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Test Bench APA95ML

Table of Contents

setup_picture.png

Figure 1: Picture of the Setup

setup_zoom.png

Figure 2: Zoom on the APA

1 Setup

1.1 Parameters

Ts = 1e-4;

1.2 Filter White Noise

Glpf = 1/(1 + s/2/pi/500);

Gz = c2d(Glpf, Ts, 'tustin');

2 Run Experiment and Save Data

2.1 Load Data

data = SimulinkRealTime.utils.getFileScopeData('data/apa95ml.dat').data;

2.2 Save Data

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');

3 Huddle Test

3.1 Time Domain Data

huddle_test_time_domain.png

Figure 3: Measurement of the Mass displacement during Huddle Test

3.2 PSD of Measurement Noise

Ts = t(end)/(length(t)-1);
Fs = 1/Ts;

win = hanning(ceil(1*Fs));

[pxx, f] = pwelch(y(1000:end), win, [], [], Fs);

huddle_test_pdf.png

Figure 4: Amplitude Spectral Density of the Displacement during Huddle Test

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

apa95ml_5kg_10V_time_domain.png

Figure 5: Time domain signals during the test

4.2 Comparison of the PSD with Huddle Test

Ts = t(end)/(length(t)-1);
Fs = 1/Ts;

win = hanning(ceil(1*Fs));

[pxx, f] = pwelch(y, win, [], [], Fs);
[pht, ~] = pwelch(ht.y, win, [], [], Fs);

apa95ml_5kg_10V_pdf_comp_huddle.png

Figure 6: Comparison of the ASD for the identification test and the huddle test

4.3 Compute TF estimate and Coherence

Ts = t(end)/(length(t)-1);
Fs = 1/Ts;

win = hann(ceil(1/Ts));

[tf_est, f] = tfestimate(u, -y, win, [], [], 1/Ts);
[co_est, ~] = mscohere(  u, -y, win, [], [], 1/Ts);

apa95ml_5kg_10V_coh.png

Figure 7: Coherence

apa95ml_5kg_10V_tf.png

Figure 8: Estimation of the transfer function from input voltage to displacement

4.4 Comparison with the FEM model

load('mat/fem_model_5kg.mat', 'Ghm');

apa95ml_5kg_comp_fem.png

Figure 9: Comparison of the identified transfer function and the one estimated from the FE model

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.

5 Transfer Function Estimation using the PI Amplifier

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;

win = hanning(ceil(1*Fs));

[pxx, f] = pwelch(y, win, [], [], Fs);
[pht, ~] = pwelch(ht.y, win, [], [], Fs);

apa95ml_5kg_PI_pdf_comp_huddle.png

Figure 10: Comparison of the ASD for the identification test and the huddle test

5.3 Compute TF estimate and Coherence

Ts = t(end)/(length(t)-1);
Fs = 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);

apa95ml_5kg_PI_coh.png

Figure 11: Coherence

apa95ml_5kg_PI_tf.png

Figure 12: Estimation of the transfer function from input voltage to displacement

5.4 Comparison with the FEM model

load('mat/fem_model_5kg.mat', 'G');

apa95ml_5kg_pi_comp_fem.png

Figure 13: Comparison of the identified transfer function and the one estimated from the FE model

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');

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);

bode_plot_force_sensor_voltage_comp_fem.png

Figure 14: Comparison of the identified dynamics from voltage output to voltage input and the FEM

6.1 System Identification

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);

iff_plant_identification_apa95ml.png

Figure 15: Identification of the IFF plant

6.2 Integral Force Feedback

root_locus_iff_apa95ml_identification.png

Figure 16: Root Locus for IFF

7 IFF Tests

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');

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_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);

iff_first_test_coherence.png

Figure 17: Coherence

iff_first_test_bode_plot.png

Figure 18: Bode plot for different values of IFF gain

7.2 Second test with many Gains

load('./mat/apa95ml_iff_test.mat', 'results');

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

iff_results_bode_plots.png 

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

iff_results_bode_plots_identification.png

iff_results_root_locus.png

Author: Dehaeze Thomas

Created: 2020-08-21 ven. 15:26