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Test Bench APA95ML

• Introduction
• Huddle Test
  • Time Domain Data
  • PSD of Measurement Noise
• Transfer Function Estimation using the PI Amplifier
  • Load Data
  • Comparison of the PSD with Huddle Test
  • Compute TF estimate and Coherence
  • Comparison with the FEM model
• Transfer function from force actuator to force sensor
  • Introduction
  • Load Data
  • Adjust gain
  • Compute TF estimate and Coherence
  • System Identification
  • Integral Force Feedback
• IFF Tests
  • First tests with few gains
  • Second test with many Gains

Introduction   ignore

Picture of the Setup

Zoom on the APA

Huddle Test

<<sec:huddle_test>>

Time Domain Data

Measurement of the Mass displacement during Huddle Test

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);

Amplitude Spectral Density of the Displacement during Huddle Test

Transfer Function Estimation using the PI Amplifier

Load Data

  ht = load('huddle_test.mat', 't', 'u', 'y');
  load('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);

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);

Comparison of the ASD for the identification test and the huddle test

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);

Coherence

Estimation of the transfer function from input voltage to displacement

Comparison with the FEM model

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

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

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.

Load Data   ignore

The data are loaded:

  a_ss = load('apa95ml_5kg_1a_2s.mat', 't', 'u', 'y', 'v');
  aa_s = load('apa95ml_5kg_2a_1s.mat', 't', 'u', 'y', 'v');
  load('G_force_sensor_5kg.mat', 'G');

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:

  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);

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.

  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);

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

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);

Identification of the IFF plant

Integral Force Feedback

Root Locus for IFF

IFF Tests

First tests with few gains

  iff_g10 = load('apa95ml_iff_g10_res.mat', 'u', 't', 'y', 'v');
  iff_g100 = load('apa95ml_iff_g100_res.mat', 'u', 't', 'y', 'v');
  iff_of = load('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);

Coherence

Bode plot for different values of IFF gain

Second test with many Gains

  load('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

  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