248 lines
7.5 KiB
Mathematica
248 lines
7.5 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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Fs = 1e4; % Sampling Frequency [Hz]
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Ts = 1/Fs; % Sampling Time [s]
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addpath('./mat/');
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addpath('./src/');
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%% Load data
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apa_sweep = load(sprintf('mat/frf_data_%i_sweep.mat', 1), 't', 'Va', 'Vs', 'da', 'de');
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%% Time vector
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t = apa_sweep.t - apa_sweep.t(1) ; % Time vector [s]
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%% Plot the excitation signal
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figure;
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plot(t, apa_sweep.Va)
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xlabel('Time [s]'); ylabel('Excitation Voltage $V_a$ [V]');
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%% Sampling Frequency / Time
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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(1*Fs)); % Hannning Windows
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% Only used to have the frequency vector "f"
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[~, f] = tfestimate(apa_sweep.Va, apa_sweep.de, win, [], [], 1/Ts);
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%% Compute the coherence
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[enc_coh, ~] = mscohere(apa_sweep.Va, apa_sweep.de, win, [], [], 1/Ts);
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[int_coh, ~] = mscohere(apa_sweep.Va, apa_sweep.da, win, [], [], 1/Ts);
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%% Plot the coherence
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figure;
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hold on;
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plot(f, enc_coh, 'DisplayName', '$d_e/V_a$');
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plot(f, int_coh, 'DisplayName', '$d_a/V_a$');
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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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%% TF - Encoder and interferometer
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[frf_enc, ~] = tfestimate(apa_sweep.Va, apa_sweep.de, win, [], [], 1/Ts);
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[frf_int, ~] = tfestimate(apa_sweep.Va, apa_sweep.da, win, [], [], 1/Ts);
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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(frf_enc), 'color', colors(1, :), ...
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'DisplayName', 'Encoder');
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plot(f, abs(frf_int), 'color', colors(2, :), ...
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'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('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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legend('location', 'northeast');
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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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plot(f, 180/pi*angle(frf_enc), 'color', colors(1, :));
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plot(f, 180/pi*angle(frf_int), 'color', colors(2, :));
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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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%% Compute the coherence from Va to Vs
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[iff_coh, ~] = mscohere(apa_sweep.Va, apa_sweep.Vs, win, [], [], 1/Ts);
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%% Plot the coherence
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figure;
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hold on;
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plot(f, iff_coh, 'k-');
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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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%% Compute the TF from Va to Vs
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[iff_sweep, ~] = tfestimate(apa_sweep.Va, apa_sweep.Vs, win, [], [], 1/Ts);
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%% Plot the TF
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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(iff_sweep), 'k-');
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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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ax2 = nexttile;
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hold on;
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plot(f, 180/pi*angle(iff_sweep), 'k-');
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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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%% Load measured data - hysteresis
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apa_hyst = load('frf_data_1_hysteresis.mat', 't', 'Va', 'de');
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% Initial time set to zero
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apa_hyst.t = apa_hyst.t - apa_hyst.t(1);
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ampls = [0.1, 0.2, 0.4, 1, 2, 4]; % Excitation voltage amplitudes
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%% Plot the excitation voltages and measured displacements
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figure;
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tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile;
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plot(apa_hyst.t, apa_hyst.Va)
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xlabel('Time [s]'); ylabel('Output Voltage [V]');
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ax2 = nexttile;
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plot(apa_hyst.t, apa_hyst.de)
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xlabel('Time [s]'); ylabel('Measured Displacement [m]');
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%% Measured displacement as a function of the output voltage
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figure;
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tiledlayout(1, 3, 'TileSpacing', 'None', 'Padding', 'None');
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ax1 = nexttile([1,2]);
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hold on;
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for i = flip(1:6)
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i_lim = apa_hyst.t > i*5-1 & apa_hyst.t < i*5;
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plot(apa_hyst.Va(i_lim) - mean(apa_hyst.Va(i_lim)), apa_hyst.de(i_lim) - mean(apa_hyst.de(i_lim)), ...
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'DisplayName', sprintf('$V_a = %.1f [V]$', ampls(i)))
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end
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hold off;
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xlabel('Output Voltage [V]'); ylabel('Measured Displacement [m]');
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legend('location', 'northeast');
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xlim([-4, 4]); ylim([-1.2e-4, 1.2e-4]);
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ax2 = nexttile;
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hold on;
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for i = flip(1:6)
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i_lim = apa_hyst.t > i*5-1 & apa_hyst.t < i*5;
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plot(apa_hyst.Va(i_lim) - mean(apa_hyst.Va(i_lim)), apa_hyst.de(i_lim) - mean(apa_hyst.de(i_lim)))
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end
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hold off;
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xlim([-0.4, 0.4]); ylim([-0.8e-5, 0.8e-5]);
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%% Load data for stiffness measurement
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apa_mass = load(sprintf('frf_data_%i_add_mass_closed_circuit.mat', 1), 't', 'de');
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apa_mass.de = apa_mass.de - mean(apa_mass.de(apa_mass.t<11));
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%% Plot the deflection at a function of time
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figure;
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plot(apa_mass.t, apa_mass.de, 'k-');
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xlabel('Time [s]'); ylabel('Displacement $d_e$ [m]');
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added_mass = 6.4; % Added mass [kg]
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k = 9.8 * added_mass / (mean(apa_mass.de(apa_mass.t > 12 & apa_mass.t < 12.5)) - mean(apa_mass.de(apa_mass.t > 20 & apa_mass.t < 20.5)));
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wz = 2*pi*94; % [rad/s]
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msus = 5.7; % [kg]
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k = msus * wz^2;
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%% Load Data
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add_mass_oc = load(sprintf('frf_data_%i_add_mass_open_circuit.mat', 1), 't', 'de');
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add_mass_cc = load(sprintf('frf_data_%i_add_mass_closed_circuit.mat', 1), 't', 'de');
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%% Zero displacement at initial time
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add_mass_oc.de = add_mass_oc.de - mean(add_mass_oc.de(add_mass_oc.t<11));
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add_mass_cc.de = add_mass_cc.de - mean(add_mass_cc.de(add_mass_cc.t<11));
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figure;
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hold on;
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plot(add_mass_oc.t, add_mass_oc.de, 'DisplayName', 'Not connected');
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plot(add_mass_cc.t, add_mass_cc.de, 'DisplayName', 'Connected');
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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');
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apa_k_oc = 9.8 * added_mass / (mean(add_mass_oc.de(add_mass_oc.t > 12 & add_mass_oc.t < 12.5)) - mean(add_mass_oc.de(add_mass_oc.t > 20 & add_mass_oc.t < 20.5)));
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apa_k_cc = 9.8 * added_mass / (mean(add_mass_cc.de(add_mass_cc.t > 12 & add_mass_cc.t < 12.5)) - mean(add_mass_cc.de(add_mass_cc.t > 20 & add_mass_cc.t < 20.5)));
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%% Load the data
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wi_k = load('frf_data_1_sweep_lf_with_R.mat', 't', 'Vs', 'Va'); % With the resistor
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wo_k = load('frf_data_1_sweep_lf.mat', 't', 'Vs', 'Va'); % Without the resistor
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win = hanning(ceil(50*Fs)); % Hannning Windows
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%% Compute the transfer functions from Va to Vs
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[frf_wo_k, f] = tfestimate(wo_k.Va, wo_k.Vs, win, [], [], 1/Ts);
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[frf_wi_k, ~] = tfestimate(wi_k.Va, wi_k.Vs, win, [], [], 1/Ts);
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%% Model for the high pass filter
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C = 5.1e-6; % Sensor Stack capacitance [F]
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R = 80.6e3; % Parallel Resistor [Ohm]
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f0 = 1/(2*pi*R*C); % Crossover frequency of RC HPF [Hz]
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G_hpf = 0.6*(s/2*pi*f0)/(1 + s/2*pi*f0);
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%% Compare the HPF model and the measured FRF
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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(frf_wo_k), 'DisplayName', 'Without $k$');
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plot(f, abs(frf_wi_k), 'DisplayName', 'With $k$');
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plot(f, abs(squeeze(freqresp(G_hpf, f, 'Hz'))), 'k--', 'DisplayName', sprintf('HPF $f_o = %.2f [Hz]$', f0));
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
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hold off;
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ylim([1e-1, 1e0]);
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legend('location', 'southeast')
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ax2 = nexttile;
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hold on;
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plot(f, 180/pi*angle(frf_wo_k));
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plot(f, 180/pi*angle(frf_wi_k));
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plot(f, 180/pi*angle(squeeze(freqresp(G_hpf, f, 'Hz'))), 'k--');
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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(-360:45:360); ylim([-45, 90]);
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linkaxes([ax1,ax2],'x');
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xlim([0.2, 8]);
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