test-bench-apa/index.org

Test Bench APA

• Setup
  • Parameters
  • Filter White Noise
• Run Experiment and Save Data
  • Load Data
  • Save Data
• Huddle Test
  • Load Data
  • Time Domain Data
  • PSD of Measurement Noise
• Transfer Function Estimation with m=5kg
  • Load Data
  • Time Domain Data
  • Comparison of the PSD with Huddle Test
  • Compute TF estimate and Coherence
  • Coherence
  • Transfer Function

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

Load Data

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

Time Domain Data

  figure;
  plot(t, y)
  ylabel('Output Displacement [m]'); xlabel('Time [s]');

PSD of Measurement Noise

  Ts = t(end)/(length(t)-1);
  Fs = 1/Ts;
 
  win = hanning(ceil(1*Fs));

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

  figure;
  plot(f, sqrt(pxx));
  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');

Transfer Function Estimation with m=5kg

Load Data

  ht = load('./mat/huddle_test.mat', 't', 'u', 'y');
  load('./mat/apa95ml_5kg.mat', 't', 'u', 'y');

Time Domain Data

  figure;

  subplot(1,2,1);
  plot(t, u)
  ylabel('Input Voltage [V]'); xlabel('Time [s]');


  subplot(1,2,2);
  plot(t, y)
  ylabel('Output Displacement [m]'); xlabel('Time [s]');

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);

  figure;
  hold on;
  plot(f, sqrt(pxx), 'DisplayName', '5kg');
  plot(f, sqrt(pht), 'DisplayName', 'Huddle Test');
  hold off;
  set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
  xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
  legend('locaation', 'norteast');

Compute TF estimate and Coherence

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

  [tf_est, f] = tfestimate(data(:, 1), -data(:, 2), win, [], [], 1/Ts);
  [co_est, ~] = mscohere(  data(:, 1), -data(:, 2), win, [], [], 1/Ts);

Coherence

  figure;

  hold on;
  plot(f, co_est, 'k-')
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
  ylabel('Coherence'); xlabel('Frequency [Hz]');
  hold off;

Transfer Function

  figure;
  ax1 = subplot(2, 1, 1);
  hold on;
  plot(f, abs(tf_est), 'k-')
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  ylabel('Amplitude'); xlabel('Frequency [Hz]');
  hold off;

  ax2 = subplot(2, 1, 2);
  hold on;
  plot(f, 180/pi*angle(tf_est), 'k-')
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
  ylabel('Phase'); xlabel('Frequency [Hz]');
  legend();
  hold off;

  linkaxes([ax1,ax2], 'x');
  xlim([10, 5000]);