218 lines
6.0 KiB
Mathematica
218 lines
6.0 KiB
Mathematica
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%% 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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colors = colororder;
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addpath('./mat/');
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addpath('./src/');
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added_mass = 6.4; % Added mass [kg]
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apa_nums = [1 2 4 5 6 7 8];
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%% Load Data
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apa_mass = {};
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for i = 1:length(apa_nums)
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apa_mass(i) = {load(sprintf('frf_data_%i_add_mass_closed_circuit.mat', apa_nums(i)), 't', 'de')};
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% The initial displacement is set to zero
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apa_mass{i}.de = apa_mass{i}.de - mean(apa_mass{i}.de(apa_mass{i}.t<11));
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end
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%% Plot the time domain measured deflection
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figure;
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hold on;
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for i = 1:length(apa_nums)
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plot(apa_mass{i}.t, apa_mass{i}.de, 'DisplayName', sprintf('APA %i', apa_nums(i)));
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end
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hold off;
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xlabel('Time [s]'); ylabel('Displacement $d_e$ [m]');
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
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%% Compute the stiffness
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apa_k = zeros(length(apa_nums), 1);
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for i = 1:length(apa_nums)
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apa_k(i) = 9.8 * added_mass / (mean(apa_mass{i}.de(apa_mass{i}.t > 12 & apa_mass{i}.t < 12.5)) - mean(apa_mass{i}.de(apa_mass{i}.t > 20 & apa_mass{i}.t < 20.5)));
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end
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%% Second identification
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apa_sweep = {};
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for i = 1:length(apa_nums)
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apa_sweep(i) = {load(sprintf('frf_data_%i_sweep.mat', apa_nums(i)), 't', 'Va', 'Vs', 'de', 'da')};
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end
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%% Third identification
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apa_noise_hf = {};
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for i = 1:length(apa_nums)
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apa_noise_hf(i) = {load(sprintf('frf_data_%i_noise_hf.mat', apa_nums(i)), 't', 'Va', 'Vs', 'de', 'da')};
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end
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%% Time vector
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t = apa_sweep{1}.t - apa_sweep{1}.t(1) ; % Time vector [s]
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%% Sampling
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Ts = (t(end) - t(1))/(length(t)-1); % Sampling Time [s]
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Fs = 1/Ts; % Sampling Frequency [Hz]
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win = hanning(ceil(0.5*Fs)); % Hannning Windows
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% Only used to have the frequency vector "f"
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[~, f] = tfestimate(apa_sweep{1}.Va, apa_sweep{1}.de, win, [], [], 1/Ts);
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i_lf = f <= 350;
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i_hf = f > 350;
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%% Coherence computation
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coh_enc = zeros(length(f), length(apa_nums));
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for i = 1:length(apa_nums)
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[coh_lf, ~] = mscohere(apa_sweep{i}.Va, apa_sweep{i}.de, win, [], [], 1/Ts);
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[coh_hf, ~] = mscohere(apa_noise_hf{i}.Va, apa_noise_hf{i}.de, win, [], [], 1/Ts);
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coh_enc(:, i) = [coh_lf(i_lf); coh_hf(i_hf)];
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end
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figure;
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hold on;
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for i = 1:length(apa_nums)
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plot(f, coh_enc(:, i));
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end;
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Coherence [-]');
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xlim([5, 5e3]); ylim([0, 1]);
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%% Transfer function estimation
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enc_frf = zeros(length(f), length(apa_nums));
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for i = 1:length(apa_nums)
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[frf_lf, ~] = tfestimate(apa_sweep{i}.Va, apa_sweep{i}.de, win, [], [], 1/Ts);
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[frf_hf, ~] = tfestimate(apa_noise_hf{i}.Va, apa_noise_hf{i}.de, win, [], [], 1/Ts);
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enc_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
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end
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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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for i = 1:length(apa_nums)
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plot(f, abs(enc_frf(:, i)), ...
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'DisplayName', sprintf('APA %i', apa_nums(i)));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
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ylim([1e-9, 1e-3]);
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ax2 = nexttile;
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hold on;
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for i = 1:length(apa_nums)
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plot(f, 180/pi*angle(enc_frf(:, i)));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360);
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linkaxes([ax1,ax2],'x');
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xlim([10, 2e3]);
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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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for i = 1:length(apa_nums)
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plot(f, abs(enc_frf(:, i)), ...
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'DisplayName', sprintf('APA %i', apa_nums(i)));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $d_e/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 2);
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ylim([2e-5, 4e-4]);
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ax2 = nexttile;
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hold on;
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for i = 1:length(apa_nums)
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plot(f, 180/pi*angle(enc_frf(:, i)));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360);
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ylim([-10, 180]);
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linkaxes([ax1,ax2],'x');
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xlim([80, 120]);
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%% Compute the Coherence
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coh_iff = zeros(length(f), length(apa_nums));
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for i = 1:length(apa_nums)
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[coh_lf, ~] = mscohere(apa_sweep{i}.Va, apa_sweep{i}.Vs, win, [], [], 1/Ts);
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[coh_hf, ~] = mscohere(apa_noise_hf{i}.Va, apa_noise_hf{i}.Vs, win, [], [], 1/Ts);
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coh_iff(:, i) = [coh_lf(i_lf); coh_hf(i_hf)];
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end
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%% Plot the coherence
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figure;
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hold on;
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for i = 1:length(apa_nums)
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plot(f, coh_iff(:, i));
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end;
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hold off;
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xlabel('Frequency [Hz]'); ylabel('Coherence [-]');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlim([5, 5e3]); ylim([0, 1]);
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%% FRF estimation of the transfer function from Va to Vs
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iff_frf = zeros(length(f), length(apa_nums));
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for i = 1:length(apa_nums)
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[frf_lf, ~] = tfestimate(apa_sweep{i}.Va, apa_sweep{i}.Vs, win, [], [], 1/Ts);
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[frf_hf, ~] = tfestimate(apa_noise_hf{i}.Va, apa_noise_hf{i}.Vs, win, [], [], 1/Ts);
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iff_frf(:, i) = [frf_lf(i_lf); frf_hf(i_hf)];
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end
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%% Plot the FRF from Va to Vs
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile;
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hold on;
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for i = 1:length(apa_nums)
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plot(f, abs(iff_frf(:, i)), ...
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'DisplayName', sprintf('APA %i', apa_nums(i)));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-2, 1e2]);
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legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
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ax2 = nexttile;
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hold on;
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for i = 1:length(apa_nums)
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plot(f, 180/pi*angle(iff_frf(:, i)));
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end
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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hold off;
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yticks(-360:90:360); ylim([-180, 180]);
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linkaxes([ax1,ax2],'x');
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xlim([10, 2e3]);
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%% Remove the APA 7 (6 in the list) from measurements
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apa_nums(6) = [];
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enc_frf(:,6) = [];
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iff_frf(:,6) = [];
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%% Save the measured FRF
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save('mat/meas_apa_frf.mat', 'f', 'Ts', 'enc_frf', 'iff_frf', 'apa_nums');
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