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# Test Bench APA95ML
Author: Dehaeze Thomas

## Table of Contents

- 1. Setup
  - 1.1. Parameters
  - 1.2. Filter White Noise
- 2. Run Experiment and Save Data
  - 2.1. Load Data
  - 2.2. Save Data
- 3. Huddle Test
  - 3.1. Time Domain Data
  - 3.2. PSD of Measurement Noise
- 4. Transfer Function Estimation with \(m=5kg\)
  - 4.1. Time Domain Data
  - 4.2. Comparison of the PSD with Huddle Test
  - 4.3. Compute TF estimate and Coherence
  - 4.4. Comparison with the FEM model

Figure 1: Picture of the Setup

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

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

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

## 4 Transfer Function Estimation with \(m=5kg\)

### 4.1 Time Domain Data

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);

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

### 4.3 Compute TF estimate and Coherence

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

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

Figure 7: Coherence

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');

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

Author: Dehaeze Thomas

Created: 2020-07-20 lun. 13:29