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Analyze first measurements

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Thomas Dehaeze 2021-06-01 23:16:49 +02:00
parent 4f7f9c4721
commit 9961970547
7 changed files with 614 additions and 59 deletions
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figs/frf_meas_sin_excitation.pdf Normal file
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61
matlab/frf_analyze.m
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@ -1,52 +1,36 @@
% Analysis %% Clear Workspace and Close figures
% :PROPERTIES: clear; close all; clc;
% :header-args: :tangle matlab/frf_analyze.m
% :END: %% Intialize Laplace variable
s = zpk('s');
addpath('./src/');
% Test with one APA
%% Load measurement data for APA number 1
load(sprintf('mat/frf_data_%i.mat', 1), 't', 'Va', 'Vs', 'de', 'da');
%% Load all the measurements
% meas_data = {};
% for i = 1:7
% meas_data(i) = {load(sprintf('mat/frf_data_%i.mat', i), 't', 'Va', 'Vs', 'da', 'de')};
% end
%% % Time domain data:
load(sprintf('mat/frf_data_%i_sweep.mat', 1), 't', 'Va', 'Vs', 'da', 'de')
%%
figure; figure;
plot(t, de); plot(t, de);
%%
figure;
plot(t, Va);
%%
% Compute transfer functions:
Ts = (t(end) - t(1))/(length(t)-1); Ts = (t(end) - t(1))/(length(t)-1);
Fs = 1/Ts; Fs = 1/Ts;
win = hanning(ceil(5*Fs)); % Hannning Windows win = hanning(ceil(0.5*Fs)); % Hannning Windows
%%
[G_dvf, f] = tfestimate(Va, de, win, [], [], 1/Ts); [G_dvf, f] = tfestimate(Va, de, win, [], [], 1/Ts);
[G_d, ~] = tfestimate(Va, da, win, [], [], 1/Ts); [G_d, ~] = tfestimate(Va, da, win, [], [], 1/Ts);
[G_iff, ~] = tfestimate(Va, Vs, 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);
%%
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]);
%%
figure; figure;
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None'); tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
@ -58,6 +42,7 @@ hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]); ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off; hold off;
ylim([10, 30]);
ax2 = nexttile; ax2 = nexttile;
hold on; hold on;
@ -72,7 +57,6 @@ yticks(-360:90:360);
linkaxes([ax1,ax2],'x'); linkaxes([ax1,ax2],'x');
xlim([5, 5e3]); xlim([5, 5e3]);
%%
figure; figure;
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None'); tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
@ -81,6 +65,7 @@ plot(f, abs(G_iff));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]); ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
hold off; hold off;
ylim([10, 30]);
ax2 = nexttile; ax2 = nexttile;
plot(f, 180/pi*angle(G_iff)); plot(f, 180/pi*angle(G_iff));
@ -91,3 +76,11 @@ yticks(-360:90:360);
linkaxes([ax1,ax2],'x'); linkaxes([ax1,ax2],'x');
xlim([5, 5e3]); xlim([5, 5e3]);
% Comparison of all APA
%% Load all the measurements
meas_data = {};
for i = 1:7
meas_data(i) = {load(sprintf('mat/frf_data_%i.mat', i), 't', 'Va', 'Vs', 'de', 'da')};
end

2
matlab/frf_save.m
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@ -1,4 +1,4 @@
% Save Data % =frf_save.m= - Save Data
% :PROPERTIES: % :PROPERTIES:
% :header-args: :tangle matlab/frf_save.m % :header-args: :tangle matlab/frf_save.m
% :END: % :END:

34
matlab/frf_setup.m
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@ -1,10 +1,16 @@
s = tf('s'); %% Clear Workspace and Close figures
addpath('src') clear; close all; clc;
%% %% Intialize Laplace variable
s = zpk('s');
addpath('./src/');
%% Simulation configuration
Fs = 10e3; % Sampling Frequency [Hz] Fs = 10e3; % Sampling Frequency [Hz]
Ts = 1/Fs; % Sampling Time [s] Ts = 1/Fs; % Sampling Time [s]
%% Data record configuration
Trec_start = 5; % Start time for Recording [s] Trec_start = 5; % Start time for Recording [s]
Trec_dur = 100; % Recording Duration [s] Trec_dur = 100; % Recording Duration [s]
@ -15,11 +21,12 @@ gc = 0.1;
xi = 0.5; xi = 0.5;
wn = 2*pi*94.3; wn = 2*pi*94.3;
% Notch filter at the resonance of the APA
G_sweep = 0.2*(s^2 + 2*gc*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2); G_sweep = 0.2*(s^2 + 2*gc*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
V_sweep = generateSweepExc('Ts', Ts, ... V_sweep = generateSweepExc('Ts', Ts, ...
'f_start', 10, ... 'f_start', 10, ...
'f_end', 2e3, ... 'f_end', 1e3, ...
'V_mean', 3.25, ... 'V_mean', 3.25, ...
't_start', Trec_start, ... 't_start', Trec_start, ...
'exc_duration', Trec_dur, ... 'exc_duration', Trec_dur, ...
@ -32,7 +39,16 @@ V_noise = generateShapedNoise('Ts', 1/Fs, ...
't_start', Trec_start, ... 't_start', Trec_start, ...
'exc_duration', Trec_dur, ... 'exc_duration', Trec_dur, ...
'smooth_ends', true, ... 'smooth_ends', true, ...
'V_exc', 0.00/(1 + s/2/pi/50)); 'V_exc', 0.05/(1 + s/2/pi/10));
%% Sinus excitation with increasing amplitude
V_sin = generateSinIncreasingAmpl('Ts', 1/Fs, ...
'V_mean', 3.25, ...
'sin_ampls', [0.1, 0.2, 0.4, 1, 2, 4], ...
'sin_period', 1, ...
'sin_num', 5, ...
't_start', 10, ...
'smooth_ends', true);
%% Select the excitation signal %% Select the excitation signal
V_exc = timeseries(V_noise(2,:), V_noise(1,:)); V_exc = timeseries(V_noise(2,:), V_noise(1,:));
@ -41,16 +57,16 @@ figure;
tiledlayout(1, 2, 'TileSpacing', 'Normal', 'Padding', 'None'); tiledlayout(1, 2, 'TileSpacing', 'Normal', 'Padding', 'None');
ax1 = nexttile; ax1 = nexttile;
plot(V_exc.Time, squeeze(V_exc.Data)); plot(V_exc(1,:), V_exc(2,:));
xlabel('Time [s]'); ylabel('Amplitude [V]'); xlabel('Time [s]'); ylabel('Amplitude [V]');
ax2 = nexttile; ax2 = nexttile;
win = hanning(floor(length(V_exc.Data)/8)); win = hanning(floor(length(V_exc)/8));
[pxx, f] = pwelch(squeeze(V_exc.Data), win, 0, [], Fs); [pxx, f] = pwelch(V_exc(2,:), win, 0, [], Fs);
plot(f, pxx) plot(f, pxx)
xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$V^2/Hz$]'); xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$V^2/Hz$]');
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log'); set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlim([1, Fs/2]); ylim([1e-10, 1e0]); xlim([1, Fs/2]); ylim([1e-10, 1e0]);
%% Save %% Save data that will be loaded in the Simulink file
save('./frf_data.mat', 'Fs', 'Ts', 'Tsim', 'Trec_start', 'Trec_dur', 'V_exc'); save('./frf_data.mat', 'Fs', 'Ts', 'Tsim', 'Trec_start', 'Trec_dur', 'V_exc');

54
matlab/src/generateSinIncreasingAmpl.m Normal file
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@ -0,0 +1,54 @@
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 - [-]
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
t_noise = 0:args.Ts:args.sin_period*args.sin_num;
sin_exc = [];
for sin_ampl = args.sin_ampls
sin_exc = [sin_exc, args.V_mean + sin_ampl*sin(2*pi/args.sin_period*t_noise)];
end
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
V_exc = [V_smooth_start, sin_exc, V_smooth_end];
t_exc = args.Ts*[0:1:length(V_exc)-1];
U_exc = [t_exc; V_exc];

514
test-bench-apa300ml.org
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@ -25,6 +25,7 @@
#+PROPERTY: header-args:matlab+ :results none #+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :eval no-export #+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :noweb yes #+PROPERTY: header-args:matlab+ :noweb yes
#+PROPERTY: header-args:matlab+ :tangle no
#+PROPERTY: header-args:matlab+ :mkdirp yes #+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:matlab+ :output-dir figs #+PROPERTY: header-args:matlab+ :output-dir figs
@ -717,18 +718,29 @@ addpath('./matlab/');
addpath('./src/'); addpath('./src/');
#+end_src #+end_src
** Measurement Setup ** =frf_setup.m= - Measurement Setup
:PROPERTIES: :PROPERTIES:
:header-args:matlab: :tangle matlab/frf_setup.m :header-args:matlab: :tangle matlab/frf_setup.m
:header-args:matlab+: :comments no :header-args:matlab+: :comments no
:END: :END:
#+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 :eval no :exports none
addpath('./src/');
#+end_src
First is defined the sampling frequency: First is defined the sampling frequency:
#+begin_src matlab #+begin_src matlab
%% Simulation configuration %% Simulation configuration
Fs = 10e3; % Sampling Frequency [Hz] Fs = 10e3; % Sampling Frequency [Hz]
Ts = 1/Fs; % Sampling Time [s] Ts = 1/Fs; % Sampling Time [s]
Tsim = 110; % Simulation Time [s]
#+end_src #+end_src
#+begin_src matlab #+begin_src matlab
@ -737,9 +749,20 @@ Trec_start = 5; % Start time for Recording [s]
Trec_dur = 100; % Recording Duration [s] Trec_dur = 100; % Recording Duration [s]
#+end_src #+end_src
#+begin_src matlab
Tsim = 2*Trec_start + Trec_dur; % Simulation Time [s]
#+end_src
The maximum excitation voltage at resonance is 9Vrms, therefore corresponding to 0.6V of output DAC voltage. The maximum excitation voltage at resonance is 9Vrms, therefore corresponding to 0.6V of output DAC voltage.
#+begin_src matlab #+begin_src matlab
%% Sweep Sine %% Sweep Sine
gc = 0.1;
xi = 0.5;
wn = 2*pi*94.3;
% Notch filter at the resonance of the APA
G_sweep = 0.2*(s^2 + 2*gc*xi*wn*s + wn^2)/(s^2 + 2*xi*wn*s + wn^2);
V_sweep = generateSweepExc('Ts', Ts, ... V_sweep = generateSweepExc('Ts', Ts, ...
'f_start', 10, ... 'f_start', 10, ...
'f_end', 1e3, ... 'f_end', 1e3, ...
@ -747,7 +770,7 @@ V_sweep = generateSweepExc('Ts', Ts, ...
't_start', Trec_start, ... 't_start', Trec_start, ...
'exc_duration', Trec_dur, ... 'exc_duration', Trec_dur, ...
'sweep_type', 'log', ... 'sweep_type', 'log', ...
'V_exc', 0.5/(1 + s/2/pi/100)); 'V_exc', G_sweep*1/(1 + s/2/pi/500));
#+end_src #+end_src
#+begin_src matlab :exports none :tangle no #+begin_src matlab :exports none :tangle no
@ -815,10 +838,36 @@ exportFig('figs/frf_meas_noise_excitation.pdf', 'width', 'full', 'height', 'norm
#+RESULTS: #+RESULTS:
[[file:figs/frf_meas_noise_excitation.png]] [[file:figs/frf_meas_noise_excitation.png]]
#+begin_src matlab
%% Sinus excitation with increasing amplitude
V_sin = generateSinIncreasingAmpl('Ts', 1/Fs, ...
'V_mean', 3.25, ...
'sin_ampls', [0.1, 0.2, 0.4, 1, 2, 4], ...
'sin_period', 1, ...
'sin_num', 5, ...
't_start', 10, ...
'smooth_ends', true);
#+end_src
#+begin_src matlab :exports none :tangle no
figure;
plot(V_sin(1,:), V_sin(2,:));
xlabel('Time [s]'); ylabel('Amplitude [V]');
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/frf_meas_sin_excitation.pdf', 'width', 'wide', 'height', 'normal');
#+end_src
#+name: fig:frf_meas_sin_excitation
#+caption: Example of Shaped noise excitation signal
#+RESULTS:
[[file:figs/frf_meas_sin_excitation.png]]
Then, we select the wanted excitation signal. Then, we select the wanted excitation signal.
#+begin_src matlab #+begin_src matlab
%% Select the excitation signal %% Select the excitation signal
V_exc = V_noise; V_exc = timeseries(V_noise(2,:), V_noise(1,:));
#+end_src #+end_src
#+begin_src matlab :exports none :eval no #+begin_src matlab :exports none :eval no
@ -838,7 +887,12 @@ set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlim([1, Fs/2]); ylim([1e-10, 1e0]); xlim([1, Fs/2]); ylim([1e-10, 1e0]);
#+end_src #+end_src
** Save Data #+begin_src matlab
%% Save data that will be loaded in the Simulink file
save('./frf_data.mat', 'Fs', 'Ts', 'Tsim', 'Trec_start', 'Trec_dur', 'V_exc');
#+end_src
** =frf_save.m= - Save Data
:PROPERTIES: :PROPERTIES:
:header-args: :tangle matlab/frf_save.m :header-args: :tangle matlab/frf_save.m
:END: :END:
@ -856,10 +910,10 @@ And we load the data on the Workspace:
#+begin_src matlab #+begin_src matlab
data = SimulinkRealTime.utils.getFileScopeData('data/data.dat').data; data = SimulinkRealTime.utils.getFileScopeData('data/data.dat').data;
Va = data(:, 1); % Excitation Voltage (input of PD200) [V] da = data(:, 1); % Excitation Voltage (input of PD200) [V]
Vs = data(:, 2); % Measured voltage (force sensor) [V] de = data(:, 2); % Measured voltage (force sensor) [V]
de = data(:, 3); % Measurment displacement (encoder) [m] Vs = data(:, 3); % Measurment displacement (encoder) [m]
da = data(:, 4); % Measurement displacement (attocube) [m] Va = data(:, 4); % Measurement displacement (attocube) [m]
t = data(:, end); % Time [s] t = data(:, end); % Time [s]
#+end_src #+end_src
@ -867,10 +921,347 @@ And we save this to a =mat= file:
#+begin_src matlab #+begin_src matlab
apa_number = 1; apa_number = 1;
save(sprintf('mat/frf_data_%i.mat', apa_number), 't', 'Va', 'Vs', 'de', 'da'); save(sprintf('mat/frf_data_%i_huddle.mat', apa_number), 't', 'Va', 'Vs', 'de', 'da');
#+end_src #+end_src
** Analysis ** Measurements on APA 1
*** Introduction :ignore:
Measurements are first performed on the APA number 1.
*** 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
*** 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: :PROPERTIES:
:header-args: :tangle matlab/frf_analyze.m :header-args: :tangle matlab/frf_analyze.m
:END: :END:
@ -3038,5 +3429,106 @@ t_exc = args.Ts*[0:1:length(V_exc)-1];
U_exc = [t_exc; V_exc]; U_exc = [t_exc; V_exc];
#+end_src #+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: * Bibliography :ignore:
#+latex: \printbibliography #+latex: \printbibliography