172 lines
5.5 KiB
Matlab
172 lines
5.5 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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addpath('./mat/');
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% Transfer function from excitation signal to displacement
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% Let's first estimate the transfer function from the excitation signal in [V] to the generated displacement in [m] as measured by the inteferometer.
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id_cl = load('identification_noise_iff_bis.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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id_cl.d = detrend(id_cl.d, 0);
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id_cl.acc_1 = detrend(id_cl.acc_1, 0);
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id_cl.acc_2 = detrend(id_cl.acc_2, 0);
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id_cl.geo_1 = detrend(id_cl.geo_1, 0);
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id_cl.geo_2 = detrend(id_cl.geo_2, 0);
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id_cl.f_meas = detrend(id_cl.f_meas, 0);
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id_cl.u = detrend(id_cl.u, 0);
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Ts = id_cl.t(2) - id_cl.t(1);
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win = hann(ceil(10/Ts));
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[tf_G_cl_est, f] = tfestimate(id_cl.u, id_cl.d, win, [], [], 1/Ts);
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[co_G_cl_est, ~] = mscohere( id_cl.u, id_cl.d, win, [], [], 1/Ts);
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% Approximate transfer function from voltage output to generated displacement when IFF is used, in [m/V].
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G_d_est = -5e-6*(2*pi*230)^2/(s^2 + 2*0.3*2*pi*240*s + (2*pi*240)^2);
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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_G_cl_est), '-')
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plot(f, abs(squeeze(freqresp(G_d_est, f, 'Hz'))), '--')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ax2 = nexttile;
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hold on;
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plot(f, 180/pi*angle(tf_G_cl_est), '-')
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plot(f, 180/pi*angle(squeeze(freqresp(G_d_est, f, 'Hz'))), '--')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
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ylabel('Phase'); xlabel('Frequency [Hz]');
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hold off;
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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linkaxes([ax1,ax2], 'x');
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xlim([10, 1000]);
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% Motion measured during Huddle test
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% We now compute the PSD of the measured motion by the inertial sensors during the huddle test.
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ht = load('huddle_test.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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ht.d = detrend(ht.d, 0);
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ht.acc_1 = detrend(ht.acc_1, 0);
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ht.acc_2 = detrend(ht.acc_2, 0);
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ht.geo_1 = detrend(ht.geo_1, 0);
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ht.geo_2 = detrend(ht.geo_2, 0);
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[p_d, f] = pwelch(ht.d, win, [], [], 1/Ts);
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[p_acc1, ~] = pwelch(ht.acc_1, win, [], [], 1/Ts);
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[p_acc2, ~] = pwelch(ht.acc_2, win, [], [], 1/Ts);
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[p_geo1, ~] = pwelch(ht.geo_1, win, [], [], 1/Ts);
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[p_geo2, ~] = pwelch(ht.geo_2, win, [], [], 1/Ts);
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% Using an estimated model of the sensor dynamics from the documentation of the sensors, we can compute the ASD of the motion in $m/\sqrt{Hz}$ measured by the sensors.
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G_acc = 1/(1 + s/2/pi/2500); % [V/(m/s2)]
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G_geo = -120*s^2/(s^2 + 2*0.7*2*pi*2*s + (2*pi*2)^2); % [V/(m/s)]
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figure;
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hold on;
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set(gca, 'ColorOrderIndex', 1);
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plot(f, sqrt(p_acc1)./abs(squeeze(freqresp(G_acc*s^2, f, 'Hz'))), ...
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'DisplayName', 'Accelerometer');
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set(gca, 'ColorOrderIndex', 1);
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plot(f, sqrt(p_acc2)./abs(squeeze(freqresp(G_acc*s^2, f, 'Hz'))), ...
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'HandleVisibility', 'off');
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set(gca, 'ColorOrderIndex', 2);
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plot(f, sqrt(p_geo1)./abs(squeeze(freqresp(G_geo*s, f, 'Hz'))), ...
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'DisplayName', 'Geophone');
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set(gca, 'ColorOrderIndex', 2);
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plot(f, sqrt(p_geo2)./abs(squeeze(freqresp(G_geo*s, f, 'Hz'))), ...
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'HandleVisibility', 'off');
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set(gca, 'ColorOrderIndex', 3);
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plot(f, sqrt(p_d), 'DisplayName', 'Interferometer');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
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title('Huddle Test')
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legend();
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% #+name: fig:huddle_test_psd_motion
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% #+caption: ASD of the motion measured by the sensors
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% #+RESULTS:
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% [[file:figs/huddle_test_psd_motion.png]]
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% From the ASD of the motion measured by the sensors, we can create an excitation signal that will generate much motion motion that the motion under no excitation.
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% We create =G_exc= that corresponds to the wanted generated motion.
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G_exc = 0.2e-6/(1 + s/2/pi/2)/(1 + s/2/pi/50);
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% And we create a time domain signal =y_d= that have the spectral density described by =G_exc=.
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Fs = 1/Ts;
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t = 0:Ts:180; % Time Vector [s]
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u = sqrt(Fs/2)*randn(length(t), 1); % Signal with an ASD equal to one
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y_d = lsim(G_exc, u, t);
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[pxx, ~] = pwelch(y_d, win, 0, [], Fs);
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figure;
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hold on;
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set(gca, 'ColorOrderIndex', 1);
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plot(f, sqrt(p_acc1)./abs(squeeze(freqresp(G_acc*s^2, f, 'Hz'))), ...
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'DisplayName', 'Accelerometer');
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set(gca, 'ColorOrderIndex', 1);
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plot(f, sqrt(p_acc2)./abs(squeeze(freqresp(G_acc*s^2, f, 'Hz'))), ...
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'HandleVisibility', 'off');
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set(gca, 'ColorOrderIndex', 2);
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plot(f, sqrt(p_geo1)./abs(squeeze(freqresp(G_geo*s, f, 'Hz'))), ...
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'DisplayName', 'Geophone');
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set(gca, 'ColorOrderIndex', 2);
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plot(f, sqrt(p_geo2)./abs(squeeze(freqresp(G_geo*s, f, 'Hz'))), ...
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'HandleVisibility', 'off');
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set(gca, 'ColorOrderIndex', 3);
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plot(f, sqrt(pxx), 'k-', ...
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'DisplayName', 'Excitation');
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plot(f, sqrt(p_d), 'DisplayName', 'Interferometer');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
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title('Huddle Test')
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legend();
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% #+name: fig:comp_huddle_test_excited_motion_psd
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% #+caption: Comparison of the ASD of the motion during Huddle and the wanted generated motion
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% #+RESULTS:
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% [[file:figs/comp_huddle_test_excited_motion_psd.png]]
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% We can now generate the voltage signal that will generate the wanted motion.
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y_v = lsim(G_exc * ... % from unit PSD to shaped PSD
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(1 + s/2/pi/50) * ... % Inverse of pre-filter included in the Simulink file
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1/G_d_est * ... % Wanted displacement => required voltage
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1/(1 + s/2/pi/5e3), ... % Add some high frequency filtering
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u, t);
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figure;
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plot(t, y_v)
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xlabel('Time [s]'); ylabel('Voltage [V]');
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