscohere( a_ss.u, a_ss.v, win, [], [], 1/Ts);
+
+ [tf_aa_s, f] = tfestimate(aa_s.u, aa_s.v, win, [], [], 1/Ts);
+ [coh_aa_s, ~] = mscohere( aa_s.u, aa_s.v, win, [], [], 1/Ts);
+#+end_src
+
+#+begin_src matlab :exports none
+ freqs = logspace(1, 4, 1000);
+
+ figure;
+ ax1 = subplot(2, 1, 1);
+ hold on;
+ set(gca,'ColorOrderIndex',1)
+ plot(f, abs(tf_aa_s), '-')
+ set(gca,'ColorOrderIndex',1)
+ plot(freqs, abs(squeeze(freqresp(Gfem_aa_s, freqs, 'Hz'))), '--')
+ set(gca,'ColorOrderIndex',2)
+ plot(f, abs(tf_a_ss), '-')
+ set(gca,'ColorOrderIndex',2)
+ plot(freqs, abs(squeeze(freqresp(Gfem_a_ss, freqs, 'Hz'))), '--')
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ ylabel('Amplitude'); xlabel('Frequency [Hz]');
+ hold off;
+ ylim([1e-2, 1e2]);
+
+ ax2 = subplot(2, 1, 2);
+ hold on;
+ set(gca,'ColorOrderIndex',1)
+ plot(f, 180/pi*angle(tf_aa_s), '-', 'DisplayName', '2 Act - 1 Sen')
+ set(gca,'ColorOrderIndex',1)
+ plot(freqs, 180/pi*angle(squeeze(freqresp(Gfem_aa_s, freqs, 'Hz'))), '--', 'DisplayName', '2 Act - 1 Sen, - FEM')
+ set(gca,'ColorOrderIndex',2)
+ plot(f, 180/pi*angle(tf_a_ss), '-', 'DisplayName', '1 Act - 2 Sen')
+ set(gca,'ColorOrderIndex',2)
+ plot(freqs, 180/pi*angle(squeeze(freqresp(Gfem_a_ss, freqs, 'Hz'))), '--', 'DisplayName', '1 Act - 2 Sen, - FEM')
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ ylabel('Phase'); xlabel('Frequency [Hz]');
+ hold off;
+ ylim([-180, 180]);
+ yticks(-180:90:180);
+ legend('location', 'northeast')
+
+ linkaxes([ax1,ax2], 'x');
+ xlim([10, 5e3]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+ exportFig('figs/bode_plot_force_sensor_voltage_comp_fem.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:bode_plot_force_sensor_voltage_comp_fem
+#+caption: Comparison of the identified dynamics from voltage output to voltage input and the FEM
+#+RESULTS:
+[[file:figs/bode_plot_force_sensor_voltage_comp_fem.png]]
+
+** System Identification
+#+begin_src matlab
+ w_z = 2*pi*111; % Zeros frequency [rad/s]
+ w_p = 2*pi*255; % Pole frequency [rad/s]
+ xi_z = 0.05;
+ xi_p = 0.015;
+ G_inf = 2;
+
+ Gi = G_inf*(s^2 - 2*xi_z*w_z*s + w_z^2)/(s^2 + 2*xi_p*w_p*s + w_p^2);
+#+end_src
+
+#+begin_src matlab :exports none
+ freqs = logspace(1, 4, 1000);
+
+ figure;
+ ax1 = subplot(2, 1, 1);
+ hold on;
+ plot(f, abs(tf_aa_s), '-')
+ plot(freqs, abs(squeeze(freqresp(Gi, freqs, 'Hz'))), '--')
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ ylabel('Amplitude'); xlabel('Frequency [Hz]');
+ hold off;
+ ylim([1e-2, 1e2]);
+
+ ax2 = subplot(2, 1, 2);
+ hold on;
+ plot(f, 180/pi*angle(tf_aa_s), '-', 'DisplayName', '2 Act - 1 Sen')
+ plot(freqs, 180/pi*angle(squeeze(freqresp(Gi, freqs, 'Hz'))), '--', 'DisplayName', '2 Act - 1 Sen, - FEM')
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ ylabel('Phase'); xlabel('Frequency [Hz]');
+ hold off;
+ ylim([-180, 180]);
+ yticks(-180:90:180);
+ legend('location', 'northeast')
+
+ linkaxes([ax1,ax2], 'x');
+ xlim([10, 5e3]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+ exportFig('figs/iff_plant_identification_apa95ml.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:iff_plant_identification_apa95ml
+#+caption: Identification of the IFF plant
+#+RESULTS:
+[[file:figs/iff_plant_identification_apa95ml.png]]
+
+
+** Integral Force Feedback
+#+begin_src matlab :exports none
+ gains = logspace(0, 5, 1000);
+
+ figure;
+ hold on;
+ plot(real(pole(Gi)), imag(pole(Gi)), 'kx');
+ plot(real(tzero(Gi)), imag(tzero(Gi)), 'ko');
+ for i = 1:length(gains)
+ cl_poles = pole(feedback(Gi, (gains(i)/s)));
+ plot(real(cl_poles), imag(cl_poles), 'k.');
+ end
+ ylim([0, 1800]);
+ xlim([-1600,200]);
+ xlabel('Real Part')
+ ylabel('Imaginary Part')
+ axis square
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+ exportFig('figs/root_locus_iff_apa95ml_identification.pdf', 'width', 'wide', 'height', 'tall');
+#+end_src
+
+#+name: fig:root_locus_iff_apa95ml_identification
+#+caption: Root Locus for IFF
+#+RESULTS:
+[[file:figs/root_locus_iff_apa95ml_identification.png]]
+
+* IFF Tests
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<>
@@ -519,87 +709,81 @@ In the next section, a current amplifier is used.
<>
#+end_src
-** Load Data :noexport:
+** Load Data
#+begin_src matlab
- load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um');
+ iff_g10 = load('./mat/apa95ml_iff_g10_res.mat', 'u', 't', 'y', 'v');
+ iff_g100 = load('./mat/apa95ml_iff_g100_res.mat', 'u', 't', 'y', 'v');
+ iff_of = load('./mat/apa95ml_iff_off_res.mat', 'u', 't', 'y', 'v');
#+end_src
-** Compute TF estimate and Coherence
-#+begin_src matlab
- Ts = t(end)/(length(t)-1);
- Fs = 1/Ts;
-#+end_src
-
-The coherence and the transfer function are estimate from the voltage input of the PI amplifier to its voltage inputs.
-
-The coherence is very good as expected (Figure [[fig:PI_E505_coh]]).
-
-The transfer function show a low pass filter behavior with a lot of phase drop (Figure [[fig:PI_E505_tf]]).
-
#+begin_src matlab
+ Ts = 1e-4;
win = hann(ceil(10/Ts));
- [tf_est, f] = tfestimate(u, um, win, [], [], 1/Ts);
- [co_est, ~] = mscohere( u, um, win, [], [], 1/Ts);
+ [tf_iff_g10, f] = tfestimate(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
+ [co_iff_g10, ~] = mscohere(iff_g10.u, iff_g10.y, win, [], [], 1/Ts);
+
+ [tf_iff_g100, f] = tfestimate(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
+ [co_iff_g100, ~] = mscohere(iff_g100.u, iff_g100.y, win, [], [], 1/Ts);
+
+ [tf_iff_of, ~] = tfestimate(iff_of.u, iff_of.y, win, [], [], 1/Ts);
+ [co_iff_of, ~] = mscohere(iff_of.u, iff_of.y, win, [], [], 1/Ts);
#+end_src
-#+begin_src matlab :exports none
+#+begin_src matlab
figure;
hold on;
- plot(f, co_est, 'k-')
+ plot(f, co_iff_of, '-', 'DisplayName', 'g=0')
+ plot(f, co_iff_g10, '-', 'DisplayName', 'g=10')
+ plot(f, co_iff_g100, '-', 'DisplayName', 'g=100')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Coherence'); xlabel('Frequency [Hz]');
hold off;
- xlim([10, 5e3]);
+ legend();
+ xlim([60, 600])
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
- exportFig('figs/PI_E505_coh.pdf', 'width', 'wide', 'height', 'normal');
+ exportFig('figs/iff_first_test_coherence.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
-#+name: fig:PI_E505_coh
+#+name: fig:iff_first_test_coherence
#+caption: Coherence
#+RESULTS:
-[[file:figs/PI_E505_coh.png]]
+[[file:figs/iff_first_test_coherence.png]]
-#+begin_src matlab :exports none
+
+#+begin_src matlab
figure;
ax1 = subplot(2, 1, 1);
hold on;
- plot(f, abs(tf_est), 'k-')
+ plot(f, abs(tf_iff_of), '-', 'DisplayName', 'g=0')
+ plot(f, abs(tf_iff_g10), '-', 'DisplayName', 'g=10')
+ plot(f, abs(tf_iff_g100), '-', 'DisplayName', 'g=100')
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ylabel('Amplitude'); xlabel('Frequency [Hz]');
hold off;
+ legend();
ax2 = subplot(2, 1, 2);
hold on;
- plot(f, 180/pi*angle(tf_est), 'k-')
- set(gca, 'Xscale', 'lin'); set(gca, 'Yscale', 'lin');
+ plot(f, 180/pi*angle(-tf_iff_of), '-')
+ plot(f, 180/pi*angle(-tf_iff_g10), '-')
+ plot(f, 180/pi*angle(-tf_iff_g100), '-')
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
ylabel('Phase'); xlabel('Frequency [Hz]');
hold off;
- ylim([-180, 180]);
- yticks(-180:90:180);
linkaxes([ax1,ax2], 'x');
- xlim([10, 5e3]);
+ xlim([60, 600]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
- exportFig('figs/PI_E505_tf.pdf', 'width', 'full', 'height', 'full');
+ exportFig('figs/iff_first_test_bode_plot.pdf', 'width', 'full', 'height', 'full');
#+end_src
-#+name: fig:PI_E505_tf
-#+caption: Estimation of the transfer function from input voltage to displacement
+#+name: fig:iff_first_test_bode_plot
+#+caption: Bode plot for different values of IFF gain
#+RESULTS:
-[[file:figs/PI_E505_tf.png]]
-
-The delay can be estimated as follow (in ms):
-#+begin_src matlab :results replace value
- finddelay(u, um)*(1000*Ts)
-#+end_src
-
-#+RESULTS:
-: 0.4
-
-This most probably corresponds to a FIR filter.
+[[file:figs/iff_first_test_bode_plot.png]]
6 Transfer function of the PI Amplifier
+ +
+
6 Transfer function from force actuator to force sensor
+
+
++Two measurements are performed: +
+-
+
- Speedgoat DAC => Voltage Amplifier (x20) => 1 Piezo Stack => … => 2 Stacks as Force Sensor (parallel) => Speedgoat ADC +
- Speedgoat DAC => Voltage Amplifier (x20) => 2 Piezo Stacks (parallel) => … => 1 Stack as Force Sensor => Speedgoat ADC +
+The obtained dynamics from force actuator to force sensor are compare with the FEM model. +
++The data are loaded: +
+
+
-a_ss = load('mat/apa95ml_5kg_1a_2s.mat', 't', 'u', 'y', 'v');
+aa_s = load('mat/apa95ml_5kg_2a_1s.mat', 't', 'u', 'y', 'v');
+load('mat/G_force_sensor_5kg.mat', 'G');
+
-
+
+6.1 Compute TF estimate and Coherence
++Let’s use the amplifier gain to obtain the true voltage applied to the actuator stack(s) +
+ ++The parameters of the piezoelectric stacks are defined below: +
+
+
+
+d33 = 3e-10; % Strain constant [m/V] +n = 80; % Number of layers per stack +eT = 1.6e-8; % Permittivity under constant stress [F/m] +sD = 2e-11; % Elastic compliance under constant electric displacement [m2/N] +ka = 235e6; % Stack stiffness [N/m] ++
+From the FEM, we construct the transfer function from DAC voltage to ADC voltage. +
+
+
+Gfem_aa_s = exp(-s/1e4)*20*(2*d33*n*ka)*(G(3,1)+G(3,2))*d33/(eT*sD*n); +Gfem_a_ss = exp(-s/1e4)*20*( d33*n*ka)*(G(3,1)+G(2,1))*d33/(eT*sD*n); ++
+The transfer function from input voltage to output voltage are computed and shown in Figure 14. +
+
+
+
+
+Ts = a_ss.t(end)/(length(a_ss.t)-1); +Fs = 1/Ts; + +win = hann(ceil(10/Ts)); + +[tf_a_ss, f] = tfestimate(a_ss.u, a_ss.v, win, [], [], 1/Ts); +[coh_a_ss, ~] = mscohere( a_ss.u, a_ss.v, win, [], [], 1/Ts); + +[tf_aa_s, f] = tfestimate(aa_s.u, aa_s.v, win, [], [], 1/Ts); +[coh_aa_s, ~] = mscohere( aa_s.u, aa_s.v, win, [], [], 1/Ts); ++
+
+
+
Figure 14: Comparison of the identified dynamics from voltage output to voltage input and the FEM
+
+
+
-6.1 System Identification
-
-Ts = t(end)/(length(t)-1); -Fs = 1/Ts; +w_z = 2*pi*111; % Zeros frequency [rad/s] +w_p = 2*pi*255; % Pole frequency [rad/s] +xi_z = 0.05; +xi_p = 0.015; +G_inf = 2; + +Gi = G_inf*(s^2 - 2*xi_z*w_z*s + w_z^2)/(s^2 + 2*xi_p*w_p*s + w_p^2);
-The coherence and the transfer function are estimate from the voltage input of the PI amplifier to its voltage inputs. -
--The coherence is very good as expected (Figure 14). +
+
+
Figure 15: Identification of the IFF plant
+-The transfer function show a low pass filter behavior with a lot of phase drop (Figure 15). + +
+
+6.2 Integral Force Feedback
+
+
+
+
+
+
Figure 16: Root Locus for IFF
+
+
7 IFF Tests
+
+
+
+
7.1 Load Data
+
+
+
iff_g10 = load('./mat/apa95ml_iff_g10_res.mat', 'u', 't', 'y', 'v');
+iff_g100 = load('./mat/apa95ml_iff_g100_res.mat', 'u', 't', 'y', 'v');
+iff_of = load('./mat/apa95ml_iff_off_res.mat', 'u', 't', 'y', 'v');
+
+
-
-
-win = hann(ceil(10/Ts)); +Ts = 1e-4; +win = hann(ceil(10/Ts)); -[tf_est, f] = tfestimate(u, um, win, [], [], 1/Ts); -[co_est, ~] = mscohere( u, um, win, [], [], 1/Ts); +[tf_iff_g10, f] = tfestimate(iff_g10.u, iff_g10.y, win, [], [], 1/Ts); +[co_iff_g10, ~] = mscohere(iff_g10.u, iff_g10.y, win, [], [], 1/Ts); + +[tf_iff_g100, f] = tfestimate(iff_g100.u, iff_g100.y, win, [], [], 1/Ts); +[co_iff_g100, ~] = mscohere(iff_g100.u, iff_g100.y, win, [], [], 1/Ts); + +[tf_iff_of, ~] = tfestimate(iff_of.u, iff_of.y, win, [], [], 1/Ts); +[co_iff_of, ~] = mscohere(iff_of.u, iff_of.y, win, [], [], 1/Ts);
-
-
-
-
-
Figure 14: Coherence
-
-
-
-
-
Figure 15: Estimation of the transfer function from input voltage to displacement
--The delay can be estimated as follow (in ms): -
-
-finddelay(u, um)*(1000*Ts)
+figure;
+
+hold on;
+plot(f, co_iff_of, '-', 'DisplayName', 'g=0')
+plot(f, co_iff_g10, '-', 'DisplayName', 'g=10')
+plot(f, co_iff_g100, '-', 'DisplayName', 'g=100')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Coherence'); xlabel('Frequency [Hz]');
+hold off;
+legend();
+xlim([60, 600])
-0.4 -- -
-This most probably corresponds to a FIR filter. +
+
+
+
+
Figure 17: Coherence
+
+
+
+
+figure;
+ax1 = subplot(2, 1, 1);
+hold on;
+plot(f, abs(tf_iff_of), '-', 'DisplayName', 'g=0')
+plot(f, abs(tf_iff_g10), '-', 'DisplayName', 'g=10')
+plot(f, abs(tf_iff_g100), '-', 'DisplayName', 'g=100')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ylabel('Amplitude'); xlabel('Frequency [Hz]');
+hold off;
+legend();
+
+ax2 = subplot(2, 1, 2);
+hold on;
+plot(f, 180/pi*angle(-tf_iff_of), '-')
+plot(f, 180/pi*angle(-tf_iff_g10), '-')
+plot(f, 180/pi*angle(-tf_iff_g100), '-')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Phase'); xlabel('Frequency [Hz]');
+hold off;
+
+linkaxes([ax1,ax2], 'x');
+xlim([60, 600]);
+
+
+
+
Figure 18: Bode plot for different values of IFF gain
+
-
diff --git a/index.org b/index.org
index 1f9d00c..9486ad1 100644
--- a/index.org
+++ b/index.org
@@ -166,6 +166,11 @@
:header-args:matlab+: :comments org :mkdirp yes
:END:
+** Introduction :ignore:
+#+begin_important
+Results presented in this sections are wrong as the ADC cannot deliver enought current to the piezoelectric actuator.
+#+end_important
+
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<Created: 2020-07-24 ven. 15:48
+Created: 2020-08-20 jeu. 23:08