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Test Bench APA95ML

• Introduction
• Setup
  • Parameters
  • Filter White Noise
• Run Experiment and Save Data
  • Load Data
  • Save Data
• Huddle Test
  • Time Domain Data
  • PSD of Measurement Noise
• Transfer Function Estimation using the DAC as the driver
  • Time Domain Data
  • Comparison of the PSD with Huddle Test
  • Compute TF estimate and Coherence
  • Comparison with the FEM model
  • Conclusion
• Transfer Function Estimation using the PI Amplifier
  • Comparison of the PSD with Huddle Test
  • Compute TF estimate and Coherence
  • Comparison with the FEM model
• Transfer function of the PI Amplifier
  • Compute TF estimate and Coherence

Introduction   ignore

Picture of the Setup

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

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 DAC as the driver

Time Domain Data

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);

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);

Coherence

Estimation of the transfer function from input voltage to displacement

Comparison with the FEM model

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

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 Estimation using the 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);

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

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

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);

Coherence

Estimation of the transfer function from input voltage to displacement

The delay can be estimated as follow (in ms):

  finddelay(u, um)*(1000*Ts)

0.4

This most probably corresponds to a FIR filter.