422 lines
12 KiB
Mathematica
422 lines
12 KiB
Mathematica
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%% Huddle Test
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ht = load('./mat/huddle_test.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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% Detrend Data
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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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ht.f_meas = detrend(ht.f_meas, 0);
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% Compute PSD
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run setup;
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win = hann(ceil(10/Ts));
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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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[p_fmeas, ~] = pwelch(ht.f_meas, win, [], [], 1/Ts);
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% Plot PSD
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figure;
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hold on;
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plot(f, p_acc1);
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plot(f, p_acc2);
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('PSD [$V^2/Hz$]'); xlabel('Frequency [Hz]');
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title('Huddle Test - Accelerometers')
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figure;
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hold on;
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plot(f, p_geo1);
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plot(f, p_geo2);
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('PSD [$V^2/Hz$]'); xlabel('Frequency [Hz]');
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title('Huddle Test - Geophones')
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figure;
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hold on;
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plot(f, p_d);
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('PSD [$m^2/Hz$]'); xlabel('Frequency [Hz]');
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title('Huddle Test - Interferometers')
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figure;
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hold on;
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plot(f, p_fmeas);
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('PSD [$V^2/Hz$]'); xlabel('Frequency [Hz]');
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title('Huddle Test - Force Sensor')
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%% Accelerometer and Geophone Models
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% Accelerometer used: https://www.pcb.com/products?model=393B05
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% Geophone used: L22 https://www.sercel.com/products/Lists/ProductSpecification/Geophones_brochure_Sercel_EN.pdf
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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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% PSD of intertial sensors in [m^2/Hz]
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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, 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, 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, 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, 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, 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('PSD [$m^2/Hz$]'); xlabel('Frequency [Hz]');
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title('Huddle Test')
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legend();
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%% Compare Theoretical model with identified one
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id_ol = load('./mat/identification_chirp_40_400.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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% Detrend Data
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id_ol.d = detrend(id_ol.d, 0);
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id_ol.acc_1 = detrend(id_ol.acc_1, 0);
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id_ol.acc_2 = detrend(id_ol.acc_2, 0);
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id_ol.geo_1 = detrend(id_ol.geo_1, 0);
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id_ol.geo_2 = detrend(id_ol.geo_2, 0);
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id_ol.f_meas = detrend(id_ol.f_meas, 0);
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id_ol.u = detrend(id_ol.u, 0);
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% Identification Parameters
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run setup;
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win = hann(ceil(10/Ts));
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% IFF Plant
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[tf_fmeas_est, f] = tfestimate(id_ol.u, id_ol.f_meas, win, [], [], 1/Ts); % [V/m]
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[co_fmeas_est, ~] = mscohere(id_ol.u, id_ol.f_meas, win, [], [], 1/Ts);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(tf_fmeas_est), '-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude'); xlabel('Frequency [Hz]');
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hold off;
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, 180/pi*unwrap(angle(tf_fmeas_est)), '-')
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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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linkaxes([ax1,ax2], 'x');
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xlim([40, 400]);
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% Geophones
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[tf_geo1_est, ~] = tfestimate(id_ol.d, id_ol.geo_1, win, [], [], 1/Ts); % [V/m]
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[co_geo1_est, ~] = mscohere(id_ol.d, id_ol.geo_1, win, [], [], 1/Ts);
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[tf_geo2_est, ~] = tfestimate(id_ol.d, id_ol.geo_2, win, [], [], 1/Ts); % [V/m]
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[co_geo2_est, ~] = mscohere(id_ol.d, id_ol.geo_2, win, [], [], 1/Ts);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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set(gca, 'ColorOrderIndex', 1);
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plot(f, abs(tf_geo1_est), '.')
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set(gca, 'ColorOrderIndex', 1);
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plot(f, abs(tf_geo2_est), '.')
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plot(f, abs(squeeze(freqresp(G_geo, f, 'Hz')).*(1i*2*pi*f)), 'k-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude'); xlabel('Frequency [Hz]');
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hold off;
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ax2 = subplot(2, 1, 2);
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hold on;
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set(gca, 'ColorOrderIndex', 1);
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plot(f, 180/pi*angle(tf_geo1_est), '.')
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set(gca, 'ColorOrderIndex', 1);
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plot(f, 180/pi*angle(tf_geo2_est), '.')
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plot(f, 180/pi*angle(-squeeze(freqresp(G_geo, f, 'Hz')).*(1i*2*pi*f)), 'k-')
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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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linkaxes([ax1,ax2], 'x');
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xlim([40, 400]);
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% Accelerometers
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[tf_acc1_est, ~] = tfestimate(id_ol.d, id_ol.acc_1, win, [], [], 1/Ts); % [V/m]
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[co_acc1_est, ~] = mscohere(id_ol.d, id_ol.acc_1, win, [], [], 1/Ts);
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[tf_acc2_est, ~] = tfestimate(id_ol.d, id_ol.acc_2, win, [], [], 1/Ts); % [V/m]
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[co_acc2_est, ~] = mscohere(id_ol.d, id_ol.acc_2, win, [], [], 1/Ts);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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set(gca, 'ColorOrderIndex', 1);
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plot(f, abs(tf_acc1_est), '.')
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set(gca, 'ColorOrderIndex', 1);
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plot(f, abs(tf_acc2_est), '.')
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plot(f, abs(squeeze(freqresp(G_acc, f, 'Hz')).*(1i*2*pi*f).^2), 'k-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude'); xlabel('Frequency [Hz]');
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hold off;
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ax2 = subplot(2, 1, 2);
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hold on;
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set(gca, 'ColorOrderIndex', 1);
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plot(f, 180/pi*angle(tf_acc1_est), '.')
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set(gca, 'ColorOrderIndex', 1);
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plot(f, 180/pi*angle(tf_acc2_est), '.')
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plot(f, 180/pi*angle(squeeze(freqresp(G_acc, f, 'Hz')).*(1i*2*pi*f).^2), 'k-')
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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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linkaxes([ax1,ax2], 'x');
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xlim([40, 400]);
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%% IFF development
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[tf_fmeas_est, f] = tfestimate(id_ol.u, id_ol.f_meas, win, [], [], 1/Ts); % [V/m]
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[co_fmeas_est, ~] = mscohere(id_ol.u, id_ol.f_meas, win, [], [], 1/Ts);
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% Model
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wz = 2*pi*103;
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xi_z = 0.01;
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wp = 2*pi*237;
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xi_p = 0.015;
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Giff = -20*(s^2 + 2*xi_z*s*wz + wz^2)/(s^2 + 2*xi_p*s*wp + wp^2);
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% Comparison model and identification
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(tf_fmeas_est), '.')
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plot(f, abs(squeeze(freqresp(Giff, f, 'Hz'))), 'k-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude'); xlabel('Frequency [Hz]');
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hold off;
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, 180/pi*angle(tf_fmeas_est), '.')
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plot(f, 180/pi*angle(squeeze(freqresp(Giff, f, 'Hz'))), 'k-')
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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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linkaxes([ax1,ax2], 'x');
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xlim([40, 400]);
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% Root Locus
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gains = logspace(0, 5, 1000);
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figure;
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hold on;
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plot(real(pole(Giff)), imag(pole(Giff)), 'kx');
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plot(real(tzero(Giff)), imag(tzero(Giff)), 'ko');
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for i = 1:length(gains)
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cl_poles = pole(feedback(Giff, -gains(i)/(s + 2*pi*2)));
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plot(real(cl_poles), imag(cl_poles), 'k.');
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end
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ylim([0, 1800]);
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xlim([-1600,200]);
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xlabel('Real Part')
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ylabel('Imaginary Part')
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axis square
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% Optimal Controller
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Kiff_opt = -110/(s + 2*pi*2);
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%% New identification
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id_ol = load('./mat/identification_chirp_40_400.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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id_cl = load('./mat/identification_chirp_40_400_iff.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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% Used controller
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Kiff = -110/(s + 2*pi*2);
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[tf_G_ol_est, f] = tfestimate(id_ol.u, id_ol.d, win, [], [], 1/Ts);
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[co_G_ol_est, ~] = mscohere(id_ol.u, id_ol.d, win, [], [], 1/Ts);
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[tf_G_cl_est, ~] = 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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figure;
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hold on;
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plot(f, co_G_ol_est, '-')
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plot(f, co_G_cl_est, '-')
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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([40, 400]); ylim([0, 1])
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% Comparison model and identification
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(tf_G_ol_est), '-')
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plot(f, abs(tf_G_cl_est), '-')
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('Amplitude'); xlabel('Frequency [Hz]');
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hold off;
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, 180/pi*angle(tf_G_ol_est), '-')
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plot(f, 180/pi*angle(tf_G_cl_est), '-')
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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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linkaxes([ax1,ax2], 'x');
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xlim([40, 400]);
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%% Estimation of the inertial sensor transfer functions
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id = load('./mat/identification_noise_iff.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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ht = load('./mat/huddle_test.mat', 'd', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 'f_meas', 'u', 't');
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% Compare PSD
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run setup;
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win = hann(ceil(1/Ts));
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[p_id_d, f] = pwelch(id.d, win, [], [], 1/Ts);
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[p_id_acc1, ~] = pwelch(id.acc_1, win, [], [], 1/Ts);
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[p_id_acc2, ~] = pwelch(id.acc_2, win, [], [], 1/Ts);
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[p_id_geo1, ~] = pwelch(id.geo_1, win, [], [], 1/Ts);
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[p_id_geo2, ~] = pwelch(id.geo_2, win, [], [], 1/Ts);
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[p_id_fmeas, ~] = pwelch(id.f_meas, win, [], [], 1/Ts);
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[p_ht_d, ~] = pwelch(ht.d, win, [], [], 1/Ts);
|
||
|
|
[p_ht_acc1, ~] = pwelch(ht.acc_1, win, [], [], 1/Ts);
|
||
|
|
[p_ht_acc2, ~] = pwelch(ht.acc_2, win, [], [], 1/Ts);
|
||
|
|
[p_ht_geo1, ~] = pwelch(ht.geo_1, win, [], [], 1/Ts);
|
||
|
|
[p_ht_geo2, ~] = pwelch(ht.geo_2, win, [], [], 1/Ts);
|
||
|
|
[p_ht_fmeas, ~] = pwelch(ht.f_meas, win, [], [], 1/Ts);
|
||
|
|
|
||
|
|
figure;
|
||
|
|
hold on;
|
||
|
|
set(gca, 'ColorOrderIndex', 1);
|
||
|
|
plot(f, p_ht_acc1, 'DisplayName', 'Huddle Test');
|
||
|
|
set(gca, 'ColorOrderIndex', 1);
|
||
|
|
plot(f, p_ht_acc2, 'HandleVisibility', 'off');
|
||
|
|
set(gca, 'ColorOrderIndex', 2);
|
||
|
|
plot(f, p_id_acc1, 'DisplayName', 'Identification Test');
|
||
|
|
set(gca, 'ColorOrderIndex', 2);
|
||
|
|
plot(f, p_id_acc2, 'HandleVisibility', 'off');
|
||
|
|
hold off;
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||
|
|
ylabel('PSD [$V^2/Hz$]'); xlabel('Frequency [Hz]');
|
||
|
|
title('Huddle Test - Accelerometers')
|
||
|
|
legend();
|
||
|
|
|
||
|
|
figure;
|
||
|
|
hold on;
|
||
|
|
set(gca, 'ColorOrderIndex', 1);
|
||
|
|
plot(f, p_ht_geo1, 'DisplayName', 'Huddle Test');
|
||
|
|
set(gca, 'ColorOrderIndex', 1);
|
||
|
|
plot(f, p_ht_geo2, 'HandleVisibility', 'off');
|
||
|
|
set(gca, 'ColorOrderIndex', 2);
|
||
|
|
plot(f, p_id_geo1, 'DisplayName', 'Identification Test');
|
||
|
|
set(gca, 'ColorOrderIndex', 2);
|
||
|
|
plot(f, p_id_geo2, 'HandleVisibility', 'off');
|
||
|
|
hold off;
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||
|
|
ylabel('PSD [$V^2/Hz$]'); xlabel('Frequency [Hz]');
|
||
|
|
title('Huddle Test - Geophones')
|
||
|
|
legend();
|
||
|
|
|
||
|
|
figure;
|
||
|
|
hold on;
|
||
|
|
plot(f, p_ht_d, 'DisplayName', 'Huddle Test');
|
||
|
|
plot(f, p_id_d, 'DisplayName', 'Identification Test');
|
||
|
|
hold off;
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||
|
|
ylabel('PSD [$m^2/Hz$]'); xlabel('Frequency [Hz]');
|
||
|
|
title('Huddle Test - Interferometers')
|
||
|
|
legend();
|
||
|
|
|
||
|
|
% tf and coh computation
|
||
|
|
[tf_acc1_est, f] = tfestimate(id.d, id.acc_1, win, [], [], 1/Ts);
|
||
|
|
[co_acc1_est, ~] = mscohere(id.d, id.acc_1, win, [], [], 1/Ts);
|
||
|
|
[tf_acc2_est, ~] = tfestimate(id.d, id.acc_2, win, [], [], 1/Ts);
|
||
|
|
[co_acc2_est, ~] = mscohere(id.d, id.acc_2, win, [], [], 1/Ts);
|
||
|
|
|
||
|
|
[tf_geo1_est, ~] = tfestimate(id.d, id.geo_1, win, [], [], 1/Ts);
|
||
|
|
[co_geo1_est, ~] = mscohere(id.d, id.geo_1, win, [], [], 1/Ts);
|
||
|
|
[tf_geo2_est, ~] = tfestimate(id.d, id.geo_2, win, [], [], 1/Ts);
|
||
|
|
[co_geo2_est, ~] = mscohere(id.d, id.geo_2, win, [], [], 1/Ts);
|
||
|
|
|
||
|
|
% Coherence
|
||
|
|
figure;
|
||
|
|
hold on;
|
||
|
|
set(gca, 'ColorOrderIndex', 1);
|
||
|
|
plot(f, co_acc1_est, '-', 'DisplayName', 'Accelerometer')
|
||
|
|
set(gca, 'ColorOrderIndex', 1);
|
||
|
|
plot(f, co_acc2_est, '-', 'HandleVisibility', 'off')
|
||
|
|
set(gca, 'ColorOrderIndex', 2);
|
||
|
|
plot(f, co_geo1_est, '-', 'DisplayName', 'Geophone')
|
||
|
|
set(gca, 'ColorOrderIndex', 2);
|
||
|
|
plot(f, co_geo2_est, '-', 'HandleVisibility', 'off')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||
|
|
ylabel('Coherence'); xlabel('Frequency [Hz]');
|
||
|
|
hold off;
|
||
|
|
xlim([2, 2e3]); ylim([0, 1])
|
||
|
|
legend();
|
||
|
|
|
||
|
|
% Transfer Functions
|
||
|
|
figure;
|
||
|
|
ax1 = subplot(2, 1, 1);
|
||
|
|
hold on;
|
||
|
|
plot(f, abs(tf_acc1_est), '-')
|
||
|
|
plot(f, abs(tf_acc2_est), '-')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||
|
|
ylabel('Amplitude'); xlabel('Frequency [Hz]');
|
||
|
|
hold off;
|
||
|
|
|
||
|
|
ax2 = subplot(2, 1, 2);
|
||
|
|
hold on;
|
||
|
|
plot(f, 180/pi*angle(tf_acc1_est), '-')
|
||
|
|
plot(f, 180/pi*angle(tf_acc2_est), '-')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
||
|
|
hold off;
|
||
|
|
|
||
|
|
linkaxes([ax1,ax2], 'x');
|
||
|
|
xlim([2, 2e3]);
|
||
|
|
|
||
|
|
|
||
|
|
figure;
|
||
|
|
ax1 = subplot(2, 1, 1);
|
||
|
|
hold on;
|
||
|
|
plot(f, abs(tf_geo1_est), '-')
|
||
|
|
plot(f, abs(tf_geo2_est), '-')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||
|
|
ylabel('Amplitude'); xlabel('Frequency [Hz]');
|
||
|
|
hold off;
|
||
|
|
|
||
|
|
ax2 = subplot(2, 1, 2);
|
||
|
|
hold on;
|
||
|
|
plot(f, 180/pi*angle(tf_geo1_est), '-')
|
||
|
|
plot(f, 180/pi*angle(tf_geo2_est), '-')
|
||
|
|
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'lin');
|
||
|
|
ylabel('Phase'); xlabel('Frequency [Hz]');
|
||
|
|
hold off;
|
||
|
|
|
||
|
|
linkaxes([ax1,ax2], 'x');
|
||
|
|
xlim([2, 2e3]);
|