Tangle + move to matlab folder

matlab/dynamics_encoder.m

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+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Load Data
+% As usual, the measurement data are loaded.
+
+load('int_enc_id_noise_bis.mat', 'interferometer', 'encoder', 'u', 't');
+
+
+
+% The first 0.1 seconds are removed as it corresponds to transient behavior.
+
+interferometer = interferometer(t>0.1);
+encoder = encoder(t>0.1);
+u = u(t>0.1);
+t = t(t>0.1);
+
+
+
+% Finally the offset are removed using the =detrend= command.
+
+interferometer = detrend(interferometer, 0);
+encoder = detrend(encoder, 0);
+u = detrend(u, 0);
+
+% Excitation and Measured Signals
+% The excitation signal is a white noise filtered by a low pass filter to not excite too much the high frequency modes.
+
+% The excitation signal is shown in Figure [[fig:encoder_identification_excitation_time]].
+
+figure;
+plot(t, u);
+xlabel('Time [s]'); ylabel('Voltage [V]');
+
+
+
+% #+name: fig:encoder_identification_excitation_time
+% #+caption:
+% #+RESULTS:
+% [[file:figs/encoder_identification_excitation_time.png]]
+
+% The measured motion by the interferometer and encoder is shown in Figure
+
+figure;
+hold on;
+plot(t, interferometer, 'DisplayName', 'Interferometer');
+plot(t, encoder, 'DisplayName', 'Encoder');
+hold off;
+xlabel('Time [s]'); ylabel('Displacement [m]');
+legend('location', 'southeast');
+
+% Identification
+% Now the dynamics from the voltage sent to the voltage amplitude driving the APA95ML to the measured displacement by both the encoder and interferometer are computed.
+
+
+Ts = 1e-4; % Sampling Time [s]
+win = hann(ceil(10/Ts));
+
+[tf_i_est, f] = tfestimate(u, interferometer, win, [], [], 1/Ts);
+[co_i_est, ~] = mscohere(u, interferometer, win, [], [], 1/Ts);
+
+[tf_e_est, ~] = tfestimate(u, encoder, win, [], [], 1/Ts);
+[co_e_est, ~] = mscohere(u, encoder, win, [], [], 1/Ts);
+
+
+
+% The obtained coherence is shown in Figure [[fig:identification_dynamics_coherence]].
+% It is shown that the identification is good until 500Hz for the interferometer and until 1kHz for the encoder.
+
+
+figure;
+hold on;
+plot(f, co_i_est, '-', 'DisplayName', 'Interferometer')
+plot(f, co_e_est, '-', 'DisplayName', 'Encoder')
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ylabel('Coherence'); xlabel('Frequency [Hz]');
+hold off;
+xlim([0.5, 5e3]);
+legend('location', 'southwest');
+
+
+
+% #+name: fig:identification_dynamics_coherence
+% #+caption:
+% #+RESULTS:
+% [[file:figs/identification_dynamics_coherence.png]]
+
+% The compared dynamics as measured by the intereferometer and encoder are shown in Figure [[fig:identification_dynamics_bode]].
+
+
+figure;
+ tiledlayout(3, 1, 'TileSpacing', 'None', 'Padding', 'None');
+
+ ax1 = nexttile([2, 1]);
+ hold on;
+ plot(f, abs(tf_i_est), '-', 'DisplayName', 'Interferometer')
+ plot(f, abs(tf_e_est), '-', 'DisplayName', 'Encoder')
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ ylabel('Amplitude'); set(gca, 'XTickLabel',[]);
+ hold off;
+ ylim([1e-7, 3e-4]);
+ legend('location', 'southwest');
+
+ ax2 = nexttile;
+ hold on;
+ plot(f, 180/pi*angle(tf_i_est), '-')
+ plot(f, 180/pi*angle(tf_e_est), '-')
+ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
+ ylabel('Phase [deg]'); xlabel('Frequency [Hz]');
+hold off;
+ yticks(-360:90:360);
+ axis padded 'auto x'
+
+ linkaxes([ax1,ax2], 'x');
+ xlim([0.5, 5e3]);

matlab/encoder_noise.m

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+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Load Data
+% The measurement data are loaded and the offset are removed using the =detrend= command.
+
+
+load('int_enc_huddle_test.mat', 'interferometer', 'encoder', 't');
+
+interferometer = detrend(interferometer, 0);
+encoder = detrend(encoder, 0);
+
+% Time Domain Results
+% The measurement of both the encoder and interferometer are shown in Figure [[fig:huddle_test_time_domain]].
+
+
+figure;
+hold on;
+plot(t, encoder, 'DisplayName', 'Encoder')
+plot(t, interferometer, 'DisplayName', 'Interferometer')
+hold off;
+xlabel('Time [s]'); ylabel('Displacement [m]');
+legend('location', 'northeast');
+
+
+
+% #+name: fig:huddle_test_time_domain
+% #+caption: Huddle test - Time domain signals
+% #+RESULTS:
+% [[file:figs/huddle_test_time_domain.png]]
+
+% The raw signals are filtered with a Low Pass filter (defined below) such that we can see the low frequency motion (Figure [[fig:huddle_test_time_domain_filtered]]).
+
+G_lpf = 1/(1 + s/2/pi/10);
+
+figure;
+hold on;
+plot(t, lsim(G_lpf, encoder, t), 'DisplayName', 'Encoder')
+plot(t, lsim(G_lpf, interferometer, t), 'DisplayName', 'Interferometer')
+hold off;
+xlabel('Time [s]'); ylabel('Displacement [m]');
+legend('location', 'northeast');
+
+% Frequency Domain Noise
+% The noise of the measurement (supposing there is no motion) is now translated in the frequency domain by computed the Amplitude Spectral Density.
+
+
+Ts = 1e-4;
+win = hann(ceil(10/Ts));
+
+[p_i, f] = pwelch(interferometer, win, [], [], 1/Ts);
+[p_e, ~] = pwelch(encoder,        win, [], [], 1/Ts);
+
+
+
+% The comparison of the ASD of the encoder and interferometer are shown in Figure [[fig:huddle_test_asd]].
+
+% It is clear that although the encoder exhibit higher frequency noise, is it more stable at low frequency as the length of the beam path in the air is much smaller and thus changed of temperature/pressure/humity of the air has much smaller effect on the measured displacement.
+
+
+figure;
+hold on;
+plot(f, sqrt(p_i), 'DisplayName', 'Interferometer');
+plot(f, sqrt(p_e), 'DisplayName', 'Encoder');
+hold off;
+set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
+ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
+legend();
+xlim([1e-1, 5e3]);