tdehaeze/nass-micro-station-measurements
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

many updates

Browse Source
This commit is contained in:
Thomas Dehaeze 2020-04-27 11:35:57 +02:00
parent dbd4320349
commit 4838b6e026
56 changed files with 2156 additions and 2248 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

34
2018-10-12 - Marc/index.org
View File

@ -101,7 +101,7 @@ Les fichiers xxx_raw sont sans traitement dans le domaine temporel (environ 10 i
| 9 | Hexa | X |
* Data Analysis
** Loading of the data
** 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
@ -110,10 +110,7 @@ Les fichiers xxx_raw sont sans traitement dans le domaine temporel (environ 10 i
<<matlab-init>>
#+end_src
#+BEGIN_SRC matlab :results none :exports none :var currentdir=(file-name-directory buffer-file-name)
cd(currentdir);
#+END_SRC
** Loading of the data
#+begin_src matlab :exports code :results none
load('./data/freq_frf.mat');
@ -141,3 +138,30 @@ Les fichiers xxx_raw sont sans traitement dans le domaine temporel (environ 10 i
load('./data/phs_ty_y.mat');
load('./data/phs_ty_z.mat');
#+end_src
** test
#+begin_src matlab
figure;
hold on;
plot(freq_frf, abs(ReIm7(:, 5))./(2*pi*freq_frf), 'DisplayName', 'Marble')
plot(freq_frf, abs(ReIm8(:, 6))./(2*pi*freq_frf), 'DisplayName', 'Ty')
% plot(freq_frf, abs(ReIm5(:, 3))./(2*pi*freq_frf), 'DisplayName', 'Tilt')
plot(freq_frf, abs(ReIm9(:, 8))./(2*pi*freq_frf), 'DisplayName', 'Hexapod')
hold off;
xlim([1, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
legend('location', 'northwest');
#+end_src
#+begin_src matlab
figure;
hold on;
plot(freq_frf, abs(ReIm5(:, 1))./(2*pi*freq_frf), 'DisplayName', 'Marble')
plot(freq_frf, abs(ReIm5(:, 2))./(2*pi*freq_frf), 'DisplayName', 'Ty')
plot(freq_frf, abs(ReIm5(:, 3))./(2*pi*freq_frf), 'DisplayName', 'Tilt')
plot(freq_frf, abs(ReIm5(:, 4))./(2*pi*freq_frf), 'DisplayName', 'Hexapod')
hold off;
xlim([1, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
legend('location', 'northwest');
#+end_src

BIN
actuators-sensors/figs/piezo_model.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 4.4 KiB

159
actuators-sensors/index.org
View File

@ -26,155 +26,31 @@
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/tikz/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100
#+PROPERTY: header-args:latex+ :results file raw replace
#+PROPERTY: header-args:latex+ :buffer no
#+PROPERTY: header-args:latex+ :eval no-export
#+PROPERTY: header-args:latex+ :exports results
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
#+PROPERTY: header-args:shell :eval no-export
:END:
* Sensors
** Inertial Sensor
*** Accelerometers
| | |
|--------------------+------|
| Micromega Dynamics | [[https://micromega-dynamics.com/products/][link]] |
| MMF | [[https://www.mmf.de/seismic_accelerometers.htm][link]] |
| PCB | [[https://www.pcb.com/products/productfinder.aspx?tx=14][link]] |
Wireless Accelerometers
- https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/
#+name: fig:characteristics_accelerometers
#+caption: Characteristics of commercially available accelerometers cite:collette11_review
[[file:figs/characteristics_accelerometers.png]]
*** Geophones
| | |
|----------+------|
| Sercel | [[http://www.sercel.com/products/Pages/seismometers.aspx][link]] |
| Wilcoxon | [[https://wilcoxon.com/][link]] |
#+name: fig:characteristics_geophone
#+caption: Characteristics of commercially available geophones cite:collette11_review
[[file:figs/characteristics_geophone.png]]
** Force Sensors
| | |
|-----+------|
| PCB | [[https://www.pcb.com/products/productfinder.aspx?tx=17][link]] |
** Position Sensor
#+name: fig:characteristics_relative_sensor
#+caption: Characteristics of relative measurement sensors cite:collette11_review
[[file:figs/characteristics_relative_sensor.png]]
#+name: fig:position_sensor_characteristics
#+caption: Position sensor characteristics cite:fleming13_review_nanom_resol_posit_sensor
[[file:figs/position_sensor_characteristics.png]]
*** Strain Gauge
*** Capacitive Sensor
Description:
- http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html
- https://www.lionprecision.com/comparing-capacitive-and-eddy-current-sensors
| | |
|----------------+------|
| Micro Sense | [[http://www.microsense.net/products-position-sensors.htm][link]] |
| Micro-Epsilon | [[https://www.micro-epsilon.com/displacement-position-sensors/capacitive-sensor/][link]] |
| PI | [[https://www.physikinstrumente.com/en/technology/sensor-technologies/capacitive-sensors/][link]] |
| Unipulse | [[https://www.unipulse.com/product/ps-ia/][link]] |
| Lion-Precision | [[https://www.lionprecision.com/products/capacitive-sensors][link]] |
*** Inductive Sensor (Eddy Current)
| | |
|----------------+------|
| Micro-Epsilon | [[https://www.micro-epsilon.com/displacement-position-sensors/eddy-current-sensor/][link]] |
| Lion Precision | [[https://www.lionprecision.com/products/eddy-current-sensors][link]] |
*** Inductive Sensor (LVDT)
| | |
|---------------+------|
| Micro-Epsilon | [[https://www.micro-epsilon.com/displacement-position-sensors/inductive-sensor-lvdt/][link]] |
| Keyence | [[https://www.keyence.eu/products/measure/contact-distance-lvdt/gt2/index.jsp][link]] |
*** Interferometers
| | |
|----------+------|
| Attocube | [[http://www.attocube.com/][link]] |
| Zygo | [[https://www.zygo.com/?/met/markets/stageposition/zmi/][link]] |
| Smaract | [[https://www.smaract.com/interferometry][link]] |
| Qutools | [[https://www.qutools.com/qudis/][link]] |
| Renishaw | [[https://www.renishaw.com/en/fibre-optic-laser-encoder-products--6594][link]] |
| Sios | [[https://sios-de.com/products/length-measurement/laser-interferometer/][link]] |
| Keysight | [[https://www.keysight.com/en/pc-1000000393%3Aepsg%3Apgr/laser-heads?nid=-536900395.0&cc=FR&lc=fre][link]] |
#+caption: Characteristics of Environmental Units
| | Temperature ($\pm\ ^oC$) | Pressure ($\pm\ hPa$) | Humidity $\pm\ \% RH$ | Wavelength Accuracy ($\pm\ \text{ppm}$) |
|-----------+--------------------------+-----------------------+-----------------------+-----------------------------------------|
| Attocube | 0.1 | 1 | 2 | 0.5 |
| Renishaw | 0.2 | 1 | 6 | 1 |
| Picoscale | 0.2 | 2 | 2 | 1 |
#+name: fig:figure_name
#+caption: Expected precision of interferometer as a function of measured distance. Taken from cite:jang17_compen_refrac_index_air_laser
[[file:figs/interferometer_precision.png]]
*** Fiber Optic Displacement Sensor
| | |
|----------+------|
| Unipulse | [[https://www.unipulse.com/product/atw200-2/][link]] |
** Bibliography
cite:collette12_compar
cite:collette12_review
cite:fleming13_review_nanom_resol_posit_sensor
* Actuators
** Piezoelectric
| | |
|--------------+------|
| Cedrat | [[http://www.cedrat-technologies.com/][link]] |
| PI | [[https://www.physikinstrumente.com/en/][link]] |
| Piezo System | [[https://www.piezosystem.com/products/piezo_actuators/stacktypeactuators/][link]] |
| Noliac | [[http://www.noliac.com/][link]] |
** Voice Coil
| | |
|----------------------+------|
| Geeplus | [[https://www.geeplus.com/][link]] |
| Maccon | [[https://www.maccon.de/en.html][link]] |
| TDS PP | [[https://www.tds-pp.com/en/][link]] |
| H2tech | [[https://www.h2wtech.com/][link]] |
| PBA Systems | [[http://www.pbasystems.com.sg/][link]] |
| Celera Motion | [[https://www.celeramotion.com/][link]] |
| Beikimco | [[http://www.beikimco.com/][link]] |
| Electromate | [[https://www.electromate.com/][link]] |
| Magnetic Innovations | [[https://www.magneticinnovations.com/][link]] |
** Shaker
| | |
|--------------------+------|
| BKSV | [[https://www.bksv.com/en/products/shakers-and-exciters][link]] |
| Vibration Research | [[https://vibrationresearch.com/shakers/][link]] |
| Sentek Dynamics | [[https://www.sentekdynamics.com/][link]] |
https://www.bksv.com/en/products/shakers-and-exciters/LDS-shaker-systems/permanent-magnet-shakers/V201
** Brushless DC Motor
cite:yedamale03_brush_dc_bldc_motor_fundam
https://www.electricaltechnology.org/2016/05/bldc-brushless-dc-motor-construction-working-principle.html
* Measurement System / Acquisition System
** Modal Analysis
https://dewesoft.com/applications/structural-dynamics/modal-analysis
Polytec 3D Scanning Laser Vibrometer https://www.polytec.com/us/vibrometry/products/full-field-vibrometers/psv-500-scanning-vibrometer/
* Control System
Dspace, Speedgoat
https://www.opal-rt.com/
https://www.speedgoat.com/
https://www.dspace.com/en/inc/home/products/hw/microlabbox.cfm
https://www.ni.com/fr-fr/shop/pc-based-measurement-and-control-system.html
* Positioning Stages
** Hexapods
@ -193,6 +69,9 @@ Dspace, Speedgoat
** Voltage Amplifiers
Amplifiers:
https://www.cedrat-technologies.com/en/products/piezo-controllers/electronic-amplifier-boards.html
* ESRF Equipment
** Geophones
*** L-28LB

BIN
actuators-sensors/piezo_model.pdf Normal file
View File

Binary file not shown.

BIN
disturbance-control-system/figs/cas_sample_comp.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 122 KiB

297
disturbance-control-system/index.html
View File

@ -4,7 +4,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-04-23 jeu. 15:28 -->
<!-- 2020-04-27 lun. 10:18 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Effect on the control system of each stages on the vibration of the station</title>
<meta name="generator" content="Org mode" />
@ -28,76 +28,77 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org31edd78">1. Effect of all the control systems on the Sample vibrations</a>
<li><a href="#org51d7a3e">1. Effect of all the control systems on the Sample vibrations</a>
<ul>
<li><a href="#org1d47683">1.1. Experimental Setup</a></li>
<li><a href="#orgfcb7154">1.2. Load data</a></li>
<li><a href="#orgbe65805">1.3. Analysis - Time Domain</a></li>
<li><a href="#orgdace4d9">1.4. Analysis - Frequency Domain</a>
<li><a href="#org053d9fe">1.1. Experimental Setup</a></li>
<li><a href="#orgcb36bc1">1.2. Load data</a></li>
<li><a href="#org5895a96">1.3. Analysis - Time Domain</a></li>
<li><a href="#org390bba0">1.4. Analysis - Frequency Domain</a>
<ul>
<li><a href="#orga76176e">1.4.1. Vibrations at the sample location</a></li>
<li><a href="#org8d92602">1.4.2. Vibrations on the marble</a></li>
<li><a href="#org3a4a488">1.4.1. Vibrations at the sample location</a></li>
<li><a href="#org49d7279">1.4.2. Vibrations on the marble</a></li>
</ul>
</li>
<li><a href="#org6f49679">1.5. Conclusion</a></li>
<li><a href="#org9b2f5fd">1.5. Conclusion</a></li>
</ul>
</li>
<li><a href="#org27d5063">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a>
<li><a href="#org4eafed3">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a>
<ul>
<li><a href="#org5e1d6ca">2.1. Experimental Setup</a></li>
<li><a href="#orgdbc788c">2.2. Load data</a></li>
<li><a href="#orgcaa00c9">2.3. Voltage to Velocity</a></li>
<li><a href="#org6392409">2.4. Analysis - Time Domain</a></li>
<li><a href="#org4e22262">2.5. Analysis - Frequency Domain</a>
<li><a href="#org4addbe8">2.1. Experimental Setup</a></li>
<li><a href="#orgb60aa2f">2.2. Load data</a></li>
<li><a href="#org68831ee">2.3. Voltage to Velocity</a></li>
<li><a href="#orgbbb370a">2.4. Analysis - Time Domain</a></li>
<li><a href="#orgd436876">2.5. Analysis - Frequency Domain</a>
<ul>
<li><a href="#org88ffac6">2.5.1. Vibrations at the sample location</a></li>
<li><a href="#org5eddb65">2.5.2. Vibrations on the marble</a></li>
<li><a href="#org2e1f962">2.5.1. Vibrations at the sample location</a></li>
<li><a href="#org8f33a44">2.5.2. Vibrations on the marble</a></li>
</ul>
</li>
<li><a href="#org60b1ca9">2.6. Conclusion</a></li>
<li><a href="#org381e6c2">2.6. Conclusion</a></li>
</ul>
</li>
<li><a href="#orgd7c39d5">3. Effect of the Symetrie Driver</a>
<li><a href="#orgce5eef9">3. Effect of the Symetrie Driver</a>
<ul>
<li><a href="#org757e668">3.1. Experimental Setup</a></li>
<li><a href="#org92c9e9b">3.2. Load data</a></li>
<li><a href="#orgb405d4d">3.3. Analysis - Time Domain</a></li>
<li><a href="#org486b9fb">3.4. Analysis - Frequency Domain</a>
<li><a href="#org6e62fbe">3.1. Experimental Setup</a></li>
<li><a href="#orgd0c4704">3.2. Load data</a></li>
<li><a href="#org30686ba">3.3. Analysis - Time Domain</a></li>
<li><a href="#orgd922ea4">3.4. Analysis - Frequency Domain</a>
<ul>
<li><a href="#orgd488281">3.4.1. Vibrations at the sample location</a></li>
<li><a href="#orgd49e7c3">3.4.1. Vibrations at the sample location</a></li>
</ul>
</li>
<li><a href="#org680fcdb">3.5. Conclusion</a></li>
<li><a href="#org031a084">3.5. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<p>
This file is organized as follow:
</p>
<ul class="org-ul">
<li>Section <a href="#orgc00965d">1</a>:
<li>Section <a href="#org3b0d32c">1</a>:
<ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one by one</li>
</ul></li>
<li>Section <a href="#org06034f4">2</a>:
<li>Section <a href="#org757823f">2</a>:
<ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one at a time</li>
</ul></li>
<li>Section <a href="#org9b94d23">3</a>:
<li>Section <a href="#orgd9c378b">3</a>:
<ul class="org-ul">
<li>We check if the Symetrie driver induces some vibrations when placed on the marble</li>
</ul></li>
</ul>
<div id="outline-container-org31edd78" class="outline-2">
<h2 id="org31edd78"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2>
<div id="outline-container-org51d7a3e" class="outline-2">
<h2 id="org51d7a3e"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2>
<div class="outline-text-2" id="text-1">
<p>
<a id="orgc00965d"></a>
<a id="org3b0d32c"></a>
</p>
<div class="note">
<p>
@ -107,8 +108,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_cont
</div>
</div>
<div id="outline-container-org1d47683" class="outline-3">
<h3 id="org1d47683"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div id="outline-container-org053d9fe" class="outline-3">
<h3 id="org053d9fe"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-1-1">
<p>
We here measure the signals of two L22 geophones:
@ -136,7 +137,7 @@ First, all the control systems are turned ON, then, they are turned one by one.
Each measurement are done during 50s.
</p>
<table id="org109e9c5" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org8234ce1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption>
<colgroup>
@ -256,8 +257,8 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div>
</div>
<div id="outline-container-orgfcb7154" class="outline-3">
<h3 id="orgfcb7154"><span class="section-number-3">1.2</span> Load data</h3>
<div id="outline-container-orgcb36bc1" class="outline-3">
<h3 id="orgcb36bc1"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2">
<p>
We load the data of the z axis of two geophones.
@ -274,15 +275,15 @@ d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
</div>
</div>
<div id="outline-container-orgbe65805" class="outline-3">
<h3 id="orgbe65805"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div id="outline-container-org5895a96" class="outline-3">
<h3 id="org5895a96"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-1-3">
<p>
First, we can look at the time domain data and compare all the measurements:
</p>
<ul class="org-ul">
<li>comparison for the geophone at the sample location (figure <a href="#org1e12b9d">1</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#orga090daf">2</a>)</li>
<li>comparison for the geophone at the sample location (figure <a href="#org2c7f590">1</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org51a2672">2</a>)</li>
</ul>
<div class="org-src-container">
@ -302,7 +303,7 @@ legend('Location', 'bestoutside');
</div>
<div id="org1e12b9d" class="figure">
<div id="org2c7f590" class="figure">
<p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
@ -325,7 +326,7 @@ legend('Location', 'bestoutside');
</div>
<div id="orga090daf" class="figure">
<div id="org51a2672" class="figure">
<p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
@ -333,8 +334,8 @@ legend('Location', 'bestoutside');
</div>
</div>
<div id="outline-container-orgdace4d9" class="outline-3">
<h3 id="orgdace4d9"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div id="outline-container-org390bba0" class="outline-3">
<h3 id="org390bba0"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4">
<div class="org-src-container">
<pre class="src src-matlab">dt = d3(2, 3) - d3(1, 3);
@ -345,8 +346,8 @@ win = hanning(ceil(10*Fs));
</div>
</div>
<div id="outline-container-orga76176e" class="outline-4">
<h4 id="orga76176e"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4>
<div id="outline-container-org3a4a488" class="outline-4">
<h4 id="org3a4a488"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-1-4-1">
<p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
@ -362,7 +363,7 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
</div>
<p>
And we compare all the signals (figures <a href="#orgc7cf107">3</a> and <a href="#org2cc793f">4</a>).
And we compare all the signals (figures <a href="#org939f58a">3</a> and <a href="#orgf26e845">4</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">figure;
@ -383,14 +384,14 @@ legend('Location', 'southwest');
</div>
<div id="orgc7cf107" class="figure">
<div id="org939f58a" class="figure">
<p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
</div>
<div id="org2cc793f" class="figure">
<div id="orgf26e845" class="figure">
<p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
@ -398,8 +399,8 @@ legend('Location', 'southwest');
</div>
</div>
<div id="outline-container-org8d92602" class="outline-4">
<h4 id="org8d92602"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4>
<div id="outline-container-org49d7279" class="outline-4">
<h4 id="org49d7279"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-1-4-2">
<p>
Now we plot the same curves for the geophone located on the marble.
@ -415,7 +416,7 @@ Now we plot the same curves for the geophone located on the marble.
</div>
<p>
And we compare the Amplitude Spectral Densities (figures <a href="#org60f624e">5</a> and <a href="#org9480bcc">6</a>)
And we compare the Amplitude Spectral Densities (figures <a href="#org3fd93c6">5</a> and <a href="#org2185be4">6</a>)
</p>
<div class="org-src-container">
<pre class="src src-matlab">figure;
@ -436,14 +437,14 @@ legend('Location', 'northeast');
</div>
<div id="org60f624e" class="figure">
<div id="org3fd93c6" class="figure">
<p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
</div>
<div id="org9480bcc" class="figure">
<div id="org2185be4" class="figure">
<p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
@ -452,8 +453,8 @@ legend('Location', 'northeast');
</div>
</div>
<div id="outline-container-org6f49679" class="outline-3">
<h3 id="org6f49679"><span class="section-number-3">1.5</span> Conclusion</h3>
<div id="outline-container-org9b2f5fd" class="outline-3">
<h3 id="org9b2f5fd"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5">
<div class="important">
<ul class="org-ul">
@ -467,11 +468,11 @@ legend('Location', 'northeast');
</div>
</div>
<div id="outline-container-org27d5063" class="outline-2">
<h2 id="org27d5063"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2>
<div id="outline-container-org4eafed3" class="outline-2">
<h2 id="org4eafed3"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org06034f4"></a>
<a id="org757823f"></a>
</p>
<div class="note">
<p>
@ -481,8 +482,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_cont
</div>
</div>
<div id="outline-container-org5e1d6ca" class="outline-3">
<h3 id="org5e1d6ca"><span class="section-number-3">2.1</span> Experimental Setup</h3>
<div id="outline-container-org4addbe8" class="outline-3">
<h3 id="org4addbe8"><span class="section-number-3">2.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-2-1">
<p>
We here measure the signals of two geophones:
@ -505,7 +506,7 @@ Each measurement are done during 100s.
</p>
<p>
The settings of the voltage amplifier are shown on figure <a href="#org8b2d864">7</a>:
The settings of the voltage amplifier are shown on figure <a href="#orgeb410b4">7</a>:
</p>
<ul class="org-ul">
<li>gain of 60dB</li>
@ -517,7 +518,7 @@ The settings of the voltage amplifier are shown on figure <a href="#org8b2d864">
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
</p>
<table id="org71b8a99" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgb3e54be" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Summary of the measurements and the states of the control systems</caption>
<colgroup>
@ -636,7 +637,7 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</table>
<div id="org8b2d864" class="figure">
<div id="orgeb410b4" class="figure">
<p><img src="./img/IMG_20190507_101459.jpg" alt="IMG_20190507_101459.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 7: </span>Voltage amplifier settings for the measurement</p>
@ -644,8 +645,8 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div>
</div>
<div id="outline-container-orgdbc788c" class="outline-3">
<h3 id="orgdbc788c"><span class="section-number-3">2.2</span> Load data</h3>
<div id="outline-container-orgb60aa2f" class="outline-3">
<h3 id="orgb60aa2f"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We load the data of the z axis of two geophones.
@ -662,8 +663,8 @@ d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
</div>
</div>
<div id="outline-container-orgcaa00c9" class="outline-3">
<h3 id="orgcaa00c9"><span class="section-number-3">2.3</span> Voltage to Velocity</h3>
<div id="outline-container-org68831ee" class="outline-3">
<h3 id="org68831ee"><span class="section-number-3">2.3</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>).
@ -690,82 +691,34 @@ d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
</div>
</div>
<div id="outline-container-org6392409" class="outline-3">
<h3 id="org6392409"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3>
<div id="outline-container-orgbbb370a" class="outline-3">
<h3 id="orgbbb370a"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
First, we can look at the time domain data and compare all the measurements:
</p>
<ul class="org-ul">
<li>comparison for the geophone at the sample location (figure <a href="#org6b5b92c">8</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org90b0f48">9</a>)</li>
<li>relative displacement of the sample with respect to the marble (figure <a href="#org90b0f48">9</a>)</li>
<li>comparison for the geophone at the sample location (figure <a href="#org03fb45e">8</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#orgc177b3a">9</a>)</li>
<li>relative displacement of the sample with respect to the marble (figure <a href="#orgc177b3a">9</a>)</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab">figure;
hold on;
plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
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;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 50]);
legend('Location', 'bestoutside');
</pre>
</div>
<div id="org6b5b92c" class="figure">
<div id="org03fb45e" class="figure">
<p><img src="figs/time_domain_sample_lpf.png" alt="time_domain_sample_lpf.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">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;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 50]);
legend('Location', 'bestoutside');
</pre>
</div>
<div id="org90b0f48" class="figure">
<div id="orgc177b3a" class="figure">
<p><img src="figs/time_domain_marble_lpf.png" alt="time_domain_marble_lpf.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
</div>
<div class="org-src-container">
<pre class="src 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');
</pre>
</div>
<div id="org5d1a458" class="figure">
<div id="orgb57231f" class="figure">
<p><img src="figs/time_domain_relative_disp.png" alt="time_domain_relative_disp.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Relative displacement of the sample with respect to the marble</p>
@ -773,8 +726,8 @@ legend('Location', 'bestoutside');
</div>
</div>
<div id="outline-container-org4e22262" class="outline-3">
<h3 id="org4e22262"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3>
<div id="outline-container-orgd436876" class="outline-3">
<h3 id="orgd436876"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-matlab">dt = d_of(2, 3) - d_of(1, 3);
@ -785,8 +738,8 @@ win = hanning(ceil(10*Fs));
</div>
</div>
<div id="outline-container-org88ffac6" class="outline-4">
<h4 id="org88ffac6"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4>
<div id="outline-container-org2e1f962" class="outline-4">
<h4 id="org2e1f962"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-2-5-1">
<p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
@ -802,7 +755,7 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
</div>
<p>
And we compare all the signals (figures <a href="#org184f693">11</a> and <a href="#orgc76db7e">12</a>).
And we compare all the signals (figures <a href="#orgb661144">11</a> and <a href="#orgd36a2b1">12</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">figure;
@ -823,7 +776,7 @@ legend('Location', 'southwest');
</div>
<div id="org184f693" class="figure">
<div id="orgb661144" class="figure">
<p><img src="figs/psd_sample_comp_lpf.png" alt="psd_sample_comp_lpf.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the sample velocity</p>
@ -831,7 +784,7 @@ legend('Location', 'southwest');
<div id="orgc76db7e" class="figure">
<div id="orgd36a2b1" class="figure">
<p><img src="figs/psd_sample_comp_high_freq_lpf.png" alt="psd_sample_comp_high_freq_lpf.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the sample velocity (zoom at high frequencies)</p>
@ -839,52 +792,22 @@ legend('Location', 'southwest');
</div>
</div>
<div id="outline-container-org5eddb65" class="outline-4">
<h4 id="org5eddb65"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4>
<div id="outline-container-org8f33a44" class="outline-4">
<h4 id="org8f33a44"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-2-5-2">
<p>
Now we plot the same curves for the geophone located on the marble.
And we compare the Amplitude Spectral Densities (figures <a href="#org57f110f">13</a> and <a href="#orgcbf8e87">14</a>)
</p>
<div class="org-src-container">
<pre class="src src-matlab">[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);
</pre>
</div>
<p>
And we compare the Amplitude Spectral Densities (figures <a href="#org8c00376">13</a> and <a href="#org1008de7">14</a>)
</p>
<div class="org-src-container">
<pre class="src src-matlab">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');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'northeast');
</pre>
</div>
<div id="org8c00376" class="figure">
<div id="org57f110f" class="figure">
<p><img src="figs/psd_marble_comp_lpf.png" alt="psd_marble_comp_lpf.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the marble velocity</p>
</div>
<div id="org1008de7" class="figure">
<div id="orgcbf8e87" class="figure">
<p><img src="figs/psd_marble_lpf_high_freq.png" alt="psd_marble_lpf_high_freq.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the marble velocity (zoom at high frequencies)</p>
@ -893,8 +816,8 @@ legend('Location', 'northeast');
</div>
</div>
<div id="outline-container-org60b1ca9" class="outline-3">
<h3 id="org60b1ca9"><span class="section-number-3">2.6</span> Conclusion</h3>
<div id="outline-container-org381e6c2" class="outline-3">
<h3 id="org381e6c2"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<ul class="org-ul">
@ -907,11 +830,11 @@ legend('Location', 'northeast');
</div>
</div>
<div id="outline-container-orgd7c39d5" class="outline-2">
<h2 id="orgd7c39d5"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2>
<div id="outline-container-orgce5eef9" class="outline-2">
<h2 id="orgce5eef9"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="org9b94d23"></a>
<a id="orgd9c378b"></a>
</p>
<div class="note">
<p>
@ -921,8 +844,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_syme
</div>
</div>
<div id="outline-container-org757e668" class="outline-3">
<h3 id="org757e668"><span class="section-number-3">3.1</span> Experimental Setup</h3>
<div id="outline-container-org6e62fbe" class="outline-3">
<h3 id="org6e62fbe"><span class="section-number-3">3.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-3-1">
<p>
We here measure the signals of two geophones:
@ -1002,8 +925,8 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div>
</div>
<div id="outline-container-org92c9e9b" class="outline-3">
<h3 id="org92c9e9b"><span class="section-number-3">3.2</span> Load data</h3>
<div id="outline-container-orgd0c4704" class="outline-3">
<h3 id="orgd0c4704"><span class="section-number-3">3.2</span> Load data</h3>
<div class="outline-text-3" id="text-3-2">
<p>
We load the data of the z axis of two geophones.
@ -1016,8 +939,8 @@ d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data;
</div>
</div>
<div id="outline-container-orgb405d4d" class="outline-3">
<h3 id="orgb405d4d"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
<div id="outline-container-org30686ba" class="outline-3">
<h3 id="org30686ba"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-3-3">
<div class="org-src-container">
<pre class="src src-matlab">figure;
@ -1032,7 +955,7 @@ legend('Location', 'bestoutside');
</div>
<div id="org33aab52" class="figure">
<div id="orgd0329f8" class="figure">
<p><img src="figs/time_domain_hexa_driver.png" alt="time_domain_hexa_driver.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
@ -1040,8 +963,8 @@ legend('Location', 'bestoutside');
</div>
</div>
<div id="outline-container-org486b9fb" class="outline-3">
<h3 id="org486b9fb"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
<div id="outline-container-orgd922ea4" class="outline-3">
<h3 id="orgd922ea4"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-3-4">
<div class="org-src-container">
<pre class="src src-matlab">dt = d_18(2, 3) - d_18(1, 3);
@ -1052,8 +975,8 @@ win = hanning(ceil(10*Fs));
</div>
</div>
<div id="outline-container-orgd488281" class="outline-4">
<h4 id="orgd488281"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4>
<div id="outline-container-orgd49e7c3" class="outline-4">
<h4 id="orgd49e7c3"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-3-4-1">
<p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
@ -1079,14 +1002,14 @@ legend('Location', 'southwest');
</div>
<div id="org23ad3aa" class="figure">
<div id="org474aa6e" class="figure">
<p><img src="figs/psd_hexa_driver.png" alt="psd_hexa_driver.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
</div>
<div id="org0b027ce" class="figure">
<div id="org01ebad8" class="figure">
<p><img src="figs/psd_hexa_driver_high_freq.png" alt="psd_hexa_driver_high_freq.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
@ -1095,8 +1018,8 @@ legend('Location', 'southwest');
</div>
</div>
<div id="outline-container-org680fcdb" class="outline-3">
<h3 id="org680fcdb"><span class="section-number-3">3.5</span> Conclusion</h3>
<div id="outline-container-org031a084" class="outline-3">
<h3 id="org031a084"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5">
<div class="important">
<p>
@ -1110,7 +1033,7 @@ Even tough the Hexapod&rsquo;s driver vibrates quite a lot, it does not generate
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-23 jeu. 15:28</p>
<p class="date">Created: 2020-04-27 lun. 10:18</p>
</div>
</body>
</html>

41
disturbance-control-system/index.org
View File

@ -29,7 +29,7 @@
#+PROPERTY: header-args:shell :eval no-export
:END:
* Introduction :ignore:
This file is organized as follow:
- Section [[sec:effect_control_all]]:
- One geophone on the marble and one at the sample location
@ -175,7 +175,7 @@ exportFig('figs/time_domain_marble.pdf', 'width', 'full', 'height', 'tall')
[[file:figs/time_domain_marble.png]]
** Analysis - Frequency Domain
#+begin_src matlab
#+begin_src matlab :exports none
dt = d3(2, 3) - d3(1, 3);
Fs = 1/dt;
@ -233,6 +233,32 @@ exportFig('figs/psd_sample_comp_high_freq.pdf', 'width', 'full', 'height', 'tall
#+RESULTS:
[[file:figs/psd_sample_comp_high_freq.png]]
#+begin_src matlab :exports none
figure;
hold on;
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(px3)))), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(px4)))), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(px5)))), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(px6)))), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(px7)))), 'DisplayName', 'Hexa');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(px8)))), 'DisplayName', 'All OFF');
hold off;
xlabel('Frequency [Hz]');
ylabel('CAS [V]');
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
legend('location', 'southwest');
xlim([0.1, 300]);
#+end_src
#+begin_src matlab :tangle no :exports results :results file replace
exportFig('figs/cas_sample_comp.pdf', 'width', 'full', 'height', 'full')
#+end_src
#+name: fig:cas_sample_comp
#+caption:
#+RESULTS:
[[file:figs/cas_sample_comp.png]]
*** Vibrations on the marble
Now we plot the same curves for the geophone located on the marble.
#+begin_src matlab :results none
@ -363,6 +389,7 @@ Each of the =mat= file contains one array =data= with 3 columns:
** 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>>
addpath('../src');
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
@ -407,7 +434,7 @@ First, we can look at the time domain data and compare all the measurements:
- comparison for the geophone on the granite (figure [[fig:time_domain_marble_lpf]])
- relative displacement of the sample with respect to the marble (figure [[fig:time_domain_marble_lpf]])
#+begin_src matlab
#+begin_src matlab :exports none
figure;
hold on;
plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
@ -431,7 +458,7 @@ exportFig('figs/time_domain_sample_lpf.pdf', 'width', 'full', 'height', 'tall')
#+RESULTS:
[[file:figs/time_domain_sample_lpf.png]]
#+begin_src matlab
#+begin_src matlab :exports none
figure;
hold on;
plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
@ -455,7 +482,7 @@ exportFig('figs/time_domain_marble_lpf.pdf', 'width', 'full', 'height', 'tall')
#+RESULTS:
[[file:figs/time_domain_marble_lpf.png]]
#+begin_src matlab
#+begin_src matlab :exports none
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');
@ -541,7 +568,7 @@ exportFig('figs/psd_sample_comp_high_freq_lpf.pdf', 'width', 'full', 'height', '
*** Vibrations on the marble
Now we plot the same curves for the geophone located on the marble.
#+begin_src matlab
#+begin_src matlab :exports none
[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);
@ -551,7 +578,7 @@ Now we plot the same curves for the geophone located on the marble.
#+end_src
And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_lpf]] and [[fig:psd_marble_lpf_high_freq]])
#+begin_src matlab
#+begin_src matlab :exports none
figure;
hold on;
plot(f, sqrt(px_of), 'DisplayName', 'All OFF');

BIN
disturbance-sr-rz/figs/dist_rz_cas.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 116 KiB

BIN
disturbance-sr-rz/figs/dist_rz_cps.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 102 KiB

BIN
disturbance-sr-rz/figs/dist_rz_cps_reverse.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 136 KiB

BIN
disturbance-sr-rz/figs/rz_psd_sample_granite_relative_comp.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 149 KiB

BIN
disturbance-sr-rz/figs/rz_relative_motion.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 34 KiB

BIN
disturbance-sr-rz/figs/rz_relative_velocity.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 48 KiB

BIN
disturbance-sr-rz/figs/slip_ring_spindle_sample_time.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 48 KiB

After

Width:  |  Height:  |  Size: 53 KiB

BIN
disturbance-sr-rz/figs/slip_ring_spindle_sample_zoom.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 75 KiB

After

Width:  |  Height:  |  Size: 82 KiB

BIN
disturbance-sr-rz/figs/sr_sp_psd_relative_compare.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 158 KiB

After

Width:  |  Height:  |  Size: 160 KiB

BIN
disturbance-sr-rz/figs/ty_comp_gm.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 158 KiB

371
disturbance-sr-rz/index.html
View File

@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-05-14 mar. 10:53 -->
<!-- 2019-10-31 jeu. 16:19 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by the Slip-Ring and the Spindle</title>
@ -258,27 +258,26 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgae707b1">1. Experimental Setup</a></li>
<li><a href="#org78dded5">2. Data Analysis</a>
<li><a href="#orga44a9d5">1. Experimental Setup</a></li>
<li><a href="#orgb5a2f1a">2. Data Analysis</a>
<ul>
<li><a href="#orgaf48712">2.1. Load data</a></li>
<li><a href="#orga3184c9">2.2. Time domain plots</a></li>
<li><a href="#org66e3cd4">2.3. Frequency Domain</a></li>
<li><a href="#orgbe56ee4">2.4. Conclusion</a></li>
<li><a href="#org239b200">2.1. Load data</a></li>
<li><a href="#org66889bf">2.2. Voltage to Velocity</a></li>
<li><a href="#orgd049ddc">2.3. Time domain plots</a></li>
<li><a href="#orgfee57e5">2.4. Frequency Domain</a></li>
<li><a href="#org7d3ac71">2.5. Relative Motion</a></li>
<li><a href="#org1464a72">2.6. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgae707b1" class="outline-2">
<h2 id="orgae707b1"><span class="section-number-2">1</span> Experimental Setup</h2>
<div id="outline-container-orga44a9d5" class="outline-2">
<h2 id="orga44a9d5"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
</div>
<ol class="org-ol">
<li><a id="orgd4a8f25"></a>Setup<br />
<div class="outline-text-6" id="text-1-0-0-0-1">
<p>
<b>Setup</b>:
All the stages are OFF.
</p>
@ -303,6 +302,7 @@ Two voltage amplifiers are used, their setup is:
A first order low pass filter is also added at the input of the voltage amplifiers.
</p>
<p>
<b>Goal</b>:
</p>
@ -383,27 +383,24 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table>
<p>
A movie showing the experiment is shown on figure <a href="#orgb52ab90">1</a>.
A movie showing the experiment is shown on figure <a href="#org1669ed1">1</a>.
</p>
<div id="orgb52ab90" class="figure">
<div id="org1669ed1" class="figure">
<p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" />
</p>
<p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p>
</div>
</div>
</li>
</ol>
</div>
<div id="outline-container-org78dded5" class="outline-2">
<h2 id="org78dded5"><span class="section-number-2">2</span> Data Analysis</h2>
<div id="outline-container-orgb5a2f1a" class="outline-2">
<h2 id="orgb5a2f1a"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org66307ff"></a>
<a id="org73b6124"></a>
</p>
<div class="note">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/spindle_slip_ring_vibrations.zip">here</a>.
@ -412,75 +409,119 @@ All the files (data and Matlab scripts) are accessible <a href="data/spindle_sli
</div>
</div>
<div id="outline-container-orgaf48712" class="outline-3">
<h3 id="orgaf48712"><span class="section-number-3">2.1</span> Load data</h3>
<div id="outline-container-org239b200" class="outline-3">
<h3 id="org239b200"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data;
sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_025.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr = sr.data;
sp = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_026.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sp = sp.data;
<pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data;
sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_025.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr = sr.data;
sp = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_026.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sp = sp.data;
</pre>
</div>
<div class="warning">
<p>
There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring.
</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orga3184c9" class="outline-3">
<h3 id="orga3184c9"><span class="section-number-3">2.2</span> Time domain plots</h3>
<div id="outline-container-org66889bf" class="outline-3">
<h3 id="org66889bf"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="../src/index.html">here</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgd049ddc" class="outline-3">
<h3 id="orgd049ddc"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">10</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orga435a98" class="figure">
<div id="org4e9bed0" class="figure">
<p><img src="figs/slip_ring_spindle_marble_time.png" alt="slip_ring_spindle_marble_time.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Measurement of the geophone located on the marble - Time domain</p>
<p><span class="figure-number">Figure 2: </span>Velocity as measured by the geophone located on the marble - Time domain</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Spindle and Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Only Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle and Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Only Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">10</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org2bafcfa" class="figure">
<div id="org8be7963" class="figure">
<p><img src="figs/slip_ring_spindle_sample_time.png" alt="slip_ring_spindle_sample_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Measurement of the geophone at the sample location - Time domain</p>
<p><span class="figure-number">Figure 3: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
</div>
<div id="orgfc19876" class="figure">
<p><img src="figs/slip_ring_spindle_sample_zoom.png" alt="slip_ring_spindle_sample_zoom.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
</div>
</div>
</div>
<div id="outline-container-org66e3cd4" class="outline-3">
<h3 id="org66e3cd4"><span class="section-number-3">2.3</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-3">
<div id="outline-container-orgfee57e5" class="outline-3">
<h3 id="orgfee57e5"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">dt = of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [s]</span>
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Window used</span>
</pre>
</div>
@ -502,79 +543,249 @@ First for the geophone located on the marble
And for the geophone located at the sample position.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And we plot the ASD of the measured signals:
And we plot the ASD of the measured velocities:
</p>
<ul class="org-ul">
<li>figure <a href="#org3fb6d61">4</a> for the geophone located on the marble</li>
<li>figure <a href="#orge9619ee">5</a> for the geophone at the sample position</li>
<li>figure <a href="#org704b4b4">5</a> for the geophone located on the marble</li>
<li>figure <a href="#orga078b66">6</a> for the geophone at the sample position</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org3fb6d61" class="figure">
<div id="org704b4b4" class="figure">
<p><img src="figs/sr_sp_psd_marble_compare.png" alt="sr_sp_psd_marble_compare.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Comparison of the ASD of the measured voltage from the Geophone on the marble</p>
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orge9619ee" class="figure">
<div id="orga078b66" class="figure">
<p><img src="figs/sr_sp_psd_sample_compare.png" alt="sr_sp_psd_sample_compare.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured voltage from the Geophone at the sample location</p>
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p>
</div>
<p>
We load the ground motion to compare with the measurements (Fig. <a href="#org71cc947">7</a>).
We see that the motion is dominated by the ground motion below 20Hz.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>gm.f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>gm.psd_gv<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org71cc947" class="figure">
<p><img src="figs/ty_comp_gm.png" alt="ty_comp_gm.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Comparison of the ground velocity with the measured velocity (<a href="./figs/ty_comp_gm.png">png</a>, <a href="./figs/ty_comp_gm.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orgbe56ee4" class="outline-3">
<h3 id="orgbe56ee4"><span class="section-number-3">2.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-4">
<div id="outline-container-org7d3ac71" class="outline-3">
<h3 id="org7d3ac71"><span class="section-number-3">2.5</span> Relative Motion</h3>
<div class="outline-text-3" id="text-2-5">
<p>
The relative velocity between the sample and the marble is shown in Fig. <a href="#org21be4d0">8</a>.
The velocity is integrated to have the relative displacement in Fig. <a href="#org2d58d24">9</a>.
</p>
<div id="org21be4d0" class="figure">
<p><img src="figs/rz_relative_velocity.png" alt="rz_relative_velocity.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Relative velocity between the hexapod and the marble (<a href="./figs/rz_relative_velocity.png">png</a>, <a href="./figs/rz_relative_velocity.pdf">pdf</a>)</p>
</div>
<p>
Time domain: Integration to have the displacement
</p>
<div id="org2d58d24" class="figure">
<p><img src="figs/rz_relative_motion.png" alt="rz_relative_motion.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Relative displacement between the Hexapod and the marble (<a href="./figs/rz_relative_motion.png">png</a>, <a href="./figs/rz_relative_motion.pdf">pdf</a>)</p>
</div>
<p>
We compute the PSD of the relative velocity between the sample and the marble.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. <a href="#org0cfb4b3">10</a>.
</p>
<div id="org0cfb4b3" class="figure">
<p><img src="figs/rz_psd_sample_granite_relative_comp.png" alt="rz_psd_sample_granite_relative_comp.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the velocity of the Sample, Granite and relative velocity (<a href="./figs/rz_psd_sample_granite_relative_comp.png">png</a>, <a href="./figs/rz_psd_sample_granite_relative_comp.pdf">pdf</a>)</p>
</div>
<p>
Then, we display the PSD of the relative velocity for all three cases in Fig. <a href="#org9d08176">11</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the relative velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org9d08176" class="figure">
<p><img src="figs/sr_sp_psd_relative_compare.png" alt="sr_sp_psd_relative_compare.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Comparison of the ASD of the relative velocity</p>
</div>
<p>
The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href="#org76a9b23">12</a> and in Fig. <a href="#org61e2e4a">13</a> (integrated in reverse direction).
</p>
<div id="org76a9b23" class="figure">
<p><img src="figs/dist_rz_cps.png" alt="dist_rz_cps.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Cumulative Power Spectrum of the relative velocity (<a href="./figs/dist_rz_cps.png">png</a>, <a href="./figs/dist_rz_cps.pdf">pdf</a>)</p>
</div>
<div id="org61e2e4a" class="figure">
<p><img src="figs/dist_rz_cps_reverse.png" alt="dist_rz_cps_reverse.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) (<a href="./figs/dist_rz_cps_reverse.png">png</a>, <a href="./figs/dist_rz_cps_reverse.pdf">pdf</a>)</p>
</div>
<p>
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. <a href="#org454a2a7">14</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsp_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsr_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxof_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'CAS of the relative displacement $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org454a2a7" class="figure">
<p><img src="figs/dist_rz_cas.png" alt="dist_rz_cas.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite (<a href="./figs/dist_rz_cas.png">png</a>, <a href="./figs/dist_rz_cas.pdf">pdf</a>)</p>
</div>
<p>
The Power Spectral Density of the relative velocity is saved for further analysis.
</p>
<div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxsp_r.mat'</span>, <span class="org-string">'pxsp_r'</span>, <span class="org-string">'f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org1464a72" class="outline-3">
<h3 id="org1464a72"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<p>
The slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz.
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
</p>
<p>
The spindle rotation induces a lot of vibrations of the sample as well as on the granite.
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration.
The Slip-Ring rotation induce almost no relative motion of the hexapod with respect to the granite (only a little above 400Hz).
</p>
<p>
The Spindle rotation induces relative motion of the hexapod with respect to the granite above 20Hz.
</p>
</div>
<div class="important">
<p>
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
</p>
<ul class="org-ul">
<li>The peak is really sharp, could this be due to magnetic effect?</li>
<li>Should redo the measurement with piezo accelerometers.</li>
</ul>
</div>
</div>
</div>
@ -582,7 +793,7 @@ There is a huge peak at 24Hz on the sample vibration but not on the granite vibr
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 10:53</p>
<p class="date">Created: 2019-10-31 jeu. 16:19</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

236
disturbance-sr-rz/index.org
View File

@ -98,22 +98,36 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
** 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>>
addpath('../src');
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab
addpath('../src');
#+end_src
** Load data
#+begin_src matlab
of = load('mat/data_024.mat', 'data'); of = of.data;
sr = load('mat/data_025.mat', 'data'); sr = sr.data;
sp = load('mat/data_026.mat', 'data'); sp = sp.data;
of = load('mat/data_024.mat', 'data'); of = of.data; % OFF
sr = load('mat/data_025.mat', 'data'); sr = sr.data; % Slip Ring
sp = load('mat/data_026.mat', 'data'); sp = sp.data; % Spindle
#+end_src
#+begin_warning
There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring.
#+end_warning
#+begin_src matlab
of(:, 2) = -of(:, 2);
sr(:, 2) = -sr(:, 2);
sp(:, 2) = -sp(:, 2);
#+end_src
** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/Cloud/These/meas/src/index.org][here]]).
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:../src/index.org][here]]).
#+begin_src matlab
gain = 60; % [dB]
@ -192,11 +206,11 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
** Frequency Domain
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
dt = of(2, 3)-of(1, 3);
dt = of(2, 3)-of(1, 3); % [s]
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
win = hanning(ceil(10*Fs)); % Window used
#+end_src
Then we compute the Power Spectral Density using =pwelch= function.
@ -215,13 +229,6 @@ And for the geophone located at the sample position.
[pxsp_s, ~] = pwelch(sp(:, 2), win, [], [], Fs);
#+end_src
And finally for the relative velocity between the sample and the marble.
#+begin_src matlab
[pxof_r, ~] = pwelch(of(:, 2)-of(:, 1), win, [], [], Fs);
[pxsr_r, ~] = pwelch(sr(:, 2)-sr(:, 1), win, [], [], Fs);
[pxsp_r, ~] = pwelch(sp(:, 2)-sp(:, 1), win, [], [], Fs);
#+end_src
And we plot the ASD of the measured velocities:
- figure [[fig:sr_sp_psd_marble_compare]] for the geophone located on the marble
- figure [[fig:sr_sp_psd_sample_compare]] for the geophone at the sample position
@ -276,6 +283,115 @@ And we plot the ASD of the measured velocities:
#+RESULTS: fig:sr_sp_psd_sample_compare
[[file:figs/sr_sp_psd_sample_compare.png]]
We load the ground motion to compare with the measurements (Fig. [[fig:ty_comp_gm]]).
We see that the motion is dominated by the ground motion below 20Hz.
#+begin_src matlab
gm = load('../ground-motion/mat/psd_gm.mat', 'f', 'psd_gv');
#+end_src
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(pxsp_m), 'DisplayName', 'Spindle - 6rpm');
plot(f, sqrt(pxsr_m), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, sqrt(pxof_m), 'DisplayName', 'OFF');
plot(gm.f, sqrt(gm.psd_gv), 'k-', 'DisplayName', 'Ground Motion');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/ty_comp_gm.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_comp_gm
#+CAPTION: Comparison of the ground velocity with the measured velocity ([[./figs/ty_comp_gm.png][png]], [[./figs/ty_comp_gm.pdf][pdf]])
[[file:figs/ty_comp_gm.png]]
** Relative Motion
The relative velocity between the sample and the marble is shown in Fig. [[fig:rz_relative_velocity]].
The velocity is integrated to have the relative displacement in Fig. [[fig:rz_relative_motion]].
#+begin_src matlab :exports results
figure;
hold on;
plot(sp(:, 3), sp(:, 2)-sp(:, 1), 'DisplayName', 'Spindle - 6rpm');
plot(sr(:, 3), sr(:, 2)-sr(:, 1), 'DisplayName', 'Slip-Ring - 6rpm');
plot(of(:, 3), of(:, 2)-of(:, 1), 'DisplayName', 'OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); ylim([-1e-4, 1e-4]);
legend('Location', 'northeast');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/rz_relative_velocity.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:rz_relative_velocity
#+CAPTION: Relative velocity between the hexapod and the marble ([[./figs/rz_relative_velocity.png][png]], [[./figs/rz_relative_velocity.pdf][pdf]])
[[file:figs/rz_relative_velocity.png]]
Time domain: Integration to have the displacement
#+begin_src matlab :exports results
figure;
hold on;
plot(sp(:, 3), lsim(1/s, sp(:, 2)-sp(:, 1), sp(:, 3)), 'DisplayName', 'Spindle - 6rpm');
plot(sr(:, 3), lsim(1/s, sr(:, 2)-sr(:, 1), sr(:, 3)), 'DisplayName', 'Slip-Ring - 6rpm');
plot(of(:, 3), lsim(1/s, of(:, 2)-of(:, 1), of(:, 3)), 'DisplayName', 'OFF');
hold off;
xlabel('Time [s]'); ylabel('Displacement [m]');
xlim([0, 100]);
legend('Location', 'northeast');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/rz_relative_motion.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:rz_relative_motion
#+CAPTION: Relative displacement between the Hexapod and the marble ([[./figs/rz_relative_motion.png][png]], [[./figs/rz_relative_motion.pdf][pdf]])
[[file:figs/rz_relative_motion.png]]
We compute the PSD of the relative velocity between the sample and the marble.
#+begin_src matlab
[pxof_r, f] = pwelch(of(:, 2)-of(:, 1), win, [], [], Fs);
[pxsr_r, ~] = pwelch(sr(:, 2)-sr(:, 1), win, [], [], Fs);
[pxsp_r, ~] = pwelch(sp(:, 2)-sp(:, 1), win, [], [], Fs);
#+end_src
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. [[fig:rz_psd_sample_granite_relative_comp]].
#+begin_src matlab :exports results
figure;
hold on;
plot(f, sqrt(pxof_m)./(2*pi*f), 'DisplayName', 'Granite');
plot(f, sqrt(pxof_s)./(2*pi*f), 'DisplayName', 'Sample');
plot(f, sqrt(pxof_r)./(2*pi*f), 'DisplayName', 'Diff');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the relative velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/rz_psd_sample_granite_relative_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:rz_psd_sample_granite_relative_comp
#+CAPTION: Comparison of the PSD of the velocity of the Sample, Granite and relative velocity ([[./figs/rz_psd_sample_granite_relative_comp.png][png]], [[./figs/rz_psd_sample_granite_relative_comp.pdf][pdf]])
[[file:figs/rz_psd_sample_granite_relative_comp.png]]
Then, we display the PSD of the relative velocity for all three cases in Fig. [[fig:sr_sp_psd_relative_compare]].
#+begin_src matlab :results none
figure;
hold on;
@ -301,12 +417,94 @@ And we plot the ASD of the measured velocities:
#+RESULTS: fig:sr_sp_psd_relative_compare
[[file:figs/sr_sp_psd_relative_compare.png]]
The Cumulative Power Spectrum of the relative velocity is shown in Fig. [[fig:dist_rz_cps]] and in Fig. [[fig:dist_rz_cps_reverse]] (integrated in reverse direction).
#+begin_src matlab :results none :exports results
figure;
hold on;
plot(f, cumtrapz(f,pxsp_r), 'DisplayName', 'Spindle - 6rpm');
plot(f, cumtrapz(f,pxsr_r), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, cumtrapz(f,pxof_r), 'DisplayName', 'OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CPS of the relative velocity $\left[\frac{(m/s)^2}{Hz}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/dist_rz_cps.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:dist_rz_cps
#+CAPTION: Cumulative Power Spectrum of the relative velocity ([[./figs/dist_rz_cps.png][png]], [[./figs/dist_rz_cps.pdf][pdf]])
[[file:figs/dist_rz_cps.png]]
#+begin_src matlab :exports results
figure;
hold on;
plot(f, flip(-cumtrapz(flip(f), flip(pxsp_r))), 'DisplayName', 'Spindle - 6rpm');
plot(f, flip(-cumtrapz(flip(f), flip(pxsr_r))), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, flip(-cumtrapz(flip(f), flip(pxof_r))), 'DisplayName', 'OFF');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CPS of the relative velocity $\left[\frac{(m/s)^2}{Hz}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/dist_rz_cps_reverse.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:dist_rz_cps_reverse
#+CAPTION: Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) ([[./figs/dist_rz_cps_reverse.png][png]], [[./figs/dist_rz_cps_reverse.pdf][pdf]])
[[file:figs/dist_rz_cps_reverse.png]]
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. [[fig:dist_rz_cas]].
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(pxsp_r./(2*pi*f).^2)))), 'DisplayName', 'Spindle - 6rpm');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(pxsr_r./(2*pi*f).^2)))), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(pxof_r./(2*pi*f).^2)))), 'DisplayName', 'OFF');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CAS of the relative displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/dist_rz_cas.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:dist_rz_cas
#+CAPTION: Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite ([[./figs/dist_rz_cas.png][png]], [[./figs/dist_rz_cas.pdf][pdf]])
[[file:figs/dist_rz_cas.png]]
** Save
The Power Spectral Density of the relative velocity and of the hexapod velocity is saved for further analysis.
#+begin_src matlab
save('mat/pxsp_r.mat', 'f', 'pxsp_r', 'pxsp_s');
#+end_src
** Conclusion
#+begin_important
- The slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz.
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
- The spindle rotation induces a lot of vibrations of the sample as well as on the granite.
- There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
- The peak is really sharp, could this be due to magnetic effect?
- Should redo the measurement with piezo accelerometers.
The Slip-Ring rotation induce almost no relative motion of the hexapod with respect to the granite (only a little above 400Hz).
The Spindle rotation induces relative motion of the hexapod with respect to the granite above 20Hz.
#+end_important
#+begin_important
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
- The peak is really sharp, could this be due to magnetic effect?
- Should redo the measurement with piezo accelerometers.
#+end_important

BIN
disturbance-sr-rz/mat/pxsp_r.mat Normal file
View File

Binary file not shown.

2
disturbance-ty-sr/matlab/disturbance_ty_sr.m
View File

@ -11,7 +11,7 @@ ty_on = load('mat/data_051.mat', 'data'); ty_on = ty_on.data;
ty_1h = load('mat/data_052.mat', 'data'); ty_1h = ty_1h.data;
% Voltage to Velocity
% We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
% We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/Cloud/thesis/meas/srcindex.org][here]]).
gain = 40; % [dB]

BIN
disturbance-ty/figs/asd_east_marble.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 187 KiB

After

Width:  |  Height:  |  Size: 188 KiB

BIN
disturbance-ty/figs/asd_east_sample.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 192 KiB

After

Width:  |  Height:  |  Size: 191 KiB

BIN
disturbance-ty/figs/asd_z_direction.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 188 KiB

After

Width:  |  Height:  |  Size: 186 KiB

BIN
disturbance-ty/figs/asd_z_relative.png Normal file
View File

Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 170 KiB

BIN
disturbance-ty/figs/ty_e_time.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 98 KiB

After

Width:  |  Height:  |  Size: 75 KiB

BIN
disturbance-ty/figs/ty_z_time.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 84 KiB

After

Width:  |  Height:  |  Size: 65 KiB

BIN
disturbance-ty/figs/x_relative_disp.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 49 KiB

After

Width:  |  Height:  |  Size: 42 KiB

BIN
disturbance-ty/figs/z_relative_disp.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 32 KiB

After

Width:  |  Height:  |  Size: 32 KiB

354
disturbance-ty/index.html
View File

@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-06-19 mer. 11:12 -->
<!-- 2019-10-31 jeu. 18:00 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by the translation stage motion</title>
@ -258,29 +258,30 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org39f8fb3">1. Measurement description</a></li>
<li><a href="#org9c1c4dc">2. Measurement Analysis</a>
<li><a href="#org810c300">1. Measurement description</a></li>
<li><a href="#orge7c9591">2. Measurement Analysis</a>
<ul>
<li><a href="#org83beca6">2.1. Load data</a></li>
<li><a href="#org6739365">2.2. Voltage to Velocity</a></li>
<li><a href="#org0e76d60">2.3. Time domain plots</a></li>
<li><a href="#orgae02709">2.4. Frequency Domain analysis</a></li>
<li><a href="#org86d8525">2.5. Transfer function from marble motion in the East direction to sample motion in the East direction</a></li>
<li><a href="#orgfdf507c">2.6. Position of the translation stage and Current</a>
<li><a href="#orgec8ecca">2.1. Load data</a></li>
<li><a href="#orgcd50803">2.2. Voltage to Velocity</a></li>
<li><a href="#org1c8a0dc">2.3. Time domain plots</a></li>
<li><a href="#org0d692f4">2.4. Frequency Domain</a></li>
<li><a href="#orgd741d6b">2.5. Relative Motion</a></li>
<li><a href="#org3ded48e">2.6. Save</a></li>
<li><a href="#org4fbe75b">2.7. Position of the translation stage and Current</a>
<ul>
<li><a href="#orgc57aee0">2.6.1. Data pre-processing</a></li>
<li><a href="#orgb39f0c9">2.6.2. Time domain data</a></li>
<li><a href="#orge07cd8f">2.7.1. Data pre-processing</a></li>
<li><a href="#org851b639">2.7.2. Time domain data</a></li>
</ul>
</li>
<li><a href="#org7881c9d">2.7. Conclusion</a></li>
<li><a href="#org011cbae">2.8. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org39f8fb3" class="outline-2">
<h2 id="org39f8fb3"><span class="section-number-2">1</span> Measurement description</h2>
<div id="outline-container-org810c300" class="outline-2">
<h2 id="org810c300"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1">
<p>
<b>Setup</b>:
@ -295,7 +296,7 @@ Two geophone are use:
Two voltage amplifiers are used, their setup is:
</p>
<ul class="org-ul">
<li>gain of 40dB (the gain at the be lowered from 60dB to 40dB to not saturate the voltage amplifiers)</li>
<li>gain of 40dB (the gain had to be lowered from 60dB to 40dB in order to not saturate the voltage amplifiers)</li>
<li>AC/DC switch on AC</li>
<li>Low pass filter at 1kHz</li>
</ul>
@ -310,7 +311,7 @@ The scans are done with the ELMO software.
</p>
<p>
The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure <a href="#orgf0c462e">1</a>).
The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure <a href="#orgc5e9621">1</a>).
</p>
<p>
@ -394,19 +395,24 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table>
<div id="orgf0c462e" class="figure">
<div id="orgc5e9621" class="figure">
<p><img src="./img/IMG_20190513_163032.jpg" alt="IMG_20190513_163032.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
</div>
<p>
We also use the file <code>mat/data_051.mat</code> when we measure the z direction when everything is off.
The setup used for the measurement is described <a href="file:///home/thomas/Cloud/thesis/matlab/meas/disturbance-ty-sr/index.html">here</a>.
</p>
</div>
</div>
<div id="outline-container-org9c1c4dc" class="outline-2">
<h2 id="org9c1c4dc"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div id="outline-container-orge7c9591" class="outline-2">
<h2 id="orge7c9591"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orgd482cbe"></a>
<a id="org8955a2d"></a>
</p>
<div class="note">
<p>
@ -416,33 +422,49 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div>
</div>
<div id="outline-container-org83beca6" class="outline-3">
<h3 id="org83beca6"><span class="section-number-3">2.1</span> Load data</h3>
<div id="outline-container-orgec8ecca" class="outline-3">
<h3 id="orgec8ecca"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">z_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_040.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_ty = z_ty.data;
e_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_041.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_ty = e_ty.data;
e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_042.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_of = e_of.data;
<pre class="src src-matlab">z_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_040.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_ty = z_ty.data;
z_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_of = z_of.data;
e_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_041.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_ty = e_ty.data;
e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_042.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_of = e_of.data;
</pre>
</div>
<div class="warning">
<p>
There is probably a sign error for the Geophone located on top of the Hexapod (only for the z direction).
The problem probably comes from the wiring in the Slip-Ring.
</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org6739365" class="outline-3">
<h3 id="org6739365"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div id="outline-container-orgcd50803" class="outline-3">
<h3 id="orgcd50803"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/These/meas/src/index.html">here</a>).
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">40</span>; <span class="org-comment">% [dB]</span>
z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
z_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
z_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
@ -450,80 +472,40 @@ e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">
</div>
</div>
<div id="outline-container-org0e76d60" class="outline-3">
<h3 id="org0e76d60"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div id="outline-container-org1c8a0dc" class="outline-3">
<h3 id="org1c8a0dc"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org34814fe">2</a>) and in the X direction (figure <a href="#org8e9b7b5">3</a>).
We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org60b7c99">2</a>) and in the X direction (figure <a href="#orgc2eb360">3</a>).
</p>
<p>
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgd86ada1">4</a> in the X direction and figure <a href="#org3e96a6b">5</a> in the Z direction).
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgdcb90f2">4</a> in the X direction and figure <a href="#orgd1edd4b">5</a> in the Z direction).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org34814fe" class="figure">
<div id="org60b7c99" class="figure">
<p><img src="figs/ty_z_time.png" alt="ty_z_time.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Z velocity of the sample and marble when scanning with the translation stage</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org8e9b7b5" class="figure">
<div id="orgc2eb360" class="figure">
<p><img src="figs/ty_e_time.png" alt="ty_e_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1e6</span><span class="org-type">*</span>lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, e_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>e_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, e_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>X Relative Displacement <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgd86ada1" class="figure">
<div id="orgdcb90f2" class="figure">
<p><img src="figs/x_relative_disp.png" alt="x_relative_disp.png" />
</p>
<p><span class="figure-number">Figure 4: </span>X relative displacement of the sample with respect to the marble</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1e6</span><span class="org-type">*</span>lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, z_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, z_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Z Relative Displacement <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org3e96a6b" class="figure">
<div id="orgd1edd4b" class="figure">
<p><img src="figs/z_relative_disp.png" alt="z_relative_disp.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Z relative disp of the sample with respect to the marble</p>
@ -531,14 +513,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div>
</div>
<div id="outline-container-orgae02709" class="outline-3">
<h3 id="orgae02709"><span class="section-number-3">2.4</span> Frequency Domain analysis</h3>
<div id="outline-container-org0d692f4" class="outline-3">
<h3 id="org0d692f4"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We get the typical ground velocity to compare with the velocities measured.
We load measured ground motion at ID31 to compare with the velocities measured.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx_gm, f_gm<span class="org-rainbow-delimiters-depth-1">]</span> = getPSDGroundVelocity<span class="org-rainbow-delimiters-depth-1">()</span>;
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
@ -563,6 +545,7 @@ First for the geophone located on the marble
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
@ -573,190 +556,139 @@ And for the geophone located at the sample position.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And finally for the relative velocity between the sample and the marble.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And we plot the ASD of the measured velocities:
</p>
<ul class="org-ul">
<li>figure <a href="#org94d27c9">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgb11f07e">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgaefec33">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
<li>figure <a href="#org0099071">9</a> shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz</li>
<li>figure <a href="#org888ff45">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgde2e042">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orga58a3f5">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Marble <span class="org-type">-</span> X'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF - Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f_gm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx_gm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k--', 'DisplayName', 'Ground Motion'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org94d27c9" class="figure">
<div id="org888ff45" class="figure">
<p><img src="figs/asd_east_marble.png" alt="asd_east_marble.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located on the marble when the translation stage is OFF and when it is scanning at 1Hz</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Sample <span class="org-type">-</span> X'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF - Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f_gm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx_gm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k--', 'DisplayName', 'Ground Motion'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgb11f07e" class="figure">
<div id="orgde2e042" class="figure">
<p><img src="figs/asd_east_sample.png" alt="asd_east_sample.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located at the sample location when the translation stage is OFF and when it is scanning at 1Hz</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_ty_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Marble <span class="org-type">-</span> Z'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_ty_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Sample <span class="org-type">-</span> Z'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f_gm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx_gm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k--', 'DisplayName', 'Ground Motion'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgaefec33" class="figure">
<div id="orga58a3f5" class="figure">
<p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p>
</div>
<div id="org1dd835a" class="figure">
<p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p>
</div>
</div>
</div>
<div id="outline-container-orgd741d6b" class="outline-3">
<h3 id="orgd741d6b"><span class="section-number-3">2.5</span> Relative Motion</h3>
<div class="outline-text-3" id="text-2-5">
<p>
And finally for the relative velocity between the sample and the marble.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_r, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Fig. <a href="#org7d4814e">11</a> shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF - Relative - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> E'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> Z<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org0099071" class="figure">
<p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" />
<div id="org61c3a2e" class="figure">
<p><img src="figs/asd_z_relative.png" alt="asd_z_relative.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
<p><span class="figure-number">Figure 10: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
</div>
</div>
</div>
<div id="outline-container-org86d8525" class="outline-3">
<h3 id="org86d8525"><span class="section-number-3">2.5</span> Transfer function from marble motion in the East direction to sample motion in the East direction</h3>
<div class="outline-text-3" id="text-2-5">
<p>
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.
</p>
<p>
We first plot the time domain motions when every stage is off (figure <a href="#orgb0f7dd4">10</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> E<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgb0f7dd4" class="figure">
<p><img src="figs/east_marble_sample.png" alt="east_marble_sample.png" />
<div id="org7d4814e" class="figure">
<p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Velocity in the east direction of the marble and sample when all the stages are OFF</p>
<p><span class="figure-number">Figure 11: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
</div>
</div>
</div>
<div id="outline-container-org3ded48e" class="outline-3">
<h3 id="org3ded48e"><span class="section-number-3">2.6</span> Save</h3>
<div class="outline-text-3" id="text-2-6">
<p>
We then compute the transfer function using <code>tfestimate</code>.
The Power Spectral Density of the relative velocity is saved for further analysis.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>T, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxz_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxz_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxe_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxe_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
The result is shown on figure <a href="#orgc32127e">11</a>.
</p>
<div id="orgc32127e" class="figure">
<p><img src="figs/tf_east_marble_sample.png" alt="tf_east_marble_sample.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction</p>
</div>
</div>
</div>
<div id="outline-container-orgfdf507c" class="outline-3">
<h3 id="orgfdf507c"><span class="section-number-3">2.6</span> Position of the translation stage and Current</h3>
<div class="outline-text-3" id="text-2-6">
<div id="outline-container-org4fbe75b" class="outline-3">
<h3 id="org4fbe75b"><span class="section-number-3">2.7</span> Position of the translation stage and Current</h3>
<div class="outline-text-3" id="text-2-7">
<p>
The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file.
</p>
</div>
<div id="outline-container-orgc57aee0" class="outline-4">
<h4 id="orgc57aee0"><span class="section-number-4">2.6.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-6-1">
<div id="outline-container-orge07cd8f" class="outline-4">
<h4 id="orge07cd8f"><span class="section-number-4">2.7.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-7-1">
<p>
Let's look at at the start of the csv file.
</p>
@ -778,13 +710,13 @@ We then load this <code>cvs</code> file starting at line 29.
</div>
</div>
<div id="outline-container-orgb39f0c9" class="outline-4">
<h4 id="orgb39f0c9"><span class="section-number-4">2.6.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-6-2">
<div id="outline-container-org851b639" class="outline-4">
<h4 id="org851b639"><span class="section-number-4">2.7.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-7-2">
<p>
We plot the position of the translation stage measured by the encoders.
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
The result is shown on figure <a href="#org3c042ab">12</a>.
The result is shown on figure <a href="#orgf3ec62f">12</a>.
</p>
<div class="org-src-container">
@ -793,26 +725,26 @@ hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org3c042ab" class="figure">
<div id="orgf3ec62f" class="figure">
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Y position of the translation stage measured by the encoders</p>
</div>
<div id="orgac4a46b" class="figure">
<div id="org501c879" class="figure">
<p><img src="figs/ty_position_time_zoom.png" alt="ty_position_time_zoom.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Y position of the translation stage measured by the encoders - Zoom</p>
</div>
<p>
We also plot the current as function of the time on figure <a href="#orgc686f17">14</a>.
We also plot the current as function of the time on figure <a href="#orge486741">14</a>.
</p>
<div class="org-src-container">
@ -821,19 +753,19 @@ hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgc686f17" class="figure">
<div id="orge486741" class="figure">
<p><img src="figs/current_time.png" alt="current_time.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Current going through the actuator of the translation stage</p>
</div>
<div id="org3b181bb" class="figure">
<div id="org8b9bcbe" class="figure">
<p><img src="figs/current_time_zoom.png" alt="current_time_zoom.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Current going through the actuator of the translation stage - Zoom</p>
@ -842,9 +774,9 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
</div>
<div id="outline-container-org7881c9d" class="outline-3">
<h3 id="org7881c9d"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-7">
<div id="outline-container-org011cbae" class="outline-3">
<h3 id="org011cbae"><span class="section-number-3">2.8</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-8">
<div class="important">
<ul class="org-ul">
<li>The acquisition is done using the Speedgoat as well as using ELMO. The two acquisition are <b>not</b> synchronize</li>
@ -858,7 +790,7 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-06-19 mer. 11:12</p>
<p class="date">Created: 2019-10-31 jeu. 18:00</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

160
disturbance-ty/index.org
View File

@ -37,7 +37,7 @@ Two geophone are use:
- One at the sample location (corresponding to the second column in the data)
Two voltage amplifiers are used, their setup is:
- gain of 40dB (the gain at the be lowered from 60dB to 40dB to not saturate the voltage amplifiers)
- gain of 40dB (the gain had to be lowered from 60dB to 40dB in order to not saturate the voltage amplifiers)
- AC/DC switch on AC
- Low pass filter at 1kHz
@ -75,6 +75,9 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
#+attr_html: :width 500px
[[file:./img/IMG_20190513_163032.jpg]]
We also use the file =mat/data_051.mat= when we measure the z direction when everything is off.
The setup used for the measurement is described [[file:~/Cloud/thesis/matlab/meas/disturbance-ty-sr/index.org][here]].
* Measurement Analysis
:PROPERTIES:
:header-args:matlab+: :tangle matlab/disturbance_ty.m
@ -113,21 +116,33 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
** Load data
#+begin_src matlab
z_ty = load('mat/data_040.mat', 'data'); z_ty = z_ty.data;
z_of = load('mat/data_051.mat', 'data'); z_of = z_of.data;
e_ty = load('mat/data_041.mat', 'data'); e_ty = e_ty.data;
e_of = load('mat/data_042.mat', 'data'); e_of = e_of.data;
#+end_src
#+begin_warning
There is probably a sign error for the Geophone located on top of the Hexapod (only for the z direction).
The problem probably comes from the wiring in the Slip-Ring.
#+end_warning
#+begin_src matlab
z_ty(:, 2) = -z_ty(:, 2);
#+end_src
** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/Cloud/These/meas/src/index.org][here]]).
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/Cloud/thesis/meas/srcindex.org][here]]).
#+begin_src matlab
gain = 40; % [dB]
z_ty(:, 1) = voltageToVelocityL22(z_ty(:, 1), z_ty(:, 3), gain);
z_of(:, 1) = voltageToVelocityL22(z_of(:, 1), z_of(:, 3), gain);
e_ty(:, 1) = voltageToVelocityL22(e_ty(:, 1), e_ty(:, 3), gain);
e_of(:, 1) = voltageToVelocityL22(e_of(:, 1), e_of(:, 3), gain);
z_ty(:, 2) = voltageToVelocityL22(z_ty(:, 2), z_ty(:, 3), gain);
z_of(:, 2) = voltageToVelocityL22(z_of(:, 2), z_of(:, 3), gain);
e_ty(:, 2) = voltageToVelocityL22(e_ty(:, 2), e_ty(:, 3), gain);
e_of(:, 2) = voltageToVelocityL22(e_of(:, 2), e_of(:, 3), gain);
#+end_src
@ -137,7 +152,7 @@ We plot the measured velocity of the marble and sample in the vertical direction
We also integrate the relative velocity to obtain the relative displacement (figure [[fig:x_relative_disp]] in the X direction and figure [[fig:z_relative_disp]] in the Z direction).
#+begin_src matlab
#+begin_src matlab :exports results
figure;
hold on;
plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z');
@ -159,7 +174,7 @@ We also integrate the relative velocity to obtain the relative displacement (fig
#+RESULTS: fig:ty_z_time
[[file:figs/ty_z_time.png]]
#+begin_src matlab
#+begin_src matlab :exports results
figure;
hold on;
plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X');
@ -181,11 +196,15 @@ We also integrate the relative velocity to obtain the relative displacement (fig
#+RESULTS: fig:ty_e_time
[[file:figs/ty_e_time.png]]
#+begin_src matlab
#+begin_src matlab :exports results
figure;
plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)));
hold on;
plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)), 'DisplayName', 'Ty Scan');
plot(e_of(:, 3), 1e6*lsim(1/s, e_of(:, 2)-e_of(:, 1), e_of(:, 3)), 'DisplayName', 'Ty OFF');
hold off;
xlabel('Time [s]'); ylabel('X Relative Displacement [$\mu m$]');
xlim([0, 2]);
legend('location', 'southeast');
#+end_src
#+NAME: fig:x_relative_disp
@ -199,9 +218,12 @@ We also integrate the relative velocity to obtain the relative displacement (fig
#+RESULTS: fig:x_relative_disp
[[file:figs/x_relative_disp.png]]
#+begin_src matlab
#+begin_src matlab :exports results
figure;
plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)));
hold on;
plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)), 'DisplayName', 'Ty Scan');
plot(z_of(:, 3), 1e6*lsim(1/s, z_of(:, 2)-z_of(:, 1), z_of(:, 3)), 'DisplayName', 'Ty OFF');
hold off;
xlabel('Time [s]'); ylabel('Z Relative Displacement [$\mu m$]');
xlim([0, 2]);
#+end_src
@ -217,10 +239,10 @@ We also integrate the relative velocity to obtain the relative displacement (fig
#+RESULTS: fig:z_relative_disp
[[file:figs/z_relative_disp.png]]
** Frequency Domain analysis
We get the typical ground velocity to compare with the velocities measured.
** Frequency Domain
We load measured ground motion at ID31 to compare with the velocities measured.
#+begin_src matlab
[pxx_gm, f_gm] = getPSDGroundVelocity();
gm = load('../ground-motion/mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv');
#+end_src
We first compute some parameters that will be used for the PSD computation.
@ -236,37 +258,31 @@ Then we compute the Power Spectral Density using =pwelch= function.
First for the geophone located on the marble
#+begin_src matlab
[pxz_ty_m, f] = pwelch(z_ty(:, 1), win, [], [], Fs);
[pxe_ty_m, ~] = pwelch(e_ty(:, 1), win, [], [], Fs);
[pxe_of_m, ~] = pwelch(e_of(:, 1), win, [], [], Fs);
[pxz_ty_m, f] = pwelch(z_ty(:, 1), win, [], gm.f, Fs);
[pxz_of_m, ~] = pwelch(z_of(:, 1), win, [], gm.f, Fs);
[pxe_ty_m, ~] = pwelch(e_ty(:, 1), win, [], gm.f, Fs);
[pxe_of_m, ~] = pwelch(e_of(:, 1), win, [], gm.f, Fs);
#+end_src
And for the geophone located at the sample position.
#+begin_src matlab
[pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], [], Fs);
[pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs);
[pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs);
#+end_src
And finally for the relative velocity between the sample and the marble.
#+begin_src matlab
[pxz_ty_r, ~] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], [], Fs);
[pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], [], Fs);
[pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], [], Fs);
[pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], gm.f, Fs);
[pxz_of_s, ~] = pwelch(z_of(:, 2), win, [], gm.f, Fs);
[pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], gm.f, Fs);
[pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], gm.f, Fs);
#+end_src
And we plot the ASD of the measured velocities:
- figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
- figure [[fig:asd_e_relative]] shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz
#+begin_src matlab
#+begin_src matlab :exports results
figure;
hold on;
plot(f, sqrt(pxe_ty_m), 'DisplayName', 'Ty 1Hz - Marble - X');
plot(f, sqrt(pxe_of_m), 'DisplayName', 'Ty OFF - Marble - X');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
plot(gm.f, sqrt(gm.psd_gv), 'k--', 'DisplayName', 'Ground Motion');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
@ -287,12 +303,12 @@ And we plot the ASD of the measured velocities:
[[file:figs/asd_east_marble.png]]
#+begin_src matlab
#+begin_src matlab :exports results
figure;
hold on;
plot(f, sqrt(pxe_ty_s), 'DisplayName', 'Ty 1Hz - Sample - X');
plot(f, sqrt(pxe_of_s), 'DisplayName', 'Ty OFF - Sample - X');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
plot(gm.f, sqrt(gm.psd_gv), 'k--', 'DisplayName', 'Ground Motion');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
@ -313,12 +329,12 @@ And we plot the ASD of the measured velocities:
[[file:figs/asd_east_sample.png]]
#+begin_src matlab
#+begin_src matlab :exports results
figure;
hold on;
plot(f, sqrt(pxz_ty_m), 'DisplayName', 'Ty 1Hz - Marble - Z');
plot(f, sqrt(pxz_ty_s), 'DisplayName', 'Ty 1Hz - Sample - Z');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
plot(f, sqrt(pxz_of_m), 'DisplayName', 'Ty OFF - Marble - Z');
plot(gm.f, sqrt(gm.psd_gv), 'k--', 'DisplayName', 'Ground Motion');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
@ -338,8 +354,79 @@ And we plot the ASD of the measured velocities:
#+RESULTS: fig:asd_z_direction
[[file:figs/asd_z_direction.png]]
#+begin_src matlab :exports results
figure;
hold on;
plot(f, sqrt(pxz_ty_s), 'DisplayName', 'Ty 1Hz - Sample - Z');
plot(f, sqrt(pxz_of_s), 'DisplayName', 'Ty OFF - Sample - Z');
plot(gm.f, sqrt(gm.psd_gv), 'k--', 'DisplayName', 'Ground Motion');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest');
xlim([0.1, 500]);
#+end_src
#+NAME: fig:asd_z_direction
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/asd_z_direction.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:asd_z_direction
#+CAPTION: Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz
#+RESULTS: fig:asd_z_direction
[[file:figs/asd_z_direction.png]]
** Relative Motion
And finally for the relative velocity between the sample and the marble.
#+begin_src matlab
[pxz_ty_r, f] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], gm.f, Fs);
[pxz_of_r, ~] = pwelch(z_of(:, 2)-z_of(:, 1), win, [], gm.f, Fs);
[pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], gm.f, Fs);
[pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], gm.f, Fs);
#+end_src
Fig. [[fig:asd_e_relative]] shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz
#+begin_src matlab :export results
figure;
hold on;
plot(f, sqrt(pxz_of_r), 'DisplayName', 'Ty OFF - Relative - Z');
plot(f, sqrt(pxz_of_s), 'DisplayName', 'Ty 1Hz - Relative - Z');
plot(f, sqrt(pxz_of_m), 'DisplayName', 'Ty 1Hz - Relative - Z');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest');
xlim([0.1, 500]);
#+end_src
#+begin_src matlab :export results
figure;
hold on;
plot(f, sqrt(pxz_of_r), 'DisplayName', 'Ty OFF - Relative - Z');
plot(f, sqrt(pxz_ty_r), 'DisplayName', 'Ty 1Hz - Relative - Z');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest');
xlim([0.1, 500]);
#+end_src
#+NAME: fig:asd_z_relative
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/asd_z_relative.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:asd_z_relative
#+CAPTION: Amplitude spectral density of the measured relative velocity in the X direction
#+RESULTS: fig:asd_z_relative
[[file:figs/asd_z_relative.png]]
#+begin_src matlab :export results
figure;
hold on;
plot(f, sqrt(pxe_of_r), 'DisplayName', 'Ty OFF - Relative - E');
@ -363,7 +450,14 @@ And we plot the ASD of the measured velocities:
#+RESULTS: fig:asd_e_relative
[[file:figs/asd_e_relative.png]]
** Transfer function from marble motion in the East direction to sample motion in the East direction
** Save
The Power Spectral Density of the relative velocity is saved for further analysis.
#+begin_src matlab
save('mat/pxz_ty_r.mat', 'f', 'pxz_ty_r', 'pxz_ty_s');
save('mat/pxe_ty_r.mat', 'f', 'pxe_ty_r', 'pxe_ty_s');
#+end_src
** Transfer function from marble motion in the East direction to sample motion in the East direction :noexport:
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.
We first plot the time domain motions when every stage is off (figure [[fig:east_marble_sample]]).

BIN
disturbance-ty/mat/data_051.mat Normal file
View File

Binary file not shown.

BIN
disturbance-ty/mat/pxe_ty_r.mat Normal file
View File

Binary file not shown.

BIN
disturbance-ty/mat/pxz_ty_r.mat Normal file
View File

Binary file not shown.

2
disturbance-ty/matlab/disturbance_ty.m
View File

@ -11,7 +11,7 @@ e_ty = load('mat/data_041.mat', 'data'); e_ty = e_ty.data;
e_of = load('mat/data_042.mat', 'data'); e_of = e_of.data;
% Voltage to Velocity
% We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
% We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/Cloud/thesis/meas/srcindex.org][here]]).
gain = 40; % [dB]

3
ground-motion/figs/nohup.out
View File

@ -1,3 +0,0 @@
invalid color string: rgba(50, 48, 47)
(termite:1468): GLib-WARNING **: 17:39:09.552: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.

3
ground-motion/img/nohup.out
View File

@ -1,3 +0,0 @@
invalid color string: rgba(50, 48, 47)
(termite:29687): GLib-WARNING **: 17:42:45.114: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.

2
huddle-test-geophones/matlab/huddle_test_compare_axis.m
View File

@ -1,6 +1,6 @@
% Matlab Init :noexport:ignore:
current_dir='/home/thomas/MEGA/These/meas/huddle-test-geophones/';
current_dir='/home/thomas/Cloud/thesis/meas/huddle-test-geophones';
%% Go to current Directory
cd(current_dir);

2
huddle-test-geophones/matlab/huddle_test_signal_processing.m
View File

@ -1,6 +1,6 @@
% Matlab Init :noexport:ignore:
current_dir='/home/thomas/MEGA/These/meas/huddle-test-geophones/';
current_dir='/home/thomas/Cloud/thesis/meas/huddle-test-geophones';
%% Go to current Directory
cd(current_dir);

2
instrumentation/index.org
View File

@ -349,7 +349,7 @@ The values of the components are:
Which makes a cut-off frequency of $f_c = \frac{1}{RC} = 1000 rad/s = 160Hz$.
#+NAME: fig:lpf
#+HEADER: :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/These/LaTeX/}{config.tex}")
#+HEADER: :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+HEADER: :imagemagick t :fit yes :iminoptions -scale 100% -density 150 :imoutoptions -quality 100
#+HEADER: :results raw replace :buffer no :eval no-export :exports both :mkdirp yes
#+HEADER: :output-dir figs

BIN
modal-analysis/data/modal_frf_coh.zip
View File

Binary file not shown.

2
modal-analysis/frf_processing.org
View File

@ -30,7 +30,7 @@
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/These/LaTeX/}{config.tex}")
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100

37
modal-analysis/mat/mode_damps.txt
View File

@ -1,21 +1,16 @@
8.72664
11.75321
6.44322
3.60695
0.24170
2.83603
4.60472
0.64145
1.58544
3.56361
0.26865
2.86851
3.30737
3.27213
1.89158
3.02795
2.71094
0.56008
1.64638
2.17368
1.39142
12.20318
11.66888
6.19561
2.79104
2.76253
4.34928
1.25546
3.65470
2.94088
3.19084
1.55526
3.13166
2.76141
1.34304
2.43201
1.38400

37
modal-analysis/mat/mode_freqs.txt
View File

@ -1,21 +1,16 @@
11.41275
18.51409
37.58431
39.43487
53.99524
56.14871
69.68561
71.58533
72.35341
84.92538
90.56538
91.00542
95.76079
105.43696
106.76771
112.58508
116.84928
124.13356
145.35893
150.10734
164.65885
11.86509
18.55747
37.82163
39.07850
56.31944
69.78452
72.49325
84.83446
91.26350
105.47266
106.57165
112.67669
124.20538
145.30034
150.52113
165.42632

37
modal-analysis/mat/mode_modal_a.txt
View File

@ -1,21 +1,16 @@
-4.50556e+003 -9.41744e+003
-1.56119e+003 -1.64408e+004
1.24918e+004 -2.00022e+004
-1.83730e+004 +8.73583e+004
-6.02120e+005 -5.53574e+004
-8.13722e+003 -4.17194e+004
9.12802e+003 -3.78264e+004
1.83523e+005 -5.45837e+005
-1.85481e+005 -8.15852e+004
-6.44647e+003 -3.91843e+004
2.02548e+005 -4.85436e+005
-1.54209e+002 -3.09920e+004
2.10759e+004 -1.47578e+004
-8.03639e+003 -7.00743e+004
1.73222e+005 +1.94075e+005
5.46351e+003 -9.46357e+003
-2.00775e+004 +5.23111e+004
-6.04037e+004 -8.70001e+004
1.50266e+004 -1.61655e+005
1.66427e+005 +1.73772e+005
-2.41033e+005 +2.81618e+005
4.13559e+003 +6.22828e+003
2.76278e+002 +1.74197e+004
-1.32270e+004 +2.17346e+004
-2.48397e+005 -1.60998e+005
-4.23967e+004 +7.06852e+004
-7.36964e+003 +4.57024e+004
1.37806e+005 +3.00336e+005
-1.31109e+004 +2.81759e+004
5.59259e+003 -4.27543e+004
-5.28869e+004 +6.38436e+003
3.71578e+004 +1.57745e+004
-4.24659e+004 +7.90956e+003
-3.57355e+004 +1.13161e+005
5.24764e+004 -1.45211e+005
1.97228e+005 +2.51758e+005
-3.00273e+005 +3.27201e+005

37
modal-analysis/mat/mode_modal_b.txt
View File

@ -1,21 +1,16 @@
-7.00928e+005 +2.62922e+005
-1.92061e+006 -4.44325e+004
-4.52363e+006 -3.24813e+006
2.14671e+007 +5.33018e+006
-1.92744e+007 +2.04231e+008
-1.47938e+007 +2.45218e+006
-1.63606e+007 -4.75508e+006
-2.44974e+008 -8.41188e+007
-3.84216e+007 +8.37228e+007
-2.10181e+007 +2.69256e+006
-2.75921e+008 -1.15999e+008
-1.77166e+007 -4.20197e+005
-8.45524e+006 -1.29677e+007
-4.65722e+007 +3.80208e+006
1.32368e+008 -1.13721e+008
-6.57437e+006 -4.06578e+006
3.79924e+007 +1.57763e+007
-6.81189e+007 +4.67313e+007
-1.47397e+008 -1.61530e+007
1.67266e+008 -1.53366e+008
2.87859e+008 +2.53398e+008
4.98475e+005 -2.49344e+005
2.02102e+006 +2.05017e+005
4.96035e+006 +3.45724e+006
-4.12180e+007 +5.98638e+007
2.45891e+007 +1.56880e+007
1.98796e+007 +4.09986e+006
1.37577e+008 -6.10466e+007
1.47532e+007 +7.53272e+006
-2.44115e+007 -3.92655e+006
3.11045e+006 +3.51656e+007
1.09485e+007 -2.47140e+007
4.65546e+006 +3.02251e+007
8.75076e+007 +3.03162e+007
-1.31915e+008 -4.96844e+007
2.42567e+008 -1.80683e+008
3.35742e+008 +3.16782e+008

2553
modal-analysis/mat/mode_shapes.txt
View File

File diff suppressed because it is too large Load Diff

2
modal-analysis/mathematical_model.org
View File

@ -28,7 +28,7 @@
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/These/LaTeX/}{config.tex}")
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100

2
modal-analysis/measurement.org
View File

@ -30,7 +30,7 @@
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/These/LaTeX/}{config.tex}")
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100

2
modal-analysis/modal_extraction.org
View File

@ -30,7 +30,7 @@
#+PROPERTY: header-args:shell :eval no-export
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/These/LaTeX/}{config.tex}")
#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}")
#+PROPERTY: header-args:latex+ :imagemagick t :fit yes
#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150
#+PROPERTY: header-args:latex+ :imoutoptions -quality 100

3
slip-ring-electrical-noise/img/nohup.out
View File

@ -1,3 +0,0 @@
invalid color string: rgba(50, 48, 47)
(termite:25037): GLib-WARNING **: 14:10:26.520: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.

2
slip-ring-electrical-noise/index.org
View File

@ -29,6 +29,7 @@
#+PROPERTY: header-args:shell :eval no-export
:END:
* Introduction :ignore:
The noise induced by the slip-ring is measured when using geophones:
- Section [[sec:meas_slip_ring_geophone]]:
- A geophone located at the sample location is measured with its signal going directly to the ADC and going through the slip-ring
@ -65,7 +66,6 @@ The noise induced by the slip-ring is measured when using geophones:
*Goal*:
The goal is to determine if some noise is added to a signal passing through the slip-ring.
*Setup*:
Two measurements are made with the control systems of all the stages turned OFF.

8
slip-ring-electrical-noise/readme.org
View File

@ -1,5 +1,5 @@
* DONE Measure of the noise of the Voltage Amplifier
CLOSED: [2019-05-06 lun. 09:00]
CLOSED: [2019-05-06 lun. 09:00]
- The two inputs (differential) of the voltage amplifier are shunted with 50Ohms
- The AC/DC option of the Voltage amplifier is on AC
- The low pass filter is set to 1hHz
@ -13,7 +13,7 @@ meas6: Ampli ON 60dB
meas7: Ampli ON 80dB
* DONE Measure of the noise induced by the Slip-Ring
CLOSED: [2019-05-06 lun. 09:28]
CLOSED: [2019-05-06 lun. 09:28]
Setup:
- 0V is generated by the DAC of the Speedgoat
- Using a T, one part goes to ADC
@ -33,7 +33,7 @@ Measurements:
- meas11: Slip-Ring ON and omega=60rpm
* DONE Measure of the noise induced by the slip ring when using a geophone
CLOSED: [2019-05-06 lun. 09:28]
CLOSED: [2019-05-06 lun. 09:28]
The geophone is located at the sample location
The two Voltage amplifiers have the following settings:
- AC
@ -58,7 +58,7 @@ Redone the measurements with 1kHz additional low pass filter:
- meas17: Slip-Ring ON
* DONE Measure of the influence of the AC/DC option on the voltage amplifiers
CLOSED: [2019-05-06 lun. 09:28]
CLOSED: [2019-05-06 lun. 09:28]
One geophone is located on the marble.
It's signal goes to two voltage amplifiers with a gain of 60dB.
On voltage amplifier is on the AC option, the other on the DC option.

3
slip-ring-noise-turning/img/nohup.out
View File

@ -1,3 +0,0 @@
invalid color string: rgba(50, 48, 47)
(termite:25037): GLib-WARNING **: 14:10:26.520: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.

8
slip-ring-noise-turning/readme.org
View File

@ -1,5 +1,5 @@
* DONE Measure of the noise of the Voltage Amplifier
CLOSED: [2019-05-06 lun. 09:00]
CLOSED: [2019-05-06 lun. 09:00]
- The two inputs (differential) of the voltage amplifier are shunted with 50Ohms
- The AC/DC option of the Voltage amplifier is on AC
- The low pass filter is set to 1hHz
@ -13,7 +13,7 @@ meas6: Ampli ON 60dB
meas7: Ampli ON 80dB
* DONE Measure of the noise induced by the Slip-Ring
CLOSED: [2019-05-06 lun. 09:28]
CLOSED: [2019-05-06 lun. 09:28]
Setup:
- 0V is generated by the DAC of the Speedgoat
- Using a T, one part goes to ADC
@ -33,7 +33,7 @@ Measurements:
- meas11: Slip-Ring ON and omega=60rpm
* DONE Measure of the noise induced by the slip ring when using a geophone
CLOSED: [2019-05-06 lun. 09:28]
CLOSED: [2019-05-06 lun. 09:28]
The geophone is located at the sample location
The two Voltage amplifiers have the following settings:
- AC
@ -58,7 +58,7 @@ Redone the measurements with 1kHz additional low pass filter:
- meas17: Slip-Ring ON
* DONE Measure of the influence of the AC/DC option on the voltage amplifiers
CLOSED: [2019-05-06 lun. 09:28]
CLOSED: [2019-05-06 lun. 09:28]
One geophone is located on the marble.
It's signal goes to two voltage amplifiers with a gain of 60dB.
On voltage amplifier is on the AC option, the other on the DC option.

3
static-spindle/figs/nohup.out
View File

@ -1,3 +0,0 @@
invalid color string: rgba(50, 48, 47)
(termite:2378): GLib-WARNING **: 15:04:00.329: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.