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Test Bench APA95ML

Introduction   ignore

figs/setup_picture.png
Picture of the Setup
figs/setup_zoom.png
Zoom on the APA

Setup

Parameters 

  Ts = 1e-4;

Filter White Noise 

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

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

Run Experiment and Save Data

Load Data 

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

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');

Huddle Test

Time Domain Data

figs/huddle_test_time_domain.png

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, win, [], [], Fs);

figs/huddle_test_pdf.png

Amplitude Spectral Density of the Displacement during Huddle Test

Transfer Function Estimation with $m=5kg$

Time Domain Data

figs/apa95ml_5kg_10V_time_domain.png

Time domain signals during the test

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);

figs/apa95ml_5kg_10V_pdf_comp_huddle.png

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

figs/apa95ml_5kg_10V_coh.png

Coherence

figs/apa95ml_5kg_10V_tf.png

Estimation of the transfer function from input voltage to displacement

Comparison with the FEM model 

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

figs/apa95ml_5kg_comp_fem.png

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

Conclusion   ignore

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.

Transfer function of the PI Amplifier

Compute TF estimate and Coherence 

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

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).

  win = hann(ceil(10/Ts));

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

figs/PI_E505_coh.png

Coherence

figs/PI_E505_tf.png

Estimation of the transfer function from input voltage to displacement

The delay can be estimated as follow:

  finddelay(u, um)*Ts
0.0004

PI Amplifier

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);

figs/apa95ml_5kg_PI_pdf_comp_huddle.png

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(10/Ts));

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

figs/apa95ml_5kg_PI_coh.png

Coherence

figs/apa95ml_5kg_PI_tf.png

Estimation of the transfer function from input voltage to displacement

Comparison with the FEM model 

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

figs/apa95ml_5kg_pi_comp_fem.png

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