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#+TITLE :Effect on the control system of each stages on the vibration of the station
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:DRAWER:
#+STARTUP : overview
#+LANGUAGE : en
#+EMAIL : dehaeze.thomas@gmail.com
#+AUTHOR : Dehaeze Thomas
#+HTML_LINK_HOME : ../index.html
#+HTML_LINK_UP : ../index.html
#+HTML_HEAD : <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
#+HTML_HEAD : <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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#+HTML_MATHJAX : align: center tagside: right font: TeX
#+PROPERTY : header-args:matlab :session *MATLAB*
#+PROPERTY : header-args:matlab+ :comments org
#+PROPERTY : header-args:matlab+ :results none
#+PROPERTY : header-args:matlab+ :exports both
#+PROPERTY : header-args:matlab+ :eval no-export
#+PROPERTY : header-args:matlab+ :output-dir figs
#+PROPERTY : header-args:shell :eval no-export
:END:
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This file is organized as follow:
- Section [[sec:effect_control_all ]]:
- One geophone on the marble and one at the sample location
- Each stage is turned on one by one
- Section [[sec:effect_control_one ]]:
- One geophone on the marble and one at the sample location
- Each stage is turned on one at a time
- Section [[sec:effect_symetrie_driver ]]:
- We check if the Symetrie driver induces some vibrations when placed on the marble
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* Effect of all the control systems on the Sample vibrations
:PROPERTIES:
:header-args:matlab+: :tangle matlab/effect_control_all.m
:header-args:matlab+: :comments org :mkdirp yes
:END:
<<sec:effect_control_all >>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
if [ matlab/effect_control_all.m -nt data/effect_control_all.zip ]; then
cp matlab/effect_control_all.m effect_control_all.m;
zip data/effect_control_all \
mat/data_003.mat \
mat/data_004.mat \
mat/data_005.mat \
mat/data_006.mat \
mat/data_007.mat \
mat/data_008.mat \
effect_control_all.m;
rm effect_control_all.m;
fi
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#+end_src
#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/effect_control_all.zip ][here ]].
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#+end_note
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** Experimental Setup
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We here measure the signals of two L22 geophones:
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- One is located on top of the Sample platform
- One is located on the marble
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The signals are amplified with voltage amplifiers with the following settings:
- gain of 60dB
- AC/DC option set on AC
- Low pass filter set at 1kHz
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The signal from the top geophone does not go trought the slip-ring.
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First, all the control systems are turned ON, then, they are turned one by one.
Each measurement are done during 50s.
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#+name : tab:control_system_on_off
#+caption : Summary of the measurements and the states of the control systems
| Ty | Ry | Slip Ring | Spindle | Hexapod | Meas. file |
|------+------+-----------+---------+---------+----------------|
| *ON* | *ON* | *ON* | *ON* | *ON* | =meas_003.mat= |
| OFF | *ON* | *ON* | *ON* | *ON* | =meas_004.mat= |
| OFF | OFF | *ON* | *ON* | *ON* | =meas_005.mat= |
| OFF | OFF | OFF | *ON* | *ON* | =meas_006.mat= |
| OFF | OFF | OFF | OFF | *ON* | =meas_007.mat= |
| OFF | OFF | OFF | OFF | OFF | =meas_008.mat= |
Each of the =mat= file contains one array =data= with 3 columns:
| Column number | Description |
|---------------+-------------------|
| 1 | Geophone - Marble |
| 2 | Geophone - Sample |
| 3 | Time |
** 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)
<<matlab-dir >>
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addpath('../src');
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#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init >>
#+end_src
** Load data
We load the data of the z axis of two geophones.
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#+begin_src matlab
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d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
#+end_src
** Analysis - Time Domain
First, we can look at the time domain data and compare all the measurements:
- comparison for the geophone at the sample location (figure [[fig:time_domain_sample ]])
- comparison for the geophone on the granite (figure [[fig:time_domain_marble ]])
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#+begin_src matlab
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figure;
hold on;
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plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF');
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hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
#+end_src
#+NAME : fig:time_domain_sample
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/time_domain_sample.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:time_domain_sample
#+CAPTION : Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location
#+RESULTS : fig:time_domain_sample
[[file:figs/time_domain_sample.png ]]
#+begin_src matlab :results none
figure;
hold on;
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plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF');
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hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
#+end_src
#+NAME : fig:time_domain_marble
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/time_domain_marble.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:time_domain_marble
#+CAPTION : Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble
#+RESULTS : fig:time_domain_marble
[[file:figs/time_domain_marble.png ]]
** Analysis - Frequency Domain
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#+begin_src matlab
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dt = d3(2, 3) - d3(1, 3);
Fs = 1/dt;
win = hanning(ceil(10*Fs));
#+end_src
*** Vibrations at the sample location
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
#+begin_src matlab :results none
[px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);
#+end_src
And we compare all the signals (figures [[fig:psd_sample_comp ]] and [[fig:psd_sample_comp_high_freq ]]).
#+begin_src matlab :results none
figure;
hold on;
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plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
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hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
legend('Location', 'southwest');
#+end_src
#+NAME : fig:psd_sample_comp
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_sample_comp.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_sample_comp
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#+CAPTION : Amplitude Spectral Density of the signal coming from the top geophone
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#+RESULTS : fig:psd_sample_comp
[[file:figs/psd_sample_comp.png ]]
#+begin_src matlab :results none :tangle no :exports none
xlim([80, 500]);
#+end_src
#+NAME : fig:psd_sample_comp_high_freq
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_sample_comp_high_freq.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_sample_comp_high_freq
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#+CAPTION : Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
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#+RESULTS : fig:psd_sample_comp_high_freq
[[file:figs/psd_sample_comp_high_freq.png ]]
*** Vibrations on the marble
Now we plot the same curves for the geophone located on the marble.
#+begin_src matlab :results none
[px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);
#+end_src
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And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp ]] and [[fig:psd_marble_comp_high_freq ]])
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#+begin_src matlab :results none
figure;
hold on;
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plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
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hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
legend('Location', 'northeast');
#+end_src
#+NAME : fig:psd_marble_comp
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_marble_comp.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_marble_comp
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#+CAPTION : Amplitude Spectral Density of the signal coming from the top geophone
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#+RESULTS : fig:psd_marble_comp
[[file:figs/psd_marble_comp.png ]]
#+begin_src matlab :results none :tangle no :exports none
legend('Location', 'southwest');
xlim([80, 500]);
#+end_src
#+NAME : fig:psd_marble_comp_high_freq
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_marble_comp_high_freq.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_marble_comp_high_freq
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#+CAPTION : Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
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#+RESULTS : fig:psd_marble_comp_high_freq
[[file:figs/psd_marble_comp_high_freq.png ]]
** Conclusion
#+begin_important
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- The control system of the Ty stage induces a lot of vibrations of the marble above 100Hz
- The hexapod control system add vibrations of the sample only above 200Hz
- When the Slip-Ring is ON, white noise appears at high frequencies. This is studied [[file:../slip-ring-electrical-noise/index.org ][here ]]
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#+end_important
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* Effect of all the control systems on the Sample vibrations - One stage at a time
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:PROPERTIES:
:header-args:matlab+: :tangle matlab/effect_control_one.m
:header-args:matlab+: :comments org :mkdirp yes
:END:
<<sec:effect_control_one >>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
if [ matlab/effect_control_one.m -nt data/effect_control_one.zip ]; then
cp matlab/effect_control_one.m effect_control_one.m;
zip data/effect_control_one \
mat/data_013.mat \
mat/data_014.mat \
mat/data_015.mat \
mat/data_016.mat \
mat/data_017.mat \
mat/data_018.mat \
effect_control_one.m
rm effect_control_one.m;
fi
#+end_src
#+begin_note
All the files (data and Matlab scripts) are accessible [[file:data/effect_control_one.zip ][here ]].
#+end_note
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** Experimental Setup
We here measure the signals of two geophones:
- One is located on top of the Sample platform
- One is located on the marble
The signal from the top geophone does go trought the slip-ring.
All the control systems are turned OFF, then, they are turned on one at a time.
Each measurement are done during 100s.
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The settings of the voltage amplifier are shown on figure [[fig:amplifier_settings ]]:
- gain of 60dB
- AC/DC option set on DC
- Low pass filter set at 1kHz
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A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
#+name : tab:control_system_on_off
#+caption : Summary of the measurements and the states of the control systems
| Ty | Ry | Slip Ring | Spindle | Hexapod | Meas. file |
|------+------+-----------+---------+---------+----------------|
| OFF | OFF | OFF | OFF | OFF | =meas_013.mat= |
| *ON* | OFF | OFF | OFF | OFF | =meas_014.mat= |
| OFF | *ON* | OFF | OFF | OFF | =meas_015.mat= |
| OFF | OFF | *ON* | OFF | OFF | =meas_016.mat= |
| OFF | OFF | OFF | *ON* | OFF | =meas_017.mat= |
| OFF | OFF | OFF | OFF | *ON* | =meas_018.mat= |
Each of the =mat= file contains one array =data= with 3 columns:
| Column number | Description |
|---------------+-------------------|
| 1 | Geophone - Marble |
| 2 | Geophone - Sample |
| 3 | Time |
#+name : fig:amplifier_settings
#+caption : Voltage amplifier settings for the measurement
#+attr_html : :width 500px
[[file:./img/IMG_20190507_101459.jpg ]]
** 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)
<<matlab-dir >>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init >>
#+end_src
** Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
d_of = load('mat/data_013.mat', 'data'); d_of = d_of.data;
d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
#+end_src
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** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org ][here ]]).
#+begin_src matlab
gain = 60; % [dB]
d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
#+end_src
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** Analysis - Time Domain
First, we can look at the time domain data and compare all the measurements:
- comparison for the geophone at the sample location (figure [[fig:time_domain_sample_lpf ]])
- comparison for the geophone on the granite (figure [[fig:time_domain_marble_lpf ]])
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- relative displacement of the sample with respect to the marble (figure [[fig:time_domain_marble_lpf ]])
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#+begin_src matlab
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figure;
hold on;
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plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
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plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([0, 50]);
legend('Location', 'bestoutside');
#+end_src
#+NAME : fig:time_domain_sample_lpf
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/time_domain_sample_lpf.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:time_domain_sample_lpf
#+CAPTION : Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location
#+RESULTS : fig:time_domain_sample_lpf
[[file:figs/time_domain_sample_lpf.png ]]
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#+begin_src matlab
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figure;
hold on;
plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
plot(d_ty(:, 3), d_ty(:, 1), 'DisplayName', 'Ty ON');
plot(d_ry(:, 3), d_ry(:, 1), 'DisplayName', 'Ry ON');
plot(d_sr(:, 3), d_sr(:, 1), 'DisplayName', 'S-R ON');
plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([0, 50]);
legend('Location', 'bestoutside');
#+end_src
#+NAME : fig:time_domain_marble_lpf
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/time_domain_marble_lpf.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:time_domain_marble_lpf
#+CAPTION : Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble
#+RESULTS : fig:time_domain_marble_lpf
[[file:figs/time_domain_marble_lpf.png ]]
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#+begin_src matlab
figure;
hold on;
plot(d_of(:, 3), 1e6*lsim(1/(1+s/ (2*pi*0.5)), d_of(:, 2)-d_of(:, 1), d_of(:, 3)), 'DisplayName', 'All OFF');
plot(d_ty(:, 3), 1e6*lsim(1/(1+s/ (2*pi*0.5)), d_ty(:, 2)-d_ty(:, 1), d_ty(:, 3)), 'DisplayName', 'Ty ON');
plot(d_ry(:, 3), 1e6*lsim(1/(1+s/ (2*pi*0.5)), d_ry(:, 2)-d_ry(:, 1), d_ry(:, 3)), 'DisplayName', 'Ry ON');
plot(d_sr(:, 3), 1e6*lsim(1/(1+s/ (2*pi*0.5)), d_sr(:, 2)-d_sr(:, 1), d_sr(:, 3)), 'DisplayName', 'S-R ON');
plot(d_rz(:, 3), 1e6*lsim(1/(1+s/ (2*pi*0.5)), d_rz(:, 2)-d_rz(:, 1), d_rz(:, 3)), 'DisplayName', 'Rz ON');
plot(d_he(:, 3), 1e6*lsim(1/(1+s/ (2*pi*0.5)), d_he(:, 2)-d_he(:, 1), d_he(:, 3)), 'DisplayName', 'Hexa ON');
hold off;
xlabel('Time [s]'); ylabel('Relative Displacement [$\mu m$]');
xlim([0, 50]);
legend('Location', 'bestoutside');
#+end_src
#+NAME : fig:time_domain_relative_disp
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/time_domain_relative_disp.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:time_domain_relative_disp
#+CAPTION : Relative displacement of the sample with respect to the marble
#+RESULTS : fig:time_domain_relative_disp
[[file:figs/time_domain_relative_disp.png ]]
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** Analysis - Frequency Domain
#+begin_src matlab :results none
dt = d_of(2, 3) - d_of(1, 3);
Fs = 1/dt;
win = hanning(ceil(10*Fs));
#+end_src
*** Vibrations at the sample location
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
#+begin_src matlab :results none
[px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
[px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
[px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
[px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
[px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
[px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);
#+end_src
And we compare all the signals (figures [[fig:psd_sample_comp_lpf ]] and [[fig:psd_sample_comp_high_freq_lpf ]]).
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
legend('Location', 'southwest');
#+end_src
#+NAME : fig:psd_sample_comp_lpf
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_sample_comp_lpf.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_sample_comp_lpf
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#+CAPTION : Amplitude Spectral Density of the sample velocity
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#+RESULTS : fig:psd_sample_comp_lpf
[[file:figs/psd_sample_comp_lpf.png ]]
#+begin_src matlab :results none :tangle no :exports none
xlim([80, 500]);
#+end_src
#+NAME : fig:psd_sample_comp_high_freq_lpf
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_sample_comp_high_freq_lpf.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_sample_comp_high_freq_lpf
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#+CAPTION : Amplitude Spectral Density of the sample velocity (zoom at high frequencies)
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#+RESULTS : fig:psd_sample_comp_high_freq_lpf
[[file:figs/psd_sample_comp_high_freq_lpf.png ]]
*** Vibrations on the marble
Now we plot the same curves for the geophone located on the marble.
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#+begin_src matlab
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[px_of, f] = pwelch(d_of(:, 1), win, [], [], Fs);
[px_ty, ~] = pwelch(d_ty(:, 1), win, [], [], Fs);
[px_ry, ~] = pwelch(d_ry(:, 1), win, [], [], Fs);
[px_sr, ~] = pwelch(d_sr(:, 1), win, [], [], Fs);
[px_rz, ~] = pwelch(d_rz(:, 1), win, [], [], Fs);
[px_he, ~] = pwelch(d_he(:, 1), win, [], [], Fs);
#+end_src
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And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_lpf ]] and [[fig:psd_marble_comp_lpf_high_freq ]])
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#+begin_src matlab
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figure;
hold on;
plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
legend('Location', 'northeast');
#+end_src
#+NAME : fig:psd_marble_comp_lpf
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_marble_comp_lpf.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_marble_comp_lpf
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#+CAPTION : Amplitude Spectral Density of the marble velocity
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#+RESULTS : fig:psd_marble_comp_lpf
[[file:figs/psd_marble_comp_lpf.png ]]
#+begin_src matlab :results none :tangle no :exports none
legend('Location', 'southwest');
xlim([80, 500]);
#+end_src
#+NAME : fig:psd_marble_comp_lpf_high_freq
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_marble_comp_lpf_high_freq.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_marble_comp_lpf_high_freq
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#+CAPTION : Amplitude Spectral Density of the marble velocity (zoom at high frequencies)
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#+RESULTS : fig:psd_marble_comp_lpf_high_freq
[[file:figs/psd_marble_comp_lpf_high_freq.png ]]
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** Cumulative Amplitude Spectrum
#+begin_src matlab
figure;
hold on;
plot(f(2:end), sqrt(cumsum(px_of(2:end)./(2*pi*f(2:end)).^2).* (f(2)-f(1))), 'DisplayName', 'All OFF');
plot(f(2:end), sqrt(cumsum(px_ty(2:end)./(2*pi*f(2:end)).^2).* (f(2)-f(1))), 'DisplayName', 'Ty ON');
plot(f(2:end), sqrt(cumsum(px_ry(2:end)./(2*pi*f(2:end)).^2).* (f(2)-f(1))), 'DisplayName', 'Ry ON');
plot(f(2:end), sqrt(cumsum(px_sr(2:end)./(2*pi*f(2:end)).^2).* (f(2)-f(1))), 'DisplayName', 'S-R ON');
plot(f(2:end), sqrt(cumsum(px_rz(2:end)./(2*pi*f(2:end)).^2).* (f(2)-f(1))), 'DisplayName', 'Rz ON');
plot(f(2:end), sqrt(cumsum(px_he(2:end)./(2*pi*f(2:end)).^2).* (f(2)-f(1))), 'DisplayName', 'Hexa ON');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'northeast');
#+end_src
#+begin_src matlab
#+end_src
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** Conclusion
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#+begin_important
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- The Ty stage induces vibrations of the marble and at the sample location above 100Hz
- The hexapod stage induces vibrations at the sample position above 220Hz
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#+end_important
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* Effect of the Symetrie Driver
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:PROPERTIES:
:header-args:matlab+: :tangle matlab/effect_symetrie_driver.m
:header-args:matlab+: :comments org :mkdirp yes
:END:
<<sec:effect_symetrie_driver >>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
if [ matlab/effect_symetrie_driver.m -nt data/effect_symetrie_driver.zip ]; then
cp matlab/effect_symetrie_driver.m effect_symetrie_driver.m;
zip data/effect_symetrie_driver \
mat/data_018.mat \
mat/data_019.mat \
effect_symetrie_driver.m
rm effect_symetrie_driver.m;
fi
#+end_src
#+begin_note
All the files (data and Matlab scripts) are accessible [[file:data/effect_symetrie_driver.zip ][here ]].
#+end_note
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** Experimental Setup
We here measure the signals of two geophones:
- One is located on top of the Sample platform
- One is located on the marble
The signal from the top geophone does go trought the slip-ring.
All the control systems are turned OFF except the Hexapod one.
Each measurement are done during 100s.
The settings of the voltage amplifier are:
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- gain of 60dB
- AC/DC option set on DC
- Low pass filter set at 1kHz
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A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
The measurements are:
- =meas_018.mat= : Hexapod's driver on the granite
- =meas_019.mat= : Hexapod's driver on the ground
Each of the =mat= file contains one array =data= with 3 columns:
| Column number | Description |
|---------------+-------------------|
| 1 | Geophone - Marble |
| 2 | Geophone - Sample |
| 3 | Time |
** 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)
<<matlab-dir >>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init >>
#+end_src
** Load data
We load the data of the z axis of two geophones.
#+begin_src matlab :results none
d_18 = load('mat/data_018.mat', 'data'); d_18 = d_18.data;
d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data;
#+end_src
** Analysis - Time Domain
#+begin_src matlab :results none
figure;
hold on;
plot(d_19(:, 3), d_19(:, 1), 'DisplayName', 'Driver - Ground');
plot(d_18(:, 3), d_18(:, 1), 'DisplayName', 'Driver - Granite');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
#+end_src
#+NAME : fig:time_domain_hexa_driver
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/time_domain_hexa_driver.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:time_domain_hexa_driver
#+CAPTION : Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location
#+RESULTS : fig:time_domain_hexa_driver
[[file:figs/time_domain_hexa_driver.png ]]
** Analysis - Frequency Domain
#+begin_src matlab :results none
dt = d_18(2, 3) - d_18(1, 3);
Fs = 1/dt;
win = hanning(ceil(10*Fs));
#+end_src
*** Vibrations at the sample location
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
#+begin_src matlab :results none
[px_18, f] = pwelch(d_18(:, 1), win, [], [], Fs);
[px_19, ~] = pwelch(d_19(:, 1), win, [], [], Fs);
#+end_src
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px_19), 'DisplayName', 'Driver - Ground');
plot(f, sqrt(px_18), 'DisplayName', 'Driver - Granite');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'southwest');
#+end_src
#+NAME : fig:psd_hexa_driver
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_hexa_driver.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_hexa_driver
#+CAPTION : Amplitude Spectral Density of the signal coming from the top geophone
#+RESULTS : fig:psd_hexa_driver
[[file:figs/psd_hexa_driver.png ]]
#+begin_src matlab :results none :tangle no :exports none
xlim([80, 500]);
#+end_src
#+NAME : fig:psd_hexa_driver_high_freq
#+HEADER : :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_hexa_driver_high_freq.pdf" :var figsize= "full-tall" :post pdf2svg(file=*this*, ext= "png")
<<plt-matlab >>
#+end_src
#+NAME : fig:psd_hexa_driver_high_freq
#+CAPTION : Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
#+RESULTS : fig:psd_hexa_driver_high_freq
[[file:figs/psd_hexa_driver_high_freq.png ]]
** Conclusion
#+begin_important
Even tough the Hexapod's driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.
#+end_important
