Analyze first measurements
This commit is contained in:
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figs/frf_meas_sin_excitation.pdf
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figs/frf_meas_sin_excitation.pdf
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figs/frf_meas_sin_excitation.png
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figs/frf_meas_sin_excitation.png
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@@ -1,52 +1,36 @@
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% Analysis
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% :PROPERTIES:
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% :header-args: :tangle matlab/frf_analyze.m
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% :END:
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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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addpath('./src/');
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% Test with one APA
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%% Load measurement data for APA number 1
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load(sprintf('mat/frf_data_%i.mat', 1), 't', 'Va', 'Vs', 'de', 'da');
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%% Load all the measurements
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% meas_data = {};
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% for i = 1:7
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% meas_data(i) = {load(sprintf('mat/frf_data_%i.mat', i), 't', 'Va', 'Vs', 'da', 'de')};
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% end
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%%
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load(sprintf('mat/frf_data_%i_sweep.mat', 1), 't', 'Va', 'Vs', 'da', 'de')
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% Time domain data:
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%%
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figure;
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plot(t, de);
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%%
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figure;
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plot(t, Va);
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%%
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% Compute transfer functions:
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Ts = (t(end) - t(1))/(length(t)-1);
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Fs = 1/Ts;
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win = hanning(ceil(5*Fs)); % Hannning Windows
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win = hanning(ceil(0.5*Fs)); % Hannning Windows
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%%
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[G_dvf, f] = tfestimate(Va, de, win, [], [], 1/Ts);
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[G_d, ~] = tfestimate(Va, da, win, [], [], 1/Ts);
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[G_iff, ~] = tfestimate(Va, Vs, win, [], [], 1/Ts);
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[coh_dvf, ~] = mscohere(Va, de, win, [], [], 1/Ts);
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[coh_d, ~] = mscohere(Va, da, win, [], [], 1/Ts);
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[coh_iff, ~] = mscohere(Va, Vs, win, [], [], 1/Ts);
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%%
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figure;
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hold on;
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plot(f, coh_dvf);
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plot(f, coh_d);
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plot(f, coh_iff);
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
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xlim([1, 5e3]); ylim([0, 1]);
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%%
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
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@@ -58,6 +42,7 @@ 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([10, 30]);
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ax2 = nexttile;
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hold on;
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@@ -72,7 +57,6 @@ yticks(-360:90:360);
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linkaxes([ax1,ax2],'x');
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xlim([5, 5e3]);
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%%
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figure;
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tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
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@@ -81,6 +65,7 @@ plot(f, abs(G_iff));
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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([10, 30]);
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ax2 = nexttile;
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plot(f, 180/pi*angle(G_iff));
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@@ -91,3 +76,11 @@ yticks(-360:90:360);
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linkaxes([ax1,ax2],'x');
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xlim([5, 5e3]);
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% Comparison of all APA
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%% Load all the measurements
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meas_data = {};
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for i = 1:7
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meas_data(i) = {load(sprintf('mat/frf_data_%i.mat', i), 't', 'Va', 'Vs', 'de', 'da')};
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end
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@@ -1,4 +1,4 @@
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% Save Data
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% =frf_save.m= - Save Data
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% :PROPERTIES:
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% :header-args: :tangle matlab/frf_save.m
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% :END:
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@@ -1,10 +1,16 @@
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s = tf('s');
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addpath('src')
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%%
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%% Intialize Laplace variable
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s = zpk('s');
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addpath('./src/');
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%% Simulation configuration
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Fs = 10e3; % Sampling Frequency [Hz]
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Ts = 1/Fs; % Sampling Time [s]
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%% Data record configuration
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Trec_start = 5; % Start time for Recording [s]
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Trec_dur = 100; % Recording Duration [s]
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@@ -15,11 +21,12 @@ gc = 0.1;
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xi = 0.5;
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wn = 2*pi*94.3;
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% Notch filter at the resonance of the APA
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G_sweep = 0.2*(s^2 + 2*gc*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
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V_sweep = generateSweepExc('Ts', Ts, ...
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'f_start', 10, ...
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'f_end', 2e3, ...
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'f_end', 1e3, ...
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'V_mean', 3.25, ...
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't_start', Trec_start, ...
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'exc_duration', Trec_dur, ...
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@@ -32,7 +39,16 @@ V_noise = generateShapedNoise('Ts', 1/Fs, ...
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't_start', Trec_start, ...
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'exc_duration', Trec_dur, ...
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'smooth_ends', true, ...
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'V_exc', 0.00/(1 + s/2/pi/50));
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'V_exc', 0.05/(1 + s/2/pi/10));
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%% Sinus excitation with increasing amplitude
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V_sin = generateSinIncreasingAmpl('Ts', 1/Fs, ...
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'V_mean', 3.25, ...
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'sin_ampls', [0.1, 0.2, 0.4, 1, 2, 4], ...
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'sin_period', 1, ...
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'sin_num', 5, ...
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't_start', 10, ...
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'smooth_ends', true);
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%% Select the excitation signal
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V_exc = timeseries(V_noise(2,:), V_noise(1,:));
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@@ -41,16 +57,16 @@ figure;
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tiledlayout(1, 2, 'TileSpacing', 'Normal', 'Padding', 'None');
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ax1 = nexttile;
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plot(V_exc.Time, squeeze(V_exc.Data));
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plot(V_exc(1,:), V_exc(2,:));
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xlabel('Time [s]'); ylabel('Amplitude [V]');
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ax2 = nexttile;
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win = hanning(floor(length(V_exc.Data)/8));
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[pxx, f] = pwelch(squeeze(V_exc.Data), win, 0, [], Fs);
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win = hanning(floor(length(V_exc)/8));
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[pxx, f] = pwelch(V_exc(2,:), win, 0, [], Fs);
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plot(f, pxx)
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xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$V^2/Hz$]');
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlim([1, Fs/2]); ylim([1e-10, 1e0]);
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%% Save
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%% Save data that will be loaded in the Simulink file
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save('./frf_data.mat', 'Fs', 'Ts', 'Tsim', 'Trec_start', 'Trec_dur', 'V_exc');
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54
matlab/src/generateSinIncreasingAmpl.m
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54
matlab/src/generateSinIncreasingAmpl.m
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@@ -0,0 +1,54 @@
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function [U_exc] = generateSinIncreasingAmpl(args)
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% generateSinIncreasingAmpl - Generate Sinus with increasing amplitude
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%
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% Syntax: [U_exc] = generateSinIncreasingAmpl(args)
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%
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% Inputs:
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% - args - Optinal arguments:
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% - Ts - Sampling Time - [s]
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% - V_mean - Mean value of the excitation voltage - [V]
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% - sin_ampls - Excitation Amplitudes - [V]
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% - sin_freq - Excitation Frequency - [Hz]
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% - sin_num - Number of period for each amplitude - [-]
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% - t_start - Time at which the excitation begins - [s]
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% - smooth_ends - 'true' or 'false': smooth transition between 0 and V_mean - [-]
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arguments
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args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-4
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args.V_mean (1,1) double {mustBeNumeric} = 0
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args.sin_ampls double {mustBeNumeric, mustBePositive} = [0.1, 0.2, 0.3]
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args.sin_period (1,1) double {mustBeNumeric, mustBePositive} = 1
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args.sin_num (1,1) double {mustBeNumeric, mustBePositive, mustBeInteger} = 3
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args.t_start (1,1) double {mustBeNumeric, mustBePositive} = 5
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args.smooth_ends logical {mustBeNumericOrLogical} = true
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end
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t_noise = 0:args.Ts:args.sin_period*args.sin_num;
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sin_exc = [];
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for sin_ampl = args.sin_ampls
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sin_exc = [sin_exc, args.V_mean + sin_ampl*sin(2*pi/args.sin_period*t_noise)];
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end
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t_smooth_start = args.Ts:args.Ts:args.t_start;
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V_smooth_start = zeros(size(t_smooth_start));
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V_smooth_end = zeros(size(t_smooth_start));
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if args.smooth_ends
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Vd_max = args.V_mean/(0.7*args.t_start);
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V_d = zeros(size(t_smooth_start));
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V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
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V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
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V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
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V_smooth_start = cumtrapz(V_d)*args.Ts;
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V_smooth_end = args.V_mean - V_smooth_start;
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end
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V_exc = [V_smooth_start, sin_exc, V_smooth_end];
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t_exc = args.Ts*[0:1:length(V_exc)-1];
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U_exc = [t_exc; V_exc];
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@@ -25,6 +25,7 @@
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :noweb yes
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#+PROPERTY: header-args:matlab+ :tangle no
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:matlab+ :output-dir figs
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@@ -717,18 +718,29 @@ addpath('./matlab/');
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addpath('./src/');
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#+end_src
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** Measurement Setup
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** =frf_setup.m= - Measurement Setup
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:PROPERTIES:
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:header-args:matlab: :tangle matlab/frf_setup.m
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:header-args:matlab+: :comments no
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:END:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :eval no :exports none
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addpath('./src/');
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#+end_src
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First is defined the sampling frequency:
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#+begin_src matlab
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%% Simulation configuration
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Fs = 10e3; % Sampling Frequency [Hz]
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Ts = 1/Fs; % Sampling Time [s]
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Tsim = 110; % Simulation Time [s]
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#+end_src
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#+begin_src matlab
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@@ -737,9 +749,20 @@ Trec_start = 5; % Start time for Recording [s]
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Trec_dur = 100; % Recording Duration [s]
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#+end_src
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#+begin_src matlab
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Tsim = 2*Trec_start + Trec_dur; % Simulation Time [s]
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#+end_src
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The maximum excitation voltage at resonance is 9Vrms, therefore corresponding to 0.6V of output DAC voltage.
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#+begin_src matlab
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%% Sweep Sine
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gc = 0.1;
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xi = 0.5;
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wn = 2*pi*94.3;
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% Notch filter at the resonance of the APA
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G_sweep = 0.2*(s^2 + 2*gc*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
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V_sweep = generateSweepExc('Ts', Ts, ...
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'f_start', 10, ...
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'f_end', 1e3, ...
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@@ -747,7 +770,7 @@ V_sweep = generateSweepExc('Ts', Ts, ...
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't_start', Trec_start, ...
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'exc_duration', Trec_dur, ...
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'sweep_type', 'log', ...
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'V_exc', 0.5/(1 + s/2/pi/100));
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'V_exc', G_sweep*1/(1 + s/2/pi/500));
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#+end_src
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#+begin_src matlab :exports none :tangle no
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@@ -815,10 +838,36 @@ exportFig('figs/frf_meas_noise_excitation.pdf', 'width', 'full', 'height', 'norm
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#+RESULTS:
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[[file:figs/frf_meas_noise_excitation.png]]
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#+begin_src matlab
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%% Sinus excitation with increasing amplitude
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V_sin = generateSinIncreasingAmpl('Ts', 1/Fs, ...
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'V_mean', 3.25, ...
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'sin_ampls', [0.1, 0.2, 0.4, 1, 2, 4], ...
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'sin_period', 1, ...
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'sin_num', 5, ...
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't_start', 10, ...
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'smooth_ends', true);
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#+end_src
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#+begin_src matlab :exports none :tangle no
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figure;
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plot(V_sin(1,:), V_sin(2,:));
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xlabel('Time [s]'); ylabel('Amplitude [V]');
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#+end_src
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#+begin_src matlab :tangle no :exports results :results file replace
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exportFig('figs/frf_meas_sin_excitation.pdf', 'width', 'wide', 'height', 'normal');
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#+end_src
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#+name: fig:frf_meas_sin_excitation
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#+caption: Example of Shaped noise excitation signal
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#+RESULTS:
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[[file:figs/frf_meas_sin_excitation.png]]
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Then, we select the wanted excitation signal.
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#+begin_src matlab
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%% Select the excitation signal
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V_exc = V_noise;
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V_exc = timeseries(V_noise(2,:), V_noise(1,:));
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#+end_src
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#+begin_src matlab :exports none :eval no
|
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@@ -838,7 +887,12 @@ set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlim([1, Fs/2]); ylim([1e-10, 1e0]);
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#+end_src
|
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** Save Data
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#+begin_src matlab
|
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%% Save data that will be loaded in the Simulink file
|
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save('./frf_data.mat', 'Fs', 'Ts', 'Tsim', 'Trec_start', 'Trec_dur', 'V_exc');
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#+end_src
|
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|
||||
** =frf_save.m= - Save Data
|
||||
:PROPERTIES:
|
||||
:header-args: :tangle matlab/frf_save.m
|
||||
:END:
|
||||
@@ -856,10 +910,10 @@ And we load the data on the Workspace:
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#+begin_src matlab
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data = SimulinkRealTime.utils.getFileScopeData('data/data.dat').data;
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Va = data(:, 1); % Excitation Voltage (input of PD200) [V]
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Vs = data(:, 2); % Measured voltage (force sensor) [V]
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de = data(:, 3); % Measurment displacement (encoder) [m]
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da = data(:, 4); % Measurement displacement (attocube) [m]
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da = data(:, 1); % Excitation Voltage (input of PD200) [V]
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de = data(:, 2); % Measured voltage (force sensor) [V]
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Vs = data(:, 3); % Measurment displacement (encoder) [m]
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Va = data(:, 4); % Measurement displacement (attocube) [m]
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t = data(:, end); % Time [s]
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#+end_src
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@@ -867,10 +921,347 @@ And we save this to a =mat= file:
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#+begin_src matlab
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apa_number = 1;
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save(sprintf('mat/frf_data_%i.mat', apa_number), 't', 'Va', 'Vs', 'de', 'da');
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save(sprintf('mat/frf_data_%i_huddle.mat', apa_number), 't', 'Va', 'Vs', 'de', 'da');
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#+end_src
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** Analysis
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** Measurements on APA 1
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||||
*** Introduction :ignore:
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Measurements are first performed on the APA number 1.
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||||
|
||||
*** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
<<matlab-dir>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :results silent :noweb yes
|
||||
<<matlab-init>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('./matlab/mat/');
|
||||
addpath('./matlab/src/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./mat/');
|
||||
addpath('./src/');
|
||||
#+end_src
|
||||
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*** Huddle Test
|
||||
#+begin_src matlab
|
||||
load(sprintf('frf_data_%i_huddle.mat', 1), 't', 'Va', 'Vs', 'de', 'da');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(t, da, 'DisplayName', '$d_a$ - Attocube')
|
||||
plot(t, de, 'DisplayName', '$d_e$ - Encoder')
|
||||
hold off;
|
||||
xlabel('Time [s]');
|
||||
ylabel('Displacement [m]');
|
||||
legend('location', 'northeast')
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(t, Vs, 'DisplayName', '$V_s$ - Force Sensor')
|
||||
hold off;
|
||||
xlabel('Time [s]');
|
||||
ylabel('Voltage [V]');
|
||||
legend('location', 'northeast')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
%% Parameter for Spectral analysis
|
||||
Ts = (t(end) - t(1))/(length(t)-1);
|
||||
Fs = 1/Ts;
|
||||
|
||||
win = hanning(ceil(10*Fs)); % Hannning Windows
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
[phh_da, f] = pwelch(da - mean(da), win, [], [], 1/Ts);
|
||||
[phh_de, ~] = pwelch(de - mean(de), win, [], [], 1/Ts);
|
||||
[phh_Vs, ~] = pwelch(Vs - mean(Vs), win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(f, phh_da, 'DisplayName', '$d_a$ - Attocube')
|
||||
plot(f, phh_de, 'DisplayName', '$d_e$ - Encoder')
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('ASD [$m/\sqrt{Hz}$]');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
legend('location', 'northeast')
|
||||
xlim([5e-1, 5e3]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, phh_Vs, 'DisplayName', '$V_s$ - Force Sensor')
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('ASD [$V/\sqrt{Hz}$]');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
legend('location', 'northeast')
|
||||
xlim([5e-1, 5e3]);
|
||||
#+end_src
|
||||
|
||||
*** First identification with Noise
|
||||
#+begin_src matlab
|
||||
load(sprintf('mat/frf_data_%i_noise.mat', 1), 't', 'Va', 'Vs', 'da', 'de')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
[pxx_da, f] = pwelch(da, win, [], [], 1/Ts);
|
||||
[pxx_de, ~] = pwelch(de, win, [], [], 1/Ts);
|
||||
[pxx_Vs, ~] = pwelch(Vs, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(f, sqrt(phh_da), 'DisplayName', 'Huddle')
|
||||
plot(f, sqrt(pxx_da), 'DisplayName', 'Noise')
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('ASD Attocube [$m/\sqrt{Hz}$]');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
legend('location', 'northeast')
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, sqrt(phh_Vs), 'DisplayName', 'Huddle')
|
||||
plot(f, sqrt(pxx_Vs), 'DisplayName', 'Noise')
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('ASD [$V/\sqrt{Hz}$]');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
legend('location', 'northeast')
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([5e-1, 5e3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
[G_dvf, f] = tfestimate(Va, de, win, [], [], 1/Ts);
|
||||
[G_d, ~] = tfestimate(Va, da, win, [], [], 1/Ts);
|
||||
[G_iff, ~] = tfestimate(Va, Vs, win, [], [], 1/Ts);
|
||||
|
||||
[coh_dvf, ~] = mscohere(Va, de, win, [], [], 1/Ts);
|
||||
[coh_d, ~] = mscohere(Va, da, win, [], [], 1/Ts);
|
||||
[coh_iff, ~] = mscohere(Va, Vs, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%%
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, coh_dvf);
|
||||
plot(f, coh_d);
|
||||
plot(f, coh_iff);
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlim([1, 5e3]); ylim([0, 1]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%%
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(f, abs(G_d), 'DisplayName', 'Attocube');
|
||||
plot(f, abs(G_dvf), 'DisplayName', 'Encoder');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-8, 1e-3]);
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(G_d));
|
||||
plot(f, 180/pi*angle(G_dvf));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([5e-1, 5e3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%%
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
plot(f, abs(G_iff));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
|
||||
ax2 = nexttile;
|
||||
plot(f, 180/pi*angle(G_iff));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1, 2e3]);
|
||||
#+end_src
|
||||
|
||||
*** Second identification with Sweep
|
||||
#+begin_src matlab
|
||||
load(sprintf('mat/frf_data_%i_sweep.mat', 1), 't', 'Va', 'Vs', 'da', 'de')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
[pxx_da, f] = pwelch(da, win, [], [], 1/Ts);
|
||||
[pxx_de, ~] = pwelch(de, win, [], [], 1/Ts);
|
||||
[pxx_Vs, ~] = pwelch(Vs, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(f, sqrt(phh_da), 'DisplayName', 'Huddle')
|
||||
plot(f, sqrt(pxx_da), 'DisplayName', 'Noise')
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('ASD Attocube [$m/\sqrt{Hz}$]');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
legend('location', 'northeast')
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, sqrt(phh_Vs), 'DisplayName', 'Huddle')
|
||||
plot(f, sqrt(pxx_Vs), 'DisplayName', 'Noise')
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('ASD [$V/\sqrt{Hz}$]');
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
legend('location', 'northeast')
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1e1, 2e3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
[G_dvf, f] = tfestimate(Va, de, win, [], [], 1/Ts);
|
||||
[G_d, ~] = tfestimate(Va, da, win, [], [], 1/Ts);
|
||||
[G_iff, ~] = tfestimate(Va, Vs, win, [], [], 1/Ts);
|
||||
|
||||
[coh_dvf, ~] = mscohere(Va, de, win, [], [], 1/Ts);
|
||||
[coh_d, ~] = mscohere(Va, da, win, [], [], 1/Ts);
|
||||
[coh_iff, ~] = mscohere(Va, Vs, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%%
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, coh_dvf);
|
||||
plot(f, coh_d);
|
||||
plot(f, coh_iff);
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlim([10, 2e3]); ylim([0, 1]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%%
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(f, abs(G_d), 'DisplayName', 'Attocube');
|
||||
plot(f, abs(G_dvf), 'DisplayName', 'Encoder');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $d/V_a$ [m/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([1e-8, 1e-3]);
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(G_d));
|
||||
plot(f, 180/pi*angle(G_dvf));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 2e3]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
%%
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
plot(f, abs(G_iff));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_s/V_a$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
|
||||
ax2 = nexttile;
|
||||
plot(f, 180/pi*angle(G_iff));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
hold off;
|
||||
yticks(-360:90:360);
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([10, 2e3]);
|
||||
#+end_src
|
||||
|
||||
*** Extract Parameters
|
||||
|
||||
Quasi static gain between $d$ and $V_a$:
|
||||
#+begin_src matlab
|
||||
g_d_Va = mean(abs(G_dvf(f > 10 & f < 15)));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results value replace :exports results
|
||||
sprintf('g_d_Va = %.1e [m/V]', g_d_Va)
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: g_d_Va = 1.7e-05 [m/V]
|
||||
|
||||
Quasi static gain between $V_s$ and $V_a$:
|
||||
#+begin_src matlab
|
||||
g_Vs_Va = mean(abs(G_iff(f > 10 & f < 15)));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results value replace :exports results
|
||||
sprintf('g_Vs_Va = %.1e [V/V]', g_Vs_Va)
|
||||
#+end_src
|
||||
|
||||
#+RESULTS:
|
||||
: g_Vs_Va = 5.7e-01 [V/V]
|
||||
|
||||
** Comparison of all APA
|
||||
:PROPERTIES:
|
||||
:header-args: :tangle matlab/frf_analyze.m
|
||||
:END:
|
||||
@@ -3038,5 +3429,106 @@ t_exc = args.Ts*[0:1:length(V_exc)-1];
|
||||
U_exc = [t_exc; V_exc];
|
||||
#+end_src
|
||||
|
||||
** =generateSinIncreasingAmpl=: Generate Sinus with increasing amplitude
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle ./matlab/src/generateSinIncreasingAmpl.m
|
||||
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
||||
:END:
|
||||
<<sec:generateSinIncreasingAmpl>>
|
||||
|
||||
*** Function description
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
function [U_exc] = generateSinIncreasingAmpl(args)
|
||||
% generateSinIncreasingAmpl - Generate Sinus with increasing amplitude
|
||||
%
|
||||
% Syntax: [U_exc] = generateSinIncreasingAmpl(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Optinal arguments:
|
||||
% - Ts - Sampling Time - [s]
|
||||
% - V_mean - Mean value of the excitation voltage - [V]
|
||||
% - sin_ampls - Excitation Amplitudes - [V]
|
||||
% - sin_freq - Excitation Frequency - [Hz]
|
||||
% - sin_num - Number of period for each amplitude - [-]
|
||||
% - t_start - Time at which the excitation begins - [s]
|
||||
% - smooth_ends - 'true' or 'false': smooth transition between 0 and V_mean - [-]
|
||||
#+end_src
|
||||
|
||||
*** Optional Parameters
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
arguments
|
||||
args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-4
|
||||
args.V_mean (1,1) double {mustBeNumeric} = 0
|
||||
args.sin_ampls double {mustBeNumeric, mustBePositive} = [0.1, 0.2, 0.3]
|
||||
args.sin_period (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
args.sin_num (1,1) double {mustBeNumeric, mustBePositive, mustBeInteger} = 3
|
||||
args.t_start (1,1) double {mustBeNumeric, mustBePositive} = 5
|
||||
args.smooth_ends logical {mustBeNumericOrLogical} = true
|
||||
end
|
||||
#+end_src
|
||||
|
||||
*** Sinus excitation
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
t_noise = 0:args.Ts:args.sin_period*args.sin_num;
|
||||
sin_exc = [];
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
for sin_ampl = args.sin_ampls
|
||||
sin_exc = [sin_exc, args.V_mean + sin_ampl*sin(2*pi/args.sin_period*t_noise)];
|
||||
end
|
||||
#+end_src
|
||||
|
||||
*** Smooth Ends
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
t_smooth_start = args.Ts:args.Ts:args.t_start;
|
||||
|
||||
V_smooth_start = zeros(size(t_smooth_start));
|
||||
V_smooth_end = zeros(size(t_smooth_start));
|
||||
|
||||
if args.smooth_ends
|
||||
Vd_max = args.V_mean/(0.7*args.t_start);
|
||||
|
||||
V_d = zeros(size(t_smooth_start));
|
||||
V_d(t_smooth_start < 0.2*args.t_start) = t_smooth_start(t_smooth_start < 0.2*args.t_start)*Vd_max/(0.2*args.t_start);
|
||||
V_d(t_smooth_start > 0.2*args.t_start & t_smooth_start < 0.7*args.t_start) = Vd_max;
|
||||
V_d(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) = Vd_max - (t_smooth_start(t_smooth_start > 0.7*args.t_start & t_smooth_start < 0.9*args.t_start) - 0.7*args.t_start)*Vd_max/(0.2*args.t_start);
|
||||
|
||||
V_smooth_start = cumtrapz(V_d)*args.Ts;
|
||||
|
||||
V_smooth_end = args.V_mean - V_smooth_start;
|
||||
end
|
||||
#+end_src
|
||||
|
||||
*** Combine Excitation signals
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
V_exc = [V_smooth_start, sin_exc, V_smooth_end];
|
||||
t_exc = args.Ts*[0:1:length(V_exc)-1];
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
U_exc = [t_exc; V_exc];
|
||||
#+end_src
|
||||
|
||||
* Bibliography :ignore:
|
||||
#+latex: \printbibliography
|
||||
|
||||
Reference in New Issue
Block a user