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; @@ -105,8 +106,8 @@
-
1.2 Filter White Noise
+
+
-
1.2 Filter White Noise
Glpf = 1/(1 + s/2/pi/500); @@ -118,13 +119,13 @@ 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;
@@ -133,8 +134,8 @@ Gz = c2d(Glpf, Ts, 'tustin');
-
2.2 Save Data
+
+
-
2.2 Save Data
u = data(:, 1); % Input Voltage [V] @@ -151,16 +152,16 @@ 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
@@ -168,8 +169,8 @@ t = data(:, 3); % Time [s]
-
3.2 PSD of Measurement Noise
+
+
-
3.2 PSD of Measurement Noise
Ts = t(end)/(length(t)-1); @@ -185,7 +186,7 @@ win = hanning(ceil(1*Fs));
+
-
Figure 4: Amplitude Spectral Density of the Displacement during Huddle Test
@@ -194,8 +195,8 @@ 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
@@ -205,11 +206,11 @@ Results presented in this sections are wrong as the ADC cannot deliver enought c
-
4.1 Time Domain Data
+
+
4.1 Time Domain Data
-
+
-
Figure 5: Time domain signals during the test
@@ -217,8 +218,8 @@ Results presented in this sections are wrong as the ADC cannot deliver enought c
-
4.2 Comparison of the PSD with Huddle Test
+
+
-
4.2 Comparison of the PSD with Huddle Test
Ts = t(end)/(length(t)-1); @@ -235,7 +236,7 @@ win = hanning(ceil(1*Fs));
+
-
Figure 6: Comparison of the ASD for the identification test and the huddle test
@@ -243,8 +244,8 @@ 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); @@ -261,14 +262,14 @@ Fs = 1/Ts;
+
-
Figure 7: Coherence
+
-
Figure 8: Estimation of the transfer function from input voltage to displacement
@@ -276,8 +277,8 @@ Fs = 1/Ts;
-
4.4 Comparison with the FEM model
+
+
-
4.4 Comparison with the FEM model
load('mat/fem_model_5kg.mat', 'Ghm');
@@ -285,7 +286,7 @@ Fs = 1/Ts;
+
-
Figure 9: Comparison of the identified transfer function and the one estimated from the FE model
@@ -304,12 +305,12 @@ 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 Load Data
+
+
-
5.1 Load Data
ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
@@ -329,8 +330,8 @@ ht.y = ht.y - mean(ht.y);
-
5.2 Comparison of the PSD with Huddle Test
+
+
-
5.2 Comparison of the PSD with Huddle Test
Ts = t(end)/(length(t)-1); @@ -347,7 +348,7 @@ win = hanning(ceil(1*Fs));
+
-
Figure 10: Comparison of the ASD for the identification test and the huddle test
@@ -355,8 +356,8 @@ win = hanning(ceil(1*Fs));
-
5.3 Compute TF estimate and Coherence
+
+
-
5.3 Compute TF estimate and Coherence
Ts = t(end)/(length(t)-1); @@ -374,14 +375,14 @@ Fs = 1/Ts;
+
-
Figure 11: Coherence
+
-
Figure 12: Estimation of the transfer function from input voltage to displacement
@@ -389,8 +390,8 @@ Fs = 1/Ts;
-
5.4 Comparison with the FEM model
+
+
-
5.4 Comparison with the FEM model
load('mat/fem_model_5kg.mat', 'G');
@@ -398,7 +399,7 @@ Fs = 1/Ts;
+
-
Figure 13: Comparison of the identified transfer function and the one estimated from the FE model
@@ -407,8 +408,8 @@ Fs = 1/Ts;
-
6 Transfer function from force actuator to force sensor
+
+
-
6 Transfer function from force actuator to force sensor
Two measurements are performed: @@ -455,7 +456,7 @@ 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. +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); @@ -472,15 +473,15 @@ win = hann(ceil(10/Ts));
+
-
Figure 14: Comparison of the identified dynamics from voltage output to voltage input and the FEM
-
6.1 System Identification
+
+
-
6.1 System Identification
w_z = 2*pi*111; % Zeros frequency [rad/s] @@ -494,7 +495,7 @@ 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);
+
-
Figure 15: Identification of the IFF plant
@@ -503,11 +504,11 @@ 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);
-
6.2 Integral Force Feedback
+
+
6.2 Integral Force Feedback
-
+
-
Figure 16: Root Locus for IFF
@@ -516,12 +517,12 @@ 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);
-
7 IFF Tests
+
+
-
7 IFF Tests
-
7.1 Load Data
+
+
-
+
+>
#+end_src
-** Load Data
+** First tests with few gains
#+begin_src matlab
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');
@@ -730,7 +730,7 @@ The transfer function from input voltage to output voltage are computed and show
[co_iff_of, ~] = mscohere(iff_of.u, iff_of.y, win, [], [], 1/Ts);
#+end_src
-#+begin_src matlab
+#+begin_src matlab :exports none
figure;
hold on;
@@ -754,7 +754,7 @@ The transfer function from input voltage to output voltage are computed and show
[[file:figs/iff_first_test_coherence.png]]
-#+begin_src matlab
+#+begin_src matlab :exports none
figure;
ax1 = subplot(2, 1, 1);
hold on;
@@ -787,3 +787,171 @@ The transfer function from input voltage to output voltage are computed and show
#+caption: Bode plot for different values of IFF gain
#+RESULTS:
[[file:figs/iff_first_test_bode_plot.png]]
+
+** Second test with many Gains
+#+begin_src matlab
+ load('./mat/apa95ml_iff_test.mat', 'results');
+#+end_src
+
+#+begin_src matlab
+ Ts = 1e-4;
+ win = hann(ceil(10/Ts));
+#+end_src
+
+#+begin_src matlab
+ tf_iff = {zeros(1, length(results))};
+ co_iff = {zeros(1, length(results))};
+ g_iff = [0, 1, 5, 10, 50, 100];
+
+ for i=1:length(results)
+ [tf_est, f] = tfestimate(results{i}.u, results{i}.y, win, [], [], 1/Ts);
+ [co_est, ~] = mscohere(results{i}.u, results{i}.y, win, [], [], 1/Ts);
+
+ tf_iff(i) = {tf_est};
+ co_iff(i) = {co_est};
+ end
+#+end_src
+
+#+begin_src matlab :exports none
+ figure;
+
+ hold on;
+ for i = 1:length(results)
+ plot(f, co_iff{i}, '-', 'DisplayName', sprintf('g = %0.f', g_iff(i)))
+ end
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ ylabel('Coherence'); xlabel('Frequency [Hz]');
+ hold off;
+ legend();
+ xlim([60, 600])
+#+end_src
+
+#+begin_src matlab :exports none
+ figure;
+ ax1 = subplot(2, 1, 1);
+ hold on;
+ for i = 1:length(results)
+ plot(f, abs(tf_iff{i}), '-', 'DisplayName', sprintf('g = %0.f', g_iff(i)))
+ end
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ ylabel('Amplitude'); xlabel('Frequency [Hz]');
+ hold off;
+ legend();
+
+ ax2 = subplot(2, 1, 2);
+ hold on;
+ for i = 1:length(results)
+ plot(f, 180/pi*angle(-tf_iff{i}), '-')
+ end
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ ylabel('Phase'); xlabel('Frequency [Hz]');
+ hold off;
+
+ linkaxes([ax1,ax2], 'x');
+ xlim([60, 600]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+ exportFig('figs/iff_results_bode_plots.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:iff_results_bode_plots
+#+caption:
+#+RESULTS:
+[[file:figs/iff_results_bode_plots.png]]
+
+#+begin_src matlab
+ G_id = {zeros(1,length(results))};
+
+ f_start = 70; % [Hz]
+ f_end = 500; % [Hz]
+
+ for i = 1:length(results)
+ tf_id = tf_iff{i}(sum(ff_end));
+ f_id = f(sum(ff_end));
+
+ gfr = idfrd(tf_id, 2*pi*f_id, Ts);
+ G_id(i) = {procest(gfr,'P2UDZ')};
+ end
+#+end_src
+
+#+begin_src matlab :exports none
+ figure;
+ ax1 = subplot(2, 1, 1);
+ hold on;
+ for i = 1:length(results)
+ set(gca,'ColorOrderIndex',i)
+ plot(f, abs(tf_iff{i}), '-', 'DisplayName', sprintf('g = %0.f', g_iff(i)))
+ set(gca,'ColorOrderIndex',i)
+ plot(f, abs(squeeze(freqresp(G_id{i}, f, 'Hz'))), '--', 'HandleVisibility', 'off')
+ end
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ ylabel('Amplitude'); xlabel('Frequency [Hz]');
+ hold off;
+ legend();
+
+ ax2 = subplot(2, 1, 2);
+ hold on;
+ for i = 1:length(results)
+ set(gca,'ColorOrderIndex',i)
+ plot(f, 180/pi*angle(tf_iff{i}), '-')
+ set(gca,'ColorOrderIndex',i)
+ plot(f, 180/pi*angle(squeeze(freqresp(G_id{i}, f, 'Hz'))), '--')
+ end
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ ylabel('Phase'); xlabel('Frequency [Hz]');
+ hold off;
+
+ linkaxes([ax1,ax2], 'x');
+ xlim([60, 600]);
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+ exportFig('figs/iff_results_bode_plots_identification.pdf', 'width', 'full', 'height', 'full');
+#+end_src
+
+#+name: fig:iff_results_bode_plots_identification
+#+caption:
+#+RESULTS:
+[[file:figs/iff_results_bode_plots_identification.png]]
+
+#+begin_src matlab :exports none
+ 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);
+
+
+ gains = logspace(0, 5, 1000);
+
+ figure;
+ hold on;
+ plot(real(pole(Gi)), imag(pole(Gi)), 'kx', 'HandleVisibility', 'off');
+ plot(real(tzero(Gi)), imag(tzero(Gi)), 'ko', 'HandleVisibility', 'off');
+ for i = 1:length(results)
+ set(gca,'ColorOrderIndex',i)
+ plot(real(pole(G_id{i})), imag(pole(G_id{i})), 'o', 'DisplayName', sprintf('g = %0.f', g_iff(i)));
+ end
+ for i = 1:length(gains)
+ cl_poles = pole(feedback(Gi, (gains(i)/(s + 2*pi*2))));
+ plot(real(cl_poles), imag(cl_poles), 'k.', 'HandleVisibility', 'off');
+ end
+ ylim([0, 1800]);
+ xlim([-1600,200]);
+ xlabel('Real Part')
+ ylabel('Imaginary Part')
+ axis square
+ legend('location', 'northwest');
+#+end_src
+
+#+begin_src matlab :tangle no :exports results :results file replace
+ exportFig('figs/iff_results_root_locus.pdf', 'width', 'wide', 'height', 'tall');
+#+end_src
+
+#+name: fig:iff_results_root_locus
+#+caption:
+#+RESULTS:
+[[file:figs/iff_results_root_locus.png]]
7.1 First tests with few gains
iff_g10 = load('./mat/apa95ml_iff_g10_res.mat', 'u', 't', 'y', 'v');
@@ -545,60 +546,84 @@ win = hann(ceil(10/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])
-
-
+
+
+
+
Figure 17: Coherence
+
+
+
Figure 18: Bode plot for different values of IFF gain
+
+
@@ -606,7 +631,7 @@ xlim([60, 600]);
7.2 Second test with many Gains
+
-
-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;
+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();
+load('./mat/apa95ml_iff_test.mat', 'results');
+
+
+
-linkaxes([ax1,ax2], 'x');
-xlim([60, 600]);
+Ts = 1e-4; +win = hann(ceil(10/Ts)); ++
+
-tf_iff = {zeros(1, length(results))};
+co_iff = {zeros(1, length(results))};
+g_iff = [0, 1, 5, 10, 50, 100];
+
+for i=1:length(results)
+ [tf_est, f] = tfestimate(results{i}.u, results{i}.y, win, [], [], 1/Ts);
+ [co_est, ~] = mscohere(results{i}.u, results{i}.y, win, [], [], 1/Ts);
+
+ tf_iff(i) = {tf_est};
+ co_iff(i) = {co_est};
+end
-
+
+
+
+
+
+
+
+
+G_id = {zeros(1,length(results))};
+
+f_start = 70; % [Hz]
+f_end = 500; % [Hz]
+
+for i = 1:length(results)
+ tf_id = tf_iff{i}(sum(f<f_start):length(f)-sum(f>f_end));
+ f_id = f(sum(f<f_start):length(f)-sum(f>f_end));
+
+ gfr = idfrd(tf_id, 2*pi*f_id, Ts);
+ G_id(i) = {procest(gfr,'P2UDZ')};
+end
+
+
+
+
+
+
+
+
Figure 18: Bode plot for different values of IFF gain
-
diff --git a/index.org b/index.org
index 9486ad1..cb64c74 100644
--- a/index.org
+++ b/index.org
@@ -709,7 +709,7 @@ The transfer function from input voltage to output voltage are computed and show
<Created: 2020-08-20 jeu. 23:08
+Created: 2020-08-21 ven. 15:26