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;
+Ts = 1e-4;
-
-1.2 Filter White Noise
+
+
1.2 Filter White Noise
-
Glpf = 1/(1 + s/2/pi/500); +Glpf = 1/(1 + s/2/pi/500); -Gz = c2d(Glpf, Ts, 'tustin'); +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;
+data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data;
-
-2.2 Save Data
+
+
2.2 Save Data
-
u = data(:, 1); % Input Voltage [V] -y = data(:, 2); % Output Displacement [m] -t = data(:, 3); % Time [s] +u = data(:, 1); % Input Voltage [V] +y = data(:, 2); % Output Displacement [m] +t = data(:, 3); % Time [s]
-
save('./mat/huddle_test.mat', 't', 'u', 'y', 'Glpf');
+save('./mat/huddle_test.mat', 't', 'u', 'y', 'Glpf');
-
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
@@ -169,24 +169,24 @@ t = data(:, 3); % Time [s]
-
3.2 PSD of Measurement Noise
+
+
3.2 PSD of Measurement Noise
-
Ts = t(end)/(length(t)-1); -Fs = 1/Ts; +Ts = t(end)/(length(t)-1); +Fs = 1/Ts; -win = hanning(ceil(1*Fs)); +win = hanning(ceil(1*Fs));
-
-[pxx, f] = pwelch(y(1000:end), win, [], [], Fs);
+[pxx, f] = pwelch(y(1000:end), win, [], [], Fs);
+
-
Figure 4: Amplitude Spectral Density of the Displacement during Huddle Test
@@ -195,10 +195,10 @@ 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.
@@ -206,11 +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
@@ -218,25 +218,25 @@ 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); -Fs = 1/Ts; +Ts = t(end)/(length(t)-1); +Fs = 1/Ts; -win = hanning(ceil(1*Fs)); +win = hanning(ceil(1*Fs));
[pxx, f] = pwelch(y, win, [], [], Fs);
-[pht, ~] = pwelch(ht.y, win, [], [], Fs);
+[pht, ~] = pwelch(ht.y, win, [], [], Fs);
+
-
Figure 6: Comparison of the ASD for the identification test and the huddle test
@@ -244,32 +244,32 @@ 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); -Fs = 1/Ts; +Ts = t(end)/(length(t)-1); +Fs = 1/Ts;
-
-win = hann(ceil(1/Ts)); +win = hann(ceil(1/Ts)); -[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts); -[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts); +[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts); +[co_est, ~] = mscohere( u, -y, win, [], [], 1/Ts);
+
-
Figure 7: Coherence
+
-
Figure 8: Estimation of the transfer function from input voltage to displacement
@@ -277,16 +277,16 @@ Fs = 1/Ts;
-
4.4 Comparison with the FEM model
+
+
4.4 Comparison with the FEM model
-
-load('mat/fem_model_5kg.mat', 'Ghm');
+load('mat/fem_model_5kg.mat', 'Ghm');
+
Figure 9: Comparison of the identified transfer function and the one estimated from the FE model
@@ -295,7 +295,7 @@ Fs = 1/Ts;
-
+
-The problem comes from the fact that the piezo is driven directly by the DAC that cannot deliver enought current. In the next section, a current amplifier is used. @@ -305,50 +305,50 @@ 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');
-load('./mat/apa95ml_5kg_Amp_E505.mat', 't', 'u', 'um', 'y');
+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] +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); +ht.u = 10*(ht.u - mean(ht.u)); +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); -Fs = 1/Ts; +Ts = t(end)/(length(t)-1); +Fs = 1/Ts; -win = hanning(ceil(1*Fs)); +win = hanning(ceil(1*Fs));
[pxx, f] = pwelch(y, win, [], [], Fs);
-[pht, ~] = pwelch(ht.y, win, [], [], Fs);
+[pht, ~] = pwelch(ht.y, win, [], [], Fs);
+
-
Figure 10: Comparison of the ASD for the identification test and the huddle test
@@ -356,33 +356,33 @@ 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); -Fs = 1/Ts; +Ts = t(end)/(length(t)-1); +Fs = 1/Ts;
-
-win = hann(ceil(1/Ts)); +win = hann(ceil(1/Ts)); -[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts); -[tf_um , ~] = tfestimate(um, -y, win, [], [], 1/Ts); -[co_est, ~] = mscohere( um, -y, win, [], [], 1/Ts); +[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts); +[tf_um , ~] = tfestimate(um, -y, win, [], [], 1/Ts); +[co_est, ~] = mscohere( um, -y, win, [], [], 1/Ts);
+
-
Figure 11: Coherence
+
-
Figure 12: Estimation of the transfer function from input voltage to displacement
@@ -390,16 +390,16 @@ Fs = 1/Ts;
-
5.4 Comparison with the FEM model
+
+
5.4 Comparison with the FEM model
-
-load('mat/fem_model_5kg.mat', 'G');
+load('mat/fem_model_5kg.mat', 'G');
+
-
Figure 13: Comparison of the identified transfer function and the one estimated from the FE model
@@ -408,8 +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: @@ -426,9 +426,9 @@ The obtained dynamics from force actuator to force sensor are compare with the F 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');
+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');
@@ -439,11 +439,11 @@ Let’s use the amplifier gain to obtain the true voltage applied to the act The parameters of the piezoelectric stacks are defined below:
-
@@ -451,51 +451,51 @@ ka = 235e6; % Stack stiffness [N/m]
From the FEM, we construct the transfer function from DAC voltage to ADC voltage.
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] +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]
-
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); +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. +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; +Ts = a_ss.t(end)/(length(a_ss.t)-1); +Fs = 1/Ts; -win = hann(ceil(10/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_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); +[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
+
+
6.1 System Identification
-
-w_z = 2*pi*111; % Zeros frequency [rad/s] -w_p = 2*pi*255; % Pole frequency [rad/s] +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); +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
@@ -504,11 +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
@@ -517,37 +517,37 @@ 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 First tests with few gains
+
+
7.1 First tests with few gains
-
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');
+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');
-
-Ts = 1e-4; -win = hann(ceil(10/Ts)); +Ts = 1e-4; +win = hann(ceil(10/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_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_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); +[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 17: Coherence
@@ -555,7 +555,7 @@ win = hann(ceil(10/Ts)); -
+
-
Figure 18: Bode plot for different values of IFF gain
@@ -563,17 +563,17 @@ win = hann(ceil(10/Ts));
-
7.2 Second test with many Gains
+
+
-
7.2 Second test with many Gains
-
load('./mat/apa95ml_iff_test.mat', 'results');
+load('./mat/apa95ml_iff_test.mat', 'results');
-
@@ -582,18 +582,18 @@ win = hann(ceil(10/Ts));
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);
+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
+ tf_iff(i) = {tf_est};
+ co_iff(i) = {co_est};
+end
Ts = 1e-4; -win = hann(ceil(10/Ts)); +Ts = 1e-4; +win = hann(ceil(10/Ts));
+
@@ -601,27 +601,27 @@ end
-
G_id = {zeros(1,length(results))};
-f_start = 70; % [Hz]
-f_end = 500; % [Hz]
+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));
+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
+ gfr = idfrd(tf_id, 2*pi*f_id, Ts);
+ G_id(i) = {procest(gfr,'P2UDZ')};
+end
+
-
+
@@ -631,7 +631,7 @@ end
-
diff --git a/index.org b/index.org
index cb64c74..b677101 100644
--- a/index.org
+++ b/index.org
@@ -680,7 +680,7 @@ The transfer function from input voltage to output voltage are computed and show
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)));
+ cl_poles = pole(feedback(Gi, (gains(i)/(s + 2*2*pi)*s/(s + 0.5*2*pi))));
plot(real(cl_poles), imag(cl_poles), 'k.');
end
ylim([0, 1800]);
diff --git a/mat/G_force_sensor_5kg.mat b/mat/G_force_sensor_5kg.mat
new file mode 100644
index 0000000..5bfa3cf
Binary files /dev/null and b/mat/G_force_sensor_5kg.mat differ
diff --git a/mat/fem_model_5kg.mat b/mat/fem_model_5kg.mat
index 8d6d744..51083ce 100644
Binary files a/mat/fem_model_5kg.mat and b/mat/fem_model_5kg.mat differ
diff --git a/mat/fem_model_Gf_5kg.mat b/mat/fem_model_Gf_5kg.mat
new file mode 100644
index 0000000..c96b7a0
Binary files /dev/null and b/mat/fem_model_Gf_5kg.mat differ
Created: 2020-08-21 ven. 15:26
+Created: 2020-11-03 mar. 10:11