phd-test-bench-struts/matlab/test_struts_2_dynamical_meas.m

%% Clear Workspace and Close figures
clear; close all; clc;

%% Intialize Laplace variable
s = zpk('s');

%% Path for functions, data and scripts
addpath('./mat/'); % Path for data
addpath('./src/'); % Path for functions

%% Colors for the figures
colors = colororder;

% Effect of the Encoder on the measured dynamics
% <<ssec:test_struts_effect_encoder>>


%% Parameters for Frequency Analysis
Ts = 1e-4; % Sampling Time [s]
Nfft = floor(1/Ts); % Number of points for the FFT computation
win = hanning(Nfft); % Hanning window
Noverlap = floor(Nfft/2); % Overlap between frequency analysis

%% Measure FRF for Strut 1 - No encoder
% Load Data
leg_sweep    = load('frf_data_leg_1_sweep.mat', 'u', 'Vs', 'de', 'da');
leg_noise_hf = load('frf_data_leg_1_noise_hf.mat', 'u', 'Vs', 'de', 'da');

% We get the frequency vector that will be the same for all the frequency domain analysis.
[~, f] = tfestimate(leg_sweep.u, leg_sweep.de, win, Noverlap, Nfft, 1/Ts);
i_lf = f <= 350; % Indices used for the low frequency
i_hf = f >  350; % Indices used for the high frequency

% Compute FRF function from u to da (interferometer)
[frf_sweep, ~]    = tfestimate(leg_sweep.u,    leg_sweep.da,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_noise_hf.u, leg_noise_hf.da, win, Noverlap, Nfft, 1/Ts);
int_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF

% Compute FRF function from u to Vs (force sensor)
[frf_sweep,    ~] = tfestimate(leg_sweep.u,    leg_sweep.Vs,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_noise_hf.u, leg_noise_hf.Vs, win, Noverlap, Nfft, 1/Ts);
iff_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF

%% Measure FRF for Strut 1 - With encoder
% Load Data
leg_enc_sweep    = load('frf_data_leg_coder_1_noise.mat',    'u', 'Vs', 'de', 'da');
leg_enc_noise_hf = load('frf_data_leg_coder_1_noise_hf.mat', 'u', 'Vs', 'de', 'da');

% Compute FRF function from u to da (interferometer)
[frf_sweep, ~]    = tfestimate(leg_enc_sweep.u,    leg_enc_sweep.da,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.da, win, Noverlap, Nfft, 1/Ts);
int_with_enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF

% Compute FRF function from u to Vs (force sensor)
[frf_sweep, ~]    = tfestimate(leg_enc_sweep.u,    leg_enc_sweep.Vs,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.Vs, win, Noverlap, Nfft, 1/Ts);
iff_with_enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF

% Compute FRF function from u to de (encoder)
[frf_sweep, ~]    = tfestimate(leg_enc_sweep.u,    leg_enc_sweep.de,    win, Noverlap, Nfft, 1/Ts);
[frf_noise_hf, ~] = tfestimate(leg_enc_noise_hf.u, leg_enc_noise_hf.de, win, Noverlap, Nfft, 1/Ts);
enc_frf = [frf_sweep(i_lf); frf_noise_hf(i_hf)]; % Combine the FRF



% Figure ref:fig:test_struts_effect_encoder_int
% Same goes for the transfer function from excitation voltage $u$ to the axial motion of the strut $d_a$ as measured by the interferometer ().

% The transfer function from the excitation voltage $u$ to the generated voltage $V_s$ by the sensor stack is not influence by the fixation of the encoder (Figure ref:fig:test_struts_effect_encoder_iff).
% This means that the IFF control strategy should be as effective whether or not the encoders are fixed to the struts.


%% Plot the FRF from u to da with and without the encoder
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile;
hold on;
plot(f, abs(int_with_enc_frf), '-', 'DisplayName', 'With encoder');
plot(f, abs(int_frf),          '-', 'DisplayName', 'Without encoder');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_a/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-7, 1e-3]);
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(int_with_enc_frf), '-');
plot(f, 180/pi*angle(int_frf), '-');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360); ylim([-180, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

%% Compare the IFF plant with and without the encoders
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(iff_with_enc_frf), 'DisplayName', 'With Encoder');
plot(f, abs(iff_frf), 'DisplayName', 'Without Encoder');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
ylim([1e-2, 1e2]);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(iff_with_enc_frf));
plot(f, 180/pi*angle(iff_frf));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360); ylim([-180, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

% Comparison of the encoder and interferometer
% <<ssec:test_struts_comp_enc_int>>

% The dynamics as measured by the encoder and by the interferometers are compared in Figure ref:fig:test_struts_comp_enc_int.

% The dynamics from the excitation voltage $u$ to the measured displacement by the encoder $d_e$ presents much more complicated behavior than the transfer function to the displacement as measured by the Interferometer (compared in Figure ref:fig:test_struts_comp_enc_int).
% It will be further investigated why the two dynamics as so different and what are causing all these resonances.

% As shown in Figure ref:fig:test_struts_comp_enc_int, we can clearly see three spurious resonances at 197Hz, 290Hz and 376Hz.
% These resonances correspond to parasitic resonances of the strut itself that was estimated using a finite element model of the strut (Figure ref:fig:test_struts_mode_shapes):
% - Mode in X-bending at 189Hz
% - Mode in Y-bending at 285Hz
% - Mode in Z-torsion at 400Hz

% The good news is that these resonances are not seen on the interferometer (they are therefore not impacting the axial motion of the strut).
% But these resonances are making the use of encoder fixed to the strut difficult.


figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
plot(f, abs(enc_frf),          'DisplayName', 'Encoder');
plot(f, abs(int_with_enc_frf), 'DisplayName', 'Interferometer');
text(93,  4e-4,  {'93Hz'}, 'VerticalAlignment','bottom','HorizontalAlignment','center')
text(200, 1.3e-4,{'197Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
text(300, 4e-6,  {'290Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
text(400, 1.4e-6,{'376Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
ylim([1e-8, 1e-3]);

ax2 = nexttile;
hold on;
plot(f, 180/pi*angle(enc_frf));
plot(f, 180/pi*angle(int_with_enc_frf));
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360); ylim([-180, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

% Comparison of all the Struts
% <<ssec:test_struts_comp_all_struts>>


%% Numbers of the measured legs
strut_nums = [1 2 3 4 5];

%% Load the measurement data
% First identification (low frequency noise)
leg_noise = {};
for i = 1:length(strut_nums)
    leg_noise(i) = {load(sprintf('frf_data_leg_coder_%i_noise.mat', strut_nums(i)), 'u', 'Vs', 'de', 'da')};
end

% Second identification (high frequency noise)
leg_noise_hf = {};
for i = 1:length(strut_nums)
    leg_noise_hf(i) = {load(sprintf('frf_data_leg_coder_%i_noise_hf.mat', strut_nums(i)), 'u', 'Vs', 'de', 'da')};
end

%% Compute FRF - From u to de (encoder)
enc_frf = zeros(length(f), length(strut_nums));

for i = 1:length(strut_nums)
    [frf_lf, ~] = tfestimate(leg_noise{i}.u,    detrend(leg_noise{i}.de, 0),    win, Noverlap, Nfft, 1/Ts);
    [frf_hf, ~] = tfestimate(leg_noise_hf{i}.u, detrend(leg_noise_hf{i}.de, 0), win, Noverlap, Nfft, 1/Ts);
    enc_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
end

%% Compute FRF - From u to da (interferometer)
int_frf = zeros(length(f), length(strut_nums));
for i = 1:length(strut_nums)
    [frf_lf, ~] = tfestimate(leg_noise{i}.u,    leg_noise{i}.da,    win, Noverlap, Nfft, 1/Ts);
    [frf_hf, ~] = tfestimate(leg_noise_hf{i}.u, leg_noise_hf{i}.da, win, Noverlap, Nfft, 1/Ts);
    int_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
end

%% Compute FRF - From u to Vs (force sensor)
iff_frf = zeros(length(f), length(strut_nums));
for i = 1:length(strut_nums)
    [frf_lf, ~] = tfestimate(leg_noise{i}.u,    leg_noise{i}.Vs,    win, Noverlap, Nfft, 1/Ts);
    [frf_hf, ~] = tfestimate(leg_noise_hf{i}.u, leg_noise_hf{i}.Vs, win, Noverlap, Nfft, 1/Ts);
    iff_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
end



% Then, the transfer function from the DAC output voltage $u$ to the measured displacement by the Attocube is computed for all the struts and shown in Figure ref:fig:test_struts_comp_interf_plants.
% All the struts are giving very similar FRF.


%% Plot the FRF from u to de (interferometer)
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(strut_nums)
    plot(f, abs(int_frf(:, i)), ...
         'DisplayName', sprintf('Leg %i', strut_nums(i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_a/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'southwest', 'FontSize', 8, 'NumColumns', 2);
ylim([1e-9, 1e-3]);

ax2 = nexttile;
hold on;
for i = 1:length(strut_nums)
    plot(f, 180/pi*angle(int_frf(:, i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360); ylim([-180 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

%% Plot the FRF from u to Vs
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(strut_nums)
    plot(f, abs(iff_frf(:, i)), ...
         'DisplayName', sprintf('Leg %i', strut_nums(i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_s/u$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off;
ylim([1e-2, 1e2]);
legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);

ax2 = nexttile;
hold on;
for i = 1:length(strut_nums)
    plot(f, 180/pi*angle(iff_frf(:, i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360); ylim([-180 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);



% #+name: fig:test_struts_comp_plants
% #+caption: Comparison of the measured plants
% #+attr_latex: :options [htbp]
% #+begin_figure
% #+attr_latex: :caption \subcaption{\label{fig:test_struts_comp_interf_plants}$u$ to $d_a$}
% #+attr_latex: :options {0.49\textwidth}
% #+begin_subfigure
% #+attr_latex: :width \linewidth
% [[file:figs/test_struts_comp_interf_plants.png]]
% #+end_subfigure
% #+attr_latex: :caption \subcaption{\label{fig:test_struts_comp_iff_plants}$u$ to $V_s$}
% #+attr_latex: :options {0.49\textwidth}
% #+begin_subfigure
% #+attr_latex: :width \linewidth
% [[file:figs/test_struts_comp_iff_plants.png]]
% #+end_subfigure
% #+end_figure

% There is a very large variability of the dynamics as measured by the encoder as shown in Figure ref:fig:test_struts_comp_enc_plants.
% Even-though the same peaks are seen for all of the struts (95Hz, 200Hz, 300Hz, 400Hz), the amplitude of the peaks are not the same.
% Moreover, the location or even the presence of complex conjugate zeros is changing from one strut to the other.

% All of this will be studied in Section ref:sec:test_struts_simscape using the Simscape model.


%% Bode plot of the FRF from u to de
figure;
tiledlayout(3, 1, 'TileSpacing', 'Compact', 'Padding', 'None');

ax1 = nexttile([2,1]);
hold on;
for i = 1:length(strut_nums)
    plot(f, abs(enc_frf(:, i)), ...
         'DisplayName', sprintf('Leg %i', strut_nums(i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $d_e/u$ [m/V]'); set(gca, 'XTickLabel',[]);
hold off;
legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
ylim([1e-8, 1e-3]);

ax2 = nexttile;
hold on;
for i = 1:length(strut_nums)
    plot(f, 180/pi*angle(enc_frf(:, i)));
end
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
yticks(-360:90:360); ylim([-180, 180]);

linkaxes([ax1,ax2],'x');
xlim([10, 2e3]);

%% Save the estimated FRF for further analysis
save('./mat/meas_struts_frf.mat', 'f', 'enc_frf', 'int_frf', 'iff_frf', 'strut_nums');