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