Add measurement of spurious resonances
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figs/apa300ml_meas_freq_torsion_z_comp.pdf
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figs/apa300ml_meas_freq_torsion_z_comp.png
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figs/measurement_setup_X_bending.jpg
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figs/measurement_setup_Y_bending.jpg
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figs/measurement_setup_torsion.jpg
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figs/measurement_setup_torsion_bis.jpg
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matlab/png/amplified_piezo_actuator.png
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matlab/png/bot_platform.png
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matlab/png/encoder.png
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matlab/png/flexible_joint_bot.png
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matlab/png/flexible_joint_top.png
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matlab/png/nano_hexapod_strut.png
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matlab/png/top_platform.png
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piezostack_apa300_mel_lab_5may2021/Measurement6.mat
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piezostack_apa300_mel_lab_5may2021/piezo_rotation.jpg
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piezostack_apa300_mel_lab_5may2021/piezo_stack_mel_5may2021.m
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@ -0,0 +1,23 @@
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% Vibration measurement on:
|
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% Piezo stack in MEL lab - 5 may 2021
|
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|
||||
% Excitation: hammer dytran with metal tip : 230e-6V/N
|
||||
% Response: laser vibro dual fibres 1mm/s/V
|
||||
|
||||
% recorded signals and saved traces
|
||||
% laser fibres on both sides edges of stack
|
||||
--> photo: piezo_rotation.jpg
|
||||
--> plot: piezo_stack_rotation_5may2021.png
|
||||
% meas3 hammer on edge right: green
|
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% meas4 hammer on centre top : blue
|
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% meas5 hammer on edge left : orange
|
||||
|
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% laser fibres on base and top of stack (vertical axis)
|
||||
--> photo: piezo_vertical.jpg
|
||||
--> plot: piezo_stack_rotation_vertical_5may2021.png
|
||||
% meas7 hammer on vertical centre top : orange
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||||
|
||||
% Stack rotated 90deg - laser fibres on upper interface of stack (top and bottom of interface plate, ~1cm apart)
|
||||
--> photo: none
|
||||
--> plot: piezo_stack_rotation_interface_5may2021.png
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% meas8 hammer on interface top : orange
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piezostack_apa300_mel_lab_5may2021/piezo_stack_rotation_5may2021.png
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piezostack_apa300_mel_lab_5may2021/piezo_stack_rotation_interface_5may2021.png
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piezostack_apa300_mel_lab_5may2021/piezo_stack_rotation_vertical_5may2021.png
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@ -230,79 +230,6 @@ The excitation frequency is set to be 1kHz.
|
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There is clearly a problem with APA300ML number 3
|
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#+end_warning
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|
||||
* Stiffness measurement
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+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>>
|
||||
#+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/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
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||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
** APA test
|
||||
#+begin_src matlab
|
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load('meas_stiff_apa_1_x.mat', 't', 'F', 'd');
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||||
#+end_src
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||||
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#+begin_src matlab
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figure;
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plot(t, F)
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#+end_src
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#+begin_src matlab
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||||
%% Automatic Zero of the force
|
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F = F - mean(F(t > 0.1 & t < 0.3));
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%% Start measurement at t = 0.2 s
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d = d(t > 0.2);
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F = F(t > 0.2);
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t = t(t > 0.2); t = t - t(1);
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#+end_src
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#+begin_src matlab
|
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i_l_start = find(F > 0.3, 1, 'first');
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[~, i_l_stop] = max(F);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
F_l = F(i_l_start:i_l_stop);
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||||
d_l = d(i_l_start:i_l_stop);
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#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
fit_l = polyfit(F_l, d_l, 1);
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||||
|
||||
% %% Reset displacement based on fit
|
||||
% d = d - fit_l(2);
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||||
% fit_s(2) = fit_s(2) - fit_l(2);
|
||||
% fit_l(2) = 0;
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||||
|
||||
% %% Estimated Stroke
|
||||
% F_max = fit_s(2)/(fit_l(1) - fit_s(1));
|
||||
% d_max = fit_l(1)*F_max;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
h^2/fit_l(1)
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||||
#+end_src
|
||||
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#+begin_src matlab
|
||||
figure;
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hold on;
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||||
plot(F,d,'k')
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plot(F_l, d_l)
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plot(F_l, F_l*fit_l(1) + fit_l(2), '--')
|
||||
#+end_src
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||||
* Stroke measurement
|
||||
** Introduction :ignore:
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||||
|
||||
@ -564,6 +491,79 @@ data2orgtable(1e6*apa300ml_stroke', {'APA 1', 'APA 2', 'APA 3', 'APA 4', 'APA 5'
|
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| APA 6 | 363.9 |
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| APA 7 | 358.4 |
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* TODO Stiffness measurement
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||||
** Matlab Init :noexport:ignore:
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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>>
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no
|
||||
addpath('./matlab/mat/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./mat/');
|
||||
#+end_src
|
||||
|
||||
** APA test
|
||||
#+begin_src matlab
|
||||
load('meas_stiff_apa_1_x.mat', 't', 'F', 'd');
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||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
figure;
|
||||
plot(t, F)
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
%% Automatic Zero of the force
|
||||
F = F - mean(F(t > 0.1 & t < 0.3));
|
||||
|
||||
%% Start measurement at t = 0.2 s
|
||||
d = d(t > 0.2);
|
||||
F = F(t > 0.2);
|
||||
t = t(t > 0.2); t = t - t(1);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
i_l_start = find(F > 0.3, 1, 'first');
|
||||
[~, i_l_stop] = max(F);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
F_l = F(i_l_start:i_l_stop);
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||||
d_l = d(i_l_start:i_l_stop);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
fit_l = polyfit(F_l, d_l, 1);
|
||||
|
||||
% %% Reset displacement based on fit
|
||||
% d = d - fit_l(2);
|
||||
% fit_s(2) = fit_s(2) - fit_l(2);
|
||||
% fit_l(2) = 0;
|
||||
|
||||
% %% Estimated Stroke
|
||||
% F_max = fit_s(2)/(fit_l(1) - fit_s(1));
|
||||
% d_max = fit_l(1)*F_max;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
h^2/fit_l(1)
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
figure;
|
||||
hold on;
|
||||
plot(F,d,'k')
|
||||
plot(F_l, d_l)
|
||||
plot(F_l, F_l*fit_l(1) + fit_l(2), '--')
|
||||
#+end_src
|
||||
* Test-Bench Description
|
||||
|
||||
#+begin_note
|
||||
@ -580,6 +580,7 @@ Here are the documentation of the equipment used for this test bench:
|
||||
[[file:figs/test_bench_apa_alone.png]]
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||||
|
||||
* Measurement Procedure
|
||||
<<sec:measurement_procedure>>
|
||||
** Introduction :ignore:
|
||||
|
||||
** Stroke Measurement
|
||||
@ -621,7 +622,7 @@ For each excitation amplitude, the vertical displacement $d$ of the mass is meas
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Then, $d$ is plotted as a function of $V_a$ for all the amplitudes.
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||||
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||||
#+name: fig:expected_hysteresis
|
||||
#+caption: Expected Hysteresis (cite:poel10_explor_activ_hard_mount_vibrat)
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||||
#+caption: Expected Hysteresis cite:poel10_explor_activ_hard_mount_vibrat
|
||||
#+attr_latex: :width 0.8\linewidth
|
||||
[[file:figs/expected_hysteresis.png]]
|
||||
|
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@ -685,6 +686,298 @@ This can also be performed with and without the encoder fixed to the APA.
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||||
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||||
Compare all the obtained parameters for all the test APA.
|
||||
|
||||
* FRF measurement
|
||||
** Introduction :ignore:
|
||||
|
||||
- [ ] Schematic of the measurement
|
||||
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||||
| Variable | | Unit | Hardware |
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||||
|----------+------------------------------+------+-------------------------------|
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||||
| =Va= | Output DAC voltage | [V] | DAC - Ch. 1 => PD200 => APA |
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||||
| =Vs= | Measured stack voltage (ADC) | [V] | APA => ADC - Ch. 1 |
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||||
| =de= | Encoder Measurement | [m] | PEPU Ch. 1 - IO318(1) - Ch. 1 |
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||||
| =da= | Attocube Measurement | [m] | PEPU Ch. 2 - IO318(1) - Ch. 2 |
|
||||
| =t= | Time | [s] | |
|
||||
|
||||
** 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/src/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./src/');
|
||||
#+end_src
|
||||
|
||||
** Measurement Setup
|
||||
:PROPERTIES:
|
||||
:header-args:matlab: :tangle matlab/frf_setup.m
|
||||
:header-args:matlab+: :comments no
|
||||
:END:
|
||||
|
||||
First is defined the sampling frequency:
|
||||
#+begin_src matlab
|
||||
%% Simulation configuration
|
||||
Fs = 10e3; % Sampling Frequency [Hz]
|
||||
Ts = 1/Fs; % Sampling Time [s]
|
||||
Tsim = 110; % Simulation Time [s]
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
%% Data record configuration
|
||||
Trec_start = 5; % Start time for Recording [s]
|
||||
Trec_dur = 100; % Recording Duration [s]
|
||||
#+end_src
|
||||
|
||||
The maximum excitation voltage at resonance is 9Vrms, therefore corresponding to 0.6V of output DAC voltage.
|
||||
#+begin_src matlab
|
||||
%% Sweep Sine
|
||||
V_sweep = generateSweepExc('Ts', Ts, ...
|
||||
'f_start', 10, ...
|
||||
'f_end', 1e3, ...
|
||||
'V_mean', 3.25, ...
|
||||
't_start', Trec_start, ...
|
||||
'exc_duration', Trec_dur, ...
|
||||
'sweep_type', 'log', ...
|
||||
'V_exc', 0.5/(1 + s/2/pi/100));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :tangle no
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'Normal', 'Padding', 'None');
|
||||
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||||
ax1 = nexttile;
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||||
plot(V_sweep(1,:), V_sweep(2,:));
|
||||
xlabel('Time [s]'); ylabel('Amplitude [V]');
|
||||
|
||||
ax2 = nexttile;
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||||
win = hanning(floor(length(V_sweep(2,:))/80));
|
||||
[pxx, f] = pwelch(V_sweep(2,:), win, 0, [], Fs);
|
||||
plot(f, pxx)
|
||||
xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$V^2/Hz$]');
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlim([1, Fs/2]); ylim([1e-10, 1e0]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/frf_meas_sweep_excitation.pdf', 'width', 'full', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:frf_meas_sweep_excitation
|
||||
#+caption: Example of Sweep Sin excitation signal
|
||||
#+RESULTS:
|
||||
[[file:figs/frf_meas_sweep_excitation.png]]
|
||||
|
||||
|
||||
A white noise excitation signal can be very useful in order to obtain a first idea of the plant FRF.
|
||||
The gain can be gradually increased until satisfactory output is obtained.
|
||||
#+begin_src matlab
|
||||
%% Shaped Noise
|
||||
V_noise = generateShapedNoise('Ts', 1/Fs, ...
|
||||
'V_mean', 3.25, ...
|
||||
't_start', Trec_start, ...
|
||||
'exc_duration', Trec_dur, ...
|
||||
'smooth_ends', true, ...
|
||||
'V_exc', 0.05/(1 + s/2/pi/10));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :tangle no
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'Normal', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
plot(V_noise(1,:), V_noise(2,:));
|
||||
xlabel('Time [s]'); ylabel('Amplitude [V]');
|
||||
|
||||
ax2 = nexttile;
|
||||
win = hanning(floor(length(V_noise)/8));
|
||||
[pxx, f] = pwelch(V_noise(2,:), win, 0, [], Fs);
|
||||
plot(f, pxx)
|
||||
xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$V^2/Hz$]');
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlim([1, Fs/2]); ylim([1e-10, 1e0]);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/frf_meas_noise_excitation.pdf', 'width', 'full', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:frf_meas_noise_excitation
|
||||
#+caption: Example of Shaped noise excitation signal
|
||||
#+RESULTS:
|
||||
[[file:figs/frf_meas_noise_excitation.png]]
|
||||
|
||||
Then, we select the wanted excitation signal.
|
||||
#+begin_src matlab
|
||||
%% Select the excitation signal
|
||||
V_exc = V_noise;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none :eval no
|
||||
figure;
|
||||
tiledlayout(1, 2, 'TileSpacing', 'Normal', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
plot(V_exc(1,:), V_exc(2,:));
|
||||
xlabel('Time [s]'); ylabel('Amplitude [V]');
|
||||
|
||||
ax2 = nexttile;
|
||||
win = hanning(floor(length(V_exc)/8));
|
||||
[pxx, f] = pwelch(V_exc(2,:), win, 0, [], Fs);
|
||||
plot(f, pxx)
|
||||
xlabel('Frequency [Hz]'); ylabel('Power Spectral Density [$V^2/Hz$]');
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlim([1, Fs/2]); ylim([1e-10, 1e0]);
|
||||
#+end_src
|
||||
|
||||
** Save Data
|
||||
:PROPERTIES:
|
||||
:header-args: :tangle matlab/frf_save.m
|
||||
:END:
|
||||
|
||||
First, we get data from the Speedgoat:
|
||||
#+begin_src matlab
|
||||
tg = slrt;
|
||||
|
||||
f = SimulinkRealTime.openFTP(tg);
|
||||
mget(f, 'data/data.dat');
|
||||
close(f);
|
||||
#+end_src
|
||||
|
||||
And we load the data on the Workspace:
|
||||
#+begin_src matlab
|
||||
data = SimulinkRealTime.utils.getFileScopeData('data/data.dat').data;
|
||||
|
||||
Va = data(:, 1); % Excitation Voltage (input of PD200) [V]
|
||||
Vs = data(:, 2); % Measured voltage (force sensor) [V]
|
||||
de = data(:, 3); % Measurment displacement (encoder) [m]
|
||||
da = data(:, 4); % Measurement displacement (attocube) [m]
|
||||
t = data(:, end); % Time [s]
|
||||
#+end_src
|
||||
|
||||
And we save this to a =mat= file:
|
||||
#+begin_src matlab
|
||||
apa_number = 1;
|
||||
|
||||
save(sprintf('mat/frf_data_%i.mat', apa_number), 't', 'Va', 'Vs', 'de', 'da');
|
||||
#+end_src
|
||||
|
||||
** Analysis
|
||||
:PROPERTIES:
|
||||
:header-args: :tangle matlab/frf_analyze.m
|
||||
:END:
|
||||
|
||||
*** 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/src/');
|
||||
addpath('./matlab/');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :eval no
|
||||
addpath('./src/');
|
||||
#+end_src
|
||||
|
||||
*** Test with one APA
|
||||
#+begin_src matlab
|
||||
%% Load measurement data for APA number 1
|
||||
load(sprintf('mat/frf_data_%i.mat', 1), 't', 'Va', 'Vs', 'de', 'da');
|
||||
#+end_src
|
||||
|
||||
Time domain data:
|
||||
#+begin_src matlab
|
||||
figure;
|
||||
plot(t, de);
|
||||
#+end_src
|
||||
|
||||
Compute transfer functions:
|
||||
#+begin_src matlab
|
||||
Ts = (t(end) - t(1))/(length(t)-1);
|
||||
Fs = 1/Ts;
|
||||
|
||||
win = hanning(ceil(0.5*Fs)); % Hannning Windows
|
||||
#+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);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
tiledlayout(2, 1, 'TileSpacing', 'None', 'Padding', 'None');
|
||||
|
||||
ax1 = nexttile;
|
||||
hold on;
|
||||
plot(f, abs(G_dvf));
|
||||
plot(f, abs(G_d));
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([10, 30]);
|
||||
|
||||
ax2 = nexttile;
|
||||
hold on;
|
||||
plot(f, 180/pi*angle(G_dvf));
|
||||
plot(f, 180/pi*angle(G_d));
|
||||
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([5, 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 $V_{out}/V_{in}$ [V/V]'); set(gca, 'XTickLabel',[]);
|
||||
hold off;
|
||||
ylim([10, 30]);
|
||||
|
||||
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([5, 5e3]);
|
||||
#+end_src
|
||||
|
||||
*** Comparison of all APA
|
||||
#+begin_src matlab :exports none
|
||||
%% 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
|
||||
#+end_src
|
||||
|
||||
* Measurement Results
|
||||
|
||||
* TODO Compare with the FEM/Simscape Model :noexport:
|
||||
@ -2307,7 +2600,7 @@ The APA is excited with an instrumented hammer and the transfer function from th
|
||||
#+name: fig:measurement_setup_torsion
|
||||
#+caption: Measurement setup with a Laser Doppler Vibrometer and one instrumental hammer
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_torsion.png]]
|
||||
[[file:figs/measurement_setup_torsion.jpg]]
|
||||
|
||||
** Bending - X
|
||||
|
||||
@ -2318,20 +2611,21 @@ The impact point is on the back-side of the APA aligned with the top measurement
|
||||
#+name: fig:measurement_setup_X_bending
|
||||
#+caption: X-Bending measurement setup
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_X_bending.png]]
|
||||
[[file:figs/measurement_setup_X_bending.jpg]]
|
||||
|
||||
The data is loaded.
|
||||
#+begin_src matlab
|
||||
bending_X = load('apa300ml_bending_X_top.mat')
|
||||
bending_X = load('apa300ml_bending_X_top.mat');
|
||||
#+end_src
|
||||
|
||||
The config for =tfestimate= is performed:
|
||||
#+begin_src matlab
|
||||
Ts = bending_X.Track1_X_Resolution; % Sampling frequency [Hz]
|
||||
win = hann(ceil(1/Ts));
|
||||
#+end_src
|
||||
|
||||
The transfer function from the input force to the output "rotation" (difference between the two measured distances).
|
||||
#+begin_src matlab
|
||||
win = hann(ceil(1/Ts));
|
||||
[G_bending_X, f] = tfestimate(bending_X.Track1, bending_X.Track2, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
@ -2369,11 +2663,11 @@ The impact point of the instrumented hammer is located on the back surface of th
|
||||
#+name: fig:measurement_setup_Y_bending
|
||||
#+caption: Y-Bending measurement setup
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_Y_bending.png]]
|
||||
[[file:figs/measurement_setup_Y_bending.jpg]]
|
||||
|
||||
The data is loaded, and the transfer function from the force to the measured rotation is computed.
|
||||
#+begin_src matlab
|
||||
bending_Y = load('apa300ml_bending_Y_top.mat')
|
||||
bending_Y = load('apa300ml_bending_Y_top.mat');
|
||||
[G_bending_Y, ~] = tfestimate(bending_Y.Track1, bending_Y.Track2, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
@ -2410,12 +2704,12 @@ The excitation is shown on the other side of the APA, on the side to excite the
|
||||
#+name: fig:measurement_setup_torsion_bis
|
||||
#+caption: Z-Torsion measurement setup
|
||||
#+attr_latex: :width 0.7\linewidth
|
||||
[[file:figs/measurement_setup_torsion_bis.png]]
|
||||
[[file:figs/measurement_setup_torsion_bis.jpg]]
|
||||
|
||||
The data is loaded, and the transfer function computed.
|
||||
#+begin_src matlab
|
||||
torsion = load('apa300ml_torsion_left.mat')
|
||||
[G_torsion, ~] = tfestimate(torsion_left.Track1, torsion_left.Track2, win, [], [], 1/Ts);
|
||||
torsion = load('apa300ml_torsion_left.mat');
|
||||
[G_torsion, ~] = tfestimate(torsion.Track1, torsion.Track2, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
The results are shown in Figure [[fig:apa300ml_meas_freq_torsion_z]].
|
||||
@ -2431,7 +2725,8 @@ set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 2e-2])
|
||||
text(415, 4.3e-3,{'415Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(267, 8e-4,{'267Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(267, 8e-4,{'267Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
text(800, 6e-4,{'800Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
@ -2443,6 +2738,39 @@ exportFig('figs/apa300ml_meas_freq_torsion_z.pdf', 'width', 'wide', 'height', 'n
|
||||
#+RESULTS:
|
||||
[[file:figs/apa300ml_meas_freq_torsion_z.png]]
|
||||
|
||||
In order to verify that, the APA is excited on the top part such that the torsion mode should not be excited.
|
||||
#+begin_src matlab
|
||||
torsion = load('apa300ml_torsion_top.mat');
|
||||
[G_torsion_top, ~] = tfestimate(torsion.Track1, torsion.Track2, win, [], [], 1/Ts);
|
||||
#+end_src
|
||||
|
||||
The two FRF are compared in Figure [[fig:apa300ml_meas_freq_torsion_z_comp]].
|
||||
It is clear that the first two modes does not correspond to the torsional mode.
|
||||
Maybe the resonance at 800Hz, or even higher resonances. It is difficult to conclude here.
|
||||
#+begin_src matlab :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, abs(G_torsion), 'k-', 'DisplayName', 'Left excitation');
|
||||
plot(f, abs(G_torsion_top), '-', 'DisplayName', 'Top excitation');
|
||||
hold off;
|
||||
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude');
|
||||
xlim([50, 2e3]); ylim([1e-5, 2e-2])
|
||||
text(415, 4.3e-3,{'415Hz'},'VerticalAlignment','bottom','HorizontalAlignment','center')
|
||||
text(267, 8e-4,{'267Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
text(800, 2e-3,{'800Hz'}, 'VerticalAlignment', 'bottom','HorizontalAlignment','center')
|
||||
legend('location', 'northwest');
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :tangle no :exports results :results file replace
|
||||
exportFig('figs/apa300ml_meas_freq_torsion_z_comp.pdf', 'width', 'wide', 'height', 'normal');
|
||||
#+end_src
|
||||
|
||||
#+name: fig:apa300ml_meas_freq_torsion_z_comp
|
||||
#+caption: Obtained FRF for the Z-torsion
|
||||
#+RESULTS:
|
||||
[[file:figs/apa300ml_meas_freq_torsion_z_comp.png]]
|
||||
|
||||
** Compare
|
||||
The three measurements are shown in Figure [[fig:apa300ml_meas_freq_compare]].
|
||||
#+begin_src matlab :exports none
|
||||
@ -2477,7 +2805,7 @@ It is however quite interesting that there is a factor $\approx \sqrt{2}$ betwee
|
||||
|
||||
#+name: tab:apa300ml_measured_modes_freq
|
||||
#+caption: Measured frequency of the modes
|
||||
#+attr_latex: :environment tabularx :width \linewidth :align lX
|
||||
#+attr_latex: :environment tabularx :width 0.6\linewidth :align ccc
|
||||
#+attr_latex: :center t :booktabs t :float t
|
||||
| Mode | Strut Mode | Measured Frequency |
|
||||
|-----------+------------+--------------------|
|
||||
@ -2485,5 +2813,230 @@ It is however quite interesting that there is a factor $\approx \sqrt{2}$ betwee
|
||||
| Y-Bending | 285Hz | 410Hz |
|
||||
| Z-Torsion | 400Hz | ? |
|
||||
|
||||
* Function
|
||||
** =generateSweepExc=: Generate sweep sinus excitation
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle ./matlab/src/generateSweepExc.m
|
||||
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
||||
:END:
|
||||
<<sec:generateSweepExc>>
|
||||
|
||||
*** Function description
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
function [U_exc] = generateSweepExc(args)
|
||||
% generateSweepExc - Generate a Sweep Sine excitation signal
|
||||
%
|
||||
% Syntax: [U_exc] = generateSweepExc(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Optinal arguments:
|
||||
% - Ts - Sampling Time - [s]
|
||||
% - f_start - Start frequency of the sweep - [Hz]
|
||||
% - f_end - End frequency of the sweep - [Hz]
|
||||
% - V_mean - Mean value of the excitation voltage - [V]
|
||||
% - V_exc - Excitation Amplitude for the Sweep, could be numeric or TF - [V]
|
||||
% - t_start - Time at which the sweep begins - [s]
|
||||
% - exc_duration - Duration of the sweep - [s]
|
||||
% - sweep_type - 'logarithmic' or 'linear' - [-]
|
||||
% - 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.f_start (1,1) double {mustBeNumeric, mustBePositive} = 1
|
||||
args.f_end (1,1) double {mustBeNumeric, mustBePositive} = 1e3
|
||||
args.V_mean (1,1) double {mustBeNumeric} = 0
|
||||
args.V_exc = 1
|
||||
args.t_start (1,1) double {mustBeNumeric, mustBeNonnegative} = 5
|
||||
args.exc_duration (1,1) double {mustBeNumeric, mustBePositive} = 10
|
||||
args.sweep_type char {mustBeMember(args.sweep_type,{'log', 'lin'})} = 'lin'
|
||||
args.smooth_ends logical {mustBeNumericOrLogical} = true
|
||||
end
|
||||
#+end_src
|
||||
|
||||
*** Sweep Sine part
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
t_sweep = 0:args.Ts:args.exc_duration;
|
||||
|
||||
if strcmp(args.sweep_type, 'log')
|
||||
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));
|
||||
elseif strcmp(args.sweep_type, 'lin')
|
||||
V_exc = sin(2*pi*(args.f_start + (args.f_end - args.f_start)/2/args.exc_duration*t_sweep).*t_sweep);
|
||||
else
|
||||
error('sweep_type should either be equal to "log" or to "lin"');
|
||||
end
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
if isnumeric(args.V_exc)
|
||||
V_sweep = args.V_mean + args.V_exc*V_exc;
|
||||
elseif isct(args.V_exc)
|
||||
if strcmp(args.sweep_type, 'log')
|
||||
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;
|
||||
elseif strcmp(args.sweep_type, 'lin')
|
||||
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;
|
||||
end
|
||||
end
|
||||
#+end_src
|
||||
|
||||
*** Smooth Ends
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
if args.t_start > 0
|
||||
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
|
||||
else
|
||||
V_smooth_start = [];
|
||||
V_smooth_end = [];
|
||||
end
|
||||
#+end_src
|
||||
|
||||
*** Combine Excitation signals
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
V_exc = [V_smooth_start, V_sweep, 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
|
||||
|
||||
** =generateShapedNoise=: Generate Shaped Noise excitation
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle ./matlab/src/generateShapedNoise.m
|
||||
:header-args:matlab+: :comments none :mkdirp yes :eval no
|
||||
:END:
|
||||
<<sec:generateShapedNoise>>
|
||||
|
||||
*** Function description
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
function [U_exc] = generateShapedNoise(args)
|
||||
% generateShapedNoise - Generate a Shaped Noise excitation signal
|
||||
%
|
||||
% Syntax: [U_exc] = generateShapedNoise(args)
|
||||
%
|
||||
% Inputs:
|
||||
% - args - Optinal arguments:
|
||||
% - Ts - Sampling Time - [s]
|
||||
% - V_mean - Mean value of the excitation voltage - [V]
|
||||
% - V_exc - Excitation Amplitude, could be numeric or TF - [V rms]
|
||||
% - t_start - Time at which the noise begins - [s]
|
||||
% - exc_duration - Duration of the noise - [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.V_exc = 1
|
||||
args.t_start (1,1) double {mustBeNumeric, mustBePositive} = 5
|
||||
args.exc_duration (1,1) double {mustBeNumeric, mustBePositive} = 10
|
||||
args.smooth_ends logical {mustBeNumericOrLogical} = true
|
||||
end
|
||||
#+end_src
|
||||
|
||||
*** Shaped Noise
|
||||
:PROPERTIES:
|
||||
:UNNUMBERED: t
|
||||
:END:
|
||||
|
||||
#+begin_src matlab
|
||||
t_noise = 0:args.Ts:args.exc_duration;
|
||||
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
if isnumeric(args.V_exc)
|
||||
V_noise = args.V_mean + args.V_exc*sqrt(1/args.Ts/2)*randn(length(t_noise), 1)';
|
||||
elseif isct(args.V_exc)
|
||||
V_noise = args.V_mean + lsim(args.V_exc, sqrt(1/args.Ts/2)*randn(length(t_noise), 1), 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, V_noise, 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
|
||||
|