Nano-Hexapod - Test Bench

1. Test-Bench Description
2. Encoders fixed to the Struts

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1 Test-Bench Description

Here are the documentation of the equipment used for this test bench:

Voltage Amplifier: PiezoDrive PD200
Amplified Piezoelectric Actuator: Cedrat APA300ML
DAC/ADC: Speedgoat IO313
Encoder: Renishaw Vionic and used Ruler
Interferometers: Attocube

Figure 1: Nano-Hexapod

Figure 2: Nano-Hexapod and the control electronics

2 Encoders fixed to the Struts

2.1 Introduction

2.2 Load Data

meas_data_lf = {};

for i = 1:6
    meas_data_lf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_lf.mat', i), 't', 'Va', 'Vs', 'de')};
    meas_data_hf(i) = {load(sprintf('mat/frf_data_exc_strut_%i_noise_hf.mat', i), 't', 'Va', 'Vs', 'de')};
end

2.3 Spectral Analysis - Setup

% Sampling Time [s]
Ts = (meas_data_lf{1}.t(end) - (meas_data_lf{1}.t(1)))/(length(meas_data_lf{1}.t)-1);

% Sampling Frequency [Hz]
Fs = 1/Ts;

% Hannning Windows
win = hanning(ceil(1*Fs));

And we get the frequency vector.

[~, f] = tfestimate(meas_data_lf{1}.Va, meas_data_lf{1}.de, win, [], [], 1/Ts);

i_lf = f < 250; % Points for low frequency excitation
i_hf = f > 250; % Points for high frequency excitation

2.4 DVF Plant

First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure 3).

%% Coherence
coh_dvf_lf = zeros(length(f), 6, 6);
coh_dvf_hf = zeros(length(f), 6, 6);

for i = 1:6
    coh_dvf_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts);
    coh_dvf_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts);
end

Figure 3: Obtained coherence for the DVF plant

Then the 6x6 transfer function matrix is estimated (Figure 4).

%% DVF Plant
G_dvf_lf = zeros(length(f), 6, 6);
G_dvf_hf = zeros(length(f), 6, 6);

for i = 1:6
    G_dvf_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.de, win, [], [], 1/Ts);
    G_dvf_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.de, win, [], [], 1/Ts);
end

Figure 4: Measured FRF for the DVF plant

2.5 IFF Plant

First, let’s compute the coherence from the excitation voltage and the displacement as measured by the encoders (Figure 5).

%% Coherence
coh_iff_lf = zeros(length(f), 6, 6);
coh_iff_hf = zeros(length(f), 6, 6);

for i = 1:6
    coh_iff_lf(:, :, i) = mscohere(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts);
    coh_iff_hf(:, :, i) = mscohere(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts);
end

Figure 5: Obtained coherence for the IFF plant

Then the 6x6 transfer function matrix is estimated (Figure 6).

%% IFF Plant
G_iff_lf = zeros(length(f), 6, 6);
G_iff_hf = zeros(length(f), 6, 6);

for i = 1:6
    G_iff_lf(:, :, i) = tfestimate(meas_data_lf{i}.Va, meas_data_lf{i}.Vs, win, [], [], 1/Ts);
    G_iff_hf(:, :, i) = tfestimate(meas_data_hf{i}.Va, meas_data_hf{i}.Vs, win, [], [], 1/Ts);
end

Figure 6: Measured FRF for the IFF plant

2.6 Jacobian

load('jacobian.mat', 'J');

G_dvf_J_lf = G_dvf_lf(i_lf, i, j)

#+end_src