Preparation of measurements
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11
matlab/frf_analyze.m
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11
matlab/frf_analyze.m
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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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%% 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', 'd')};
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end
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32
matlab/frf_save.m
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32
matlab/frf_save.m
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% 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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% First, we get data from the Speedgoat:
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tg = slrt;
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f = SimulinkRealTime.openFTP(tg);
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mget(f, 'data/data.dat');
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close(f);
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% And we load the data on the Workspace:
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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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t = data(:, end); % Time [s]
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% And we save this to a =mat= file:
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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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43
matlab/frf_setup.m
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43
matlab/frf_setup.m
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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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Trec_start = 5; % Start time for Recording [s]
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Trec_dur = 100; % Recording Duration [s]
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%% Sweep Sine
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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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'V_mean', 3.25, ...
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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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%% Shaped Noise
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V_noise = generateShapedNoise('Ts', 1/Fs, ...
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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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'smooth_ends', true, ...
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'V_exc', 0.05/(1 + s/2/pi/10));
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%% Select the excitation signal
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V_exc = V_noise;
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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(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)/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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53
matlab/src/generateShapedNoise.m
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53
matlab/src/generateShapedNoise.m
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function [U_exc] = generateShapedNoise(args)
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% generateShapedNoise - Generate a Shaped Noise excitation signal
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%
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% Syntax: [U_exc] = generateShapedNoise(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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% - V_exc - Excitation Amplitude, could be numeric or TF - [V rms]
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% - t_start - Time at which the noise begins - [s]
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% - exc_duration - Duration of the noise - [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.V_exc = 1
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args.t_start (1,1) double {mustBeNumeric, mustBePositive} = 5
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args.exc_duration (1,1) double {mustBeNumeric, mustBePositive} = 10
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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.exc_duration;
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if isnumeric(args.V_exc)
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V_noise = args.V_mean + args.V_exc*sqrt(1/args.Ts/2)*randn(length(t_noise), 1)';
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elseif isct(args.V_exc)
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V_noise = args.V_mean + lsim(args.V_exc, sqrt(1/args.Ts/2)*randn(length(t_noise), 1), 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, V_noise, 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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76
matlab/src/generateSweepExc.m
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76
matlab/src/generateSweepExc.m
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function [U_exc] = generateSweepExc(args)
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% generateSweepExc - Generate a Sweep Sine excitation signal
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%
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% Syntax: [U_exc] = generateSweepExc(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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% - f_start - Start frequency of the sweep - [Hz]
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% - f_end - End frequency of the sweep - [Hz]
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% - V_mean - Mean value of the excitation voltage - [V]
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% - V_exc - Excitation Amplitude for the Sweep, could be numeric or TF - [V]
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% - t_start - Time at which the sweep begins - [s]
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% - exc_duration - Duration of the sweep - [s]
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% - sweep_type - 'logarithmic' or 'linear' - [-]
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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.f_start (1,1) double {mustBeNumeric, mustBePositive} = 1
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args.f_end (1,1) double {mustBeNumeric, mustBePositive} = 1e3
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args.V_mean (1,1) double {mustBeNumeric} = 0
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args.V_exc = 1
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args.t_start (1,1) double {mustBeNumeric, mustBeNonnegative} = 5
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args.exc_duration (1,1) double {mustBeNumeric, mustBePositive} = 10
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args.sweep_type char {mustBeMember(args.sweep_type,{'log', 'lin'})} = 'lin'
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args.smooth_ends logical {mustBeNumericOrLogical} = true
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end
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t_sweep = 0:args.Ts:args.exc_duration;
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if strcmp(args.sweep_type, 'log')
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V_exc = sin(2*pi*args.f_start * args.exc_duration/log(args.f_end/args.f_start) * (exp(log(args.f_end/args.f_start)*t_sweep/args.exc_duration) - 1));
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elseif strcmp(args.sweep_type, 'lin')
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V_exc = sin(2*pi*(args.f_start + (args.f_end - args.f_start)/2/args.exc_duration*t_sweep).*t_sweep);
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else
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error('sweep_type should either be equal to "log" or to "lin"');
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end
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if isnumeric(args.V_exc)
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V_sweep = args.V_mean + args.V_exc*V_exc;
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elseif isct(args.V_exc)
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if strcmp(args.sweep_type, 'log')
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V_sweep = args.V_mean + abs(squeeze(freqresp(args.V_exc, args.f_start*(args.f_end/args.f_start).^(t_sweep/args.exc_duration), 'Hz')))'.*V_exc;
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elseif strcmp(args.sweep_type, 'lin')
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V_sweep = args.V_mean + abs(squeeze(freqresp(args.V_exc, args.f_start+(args.f_end-args.f_start)/args.exc_duration*t_sweep, 'Hz')))'.*V_exc;
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end
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end
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if args.t_start > 0
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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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else
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V_smooth_start = [];
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V_smooth_end = [];
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end
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V_exc = [V_smooth_start, V_sweep, 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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