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Add analysis about simultaneous rotation and translation

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Thomas Dehaeze 2019-05-15 15:49:48 +02:00
parent dd484e8a3b
commit df4d100ddf
25 changed files with 1054 additions and 141 deletions
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51
disturbance-sr-rz/index.org
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@ -97,11 +97,12 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
addpath('../src');
#+end_src #+end_src
#+begin_src matlab :exports none :results silent :noweb yes #+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>> <<matlab-init>>
#+end_src #+end_src
** Load data ** Load data
@ -111,6 +112,19 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
sp = load('mat/data_026.mat', 'data'); sp = sp.data; sp = load('mat/data_026.mat', 'data'); sp = sp.data;
#+end_src #+end_src
** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
#+begin_src matlab
of(:, 1) = voltageToVelocityL22(of(:, 1), of(:, 3), 60);
sr(:, 1) = voltageToVelocityL22(sr(:, 1), sr(:, 3), 60);
sp(:, 1) = voltageToVelocityL22(sp(:, 1), sp(:, 3), 60);
of(:, 2) = voltageToVelocityL22(of(:, 2), of(:, 3), 60);
sr(:, 2) = voltageToVelocityL22(sr(:, 2), sr(:, 3), 60);
sp(:, 2) = voltageToVelocityL22(sp(:, 2), sp(:, 3), 60);
#+end_src
** Time domain plots ** Time domain plots
#+begin_src matlab #+begin_src matlab
figure; figure;
@ -119,8 +133,8 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
plot(sr(:, 3), sr(:, 1), 'DisplayName', 'Slip-Ring - 6rpm'); plot(sr(:, 3), sr(:, 1), 'DisplayName', 'Slip-Ring - 6rpm');
plot(of(:, 3), of(:, 1), 'DisplayName', 'OFF'); plot(of(:, 3), of(:, 1), 'DisplayName', 'OFF');
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); ylim([-10 10]); xlim([0, 100]);
legend('Location', 'northeast'); legend('Location', 'northeast');
#+end_src #+end_src
@ -131,7 +145,7 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
#+end_src #+end_src
#+NAME: fig:slip_ring_spindle_marble_time #+NAME: fig:slip_ring_spindle_marble_time
#+CAPTION: Measurement of the geophone located on the marble - Time domain #+CAPTION: Velocity as measured by the geophone located on the marble - Time domain
#+RESULTS: fig:slip_ring_spindle_marble_time #+RESULTS: fig:slip_ring_spindle_marble_time
[[file:figs/slip_ring_spindle_marble_time.png]] [[file:figs/slip_ring_spindle_marble_time.png]]
@ -142,8 +156,8 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
plot(sr(:, 3), sr(:, 2), 'DisplayName', 'Only Slip-Ring'); plot(sr(:, 3), sr(:, 2), 'DisplayName', 'Only Slip-Ring');
plot(of(:, 3), of(:, 2), 'DisplayName', 'OFF'); plot(of(:, 3), of(:, 2), 'DisplayName', 'OFF');
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); ylim([-10 10]); xlim([0, 100]);
legend('Location', 'northeast'); legend('Location', 'northeast');
#+end_src #+end_src
@ -154,7 +168,7 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
#+end_src #+end_src
#+NAME: fig:slip_ring_spindle_sample_time #+NAME: fig:slip_ring_spindle_sample_time
#+CAPTION: Measurement of the geophone at the sample location - Time domain #+CAPTION: Velocity as measured by the geophone at the sample location - Time domain
#+RESULTS: fig:slip_ring_spindle_sample_time #+RESULTS: fig:slip_ring_spindle_sample_time
[[file:figs/slip_ring_spindle_sample_time.png]] [[file:figs/slip_ring_spindle_sample_time.png]]
@ -184,7 +198,7 @@ And for the geophone located at the sample position.
[pxsp_s, ~] = pwelch(sp(:, 2), win, [], [], Fs); [pxsp_s, ~] = pwelch(sp(:, 2), win, [], [], Fs);
#+end_src #+end_src
And we plot the ASD of the measured signals: 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_marble_compare]] for the geophone located on the marble
- figure [[fig:sr_sp_psd_sample_compare]] for the geophone at the sample position - figure [[fig:sr_sp_psd_sample_compare]] for the geophone at the sample position
@ -197,9 +211,9 @@ And we plot the ASD of the measured signals:
hold off; hold off;
set(gca, 'xscale', 'log'); set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$') xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest'); legend('Location', 'southwest');
xlim([0.1, 500]); xlim([2, 500]);
#+end_src #+end_src
#+NAME: fig:sr_sp_psd_marble_compare #+NAME: fig:sr_sp_psd_marble_compare
@ -209,7 +223,7 @@ And we plot the ASD of the measured signals:
#+end_src #+end_src
#+NAME: fig:sr_sp_psd_marble_compare #+NAME: fig:sr_sp_psd_marble_compare
#+CAPTION: Comparison of the ASD of the measured voltage from the Geophone on the marble #+CAPTION: Comparison of the ASD of the measured velocities from the Geophone on the marble
#+RESULTS: fig:sr_sp_psd_marble_compare #+RESULTS: fig:sr_sp_psd_marble_compare
[[file:figs/sr_sp_psd_marble_compare.png]] [[file:figs/sr_sp_psd_marble_compare.png]]
@ -222,9 +236,9 @@ And we plot the ASD of the measured signals:
hold off; hold off;
set(gca, 'xscale', 'log'); set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$') xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest'); legend('Location', 'southwest');
xlim([0.1, 500]); xlim([2, 500]);
#+end_src #+end_src
#+NAME: fig:sr_sp_psd_sample_compare #+NAME: fig:sr_sp_psd_sample_compare
@ -234,14 +248,15 @@ And we plot the ASD of the measured signals:
#+end_src #+end_src
#+NAME: fig:sr_sp_psd_sample_compare #+NAME: fig:sr_sp_psd_sample_compare
#+CAPTION: Comparison of the ASD of the measured voltage from the Geophone at the sample location #+CAPTION: Comparison of the ASD of the measured velocities from the Geophone at the sample location
#+RESULTS: fig:sr_sp_psd_sample_compare #+RESULTS: fig:sr_sp_psd_sample_compare
[[file:figs/sr_sp_psd_sample_compare.png]] [[file:figs/sr_sp_psd_sample_compare.png]]
** Conclusion ** Conclusion
#+begin_important #+begin_important
The slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz. - The slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz.
The spindle rotation induces a lot of vibrations of the sample as well as on the granite. - 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. - 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 #+end_important

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disturbance-ty-sr/index.html
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2019-05-15 mer. 08:38 --> <!-- 2019-05-15 mer. 15:49 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by simultaneous scans of the translation stage and of the slip-ring</title> <title>Vibrations induced by simultaneous scans of the translation stage and of the slip-ring</title>
@ -258,19 +258,28 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org8a17ec6">1. Measurement description</a></li> <li><a href="#orge303e87">1. Measurement description</a></li>
<li><a href="#orgf15470a">2. Data Analysis</a> <li><a href="#orgc23d6dc">2. Data Analysis</a>
<ul> <ul>
<li><a href="#org2066778">2.1. Load data</a></li> <li><a href="#org629d4b4">2.1. Load data</a></li>
<li><a href="#org5bdcb1d">2.2. Time domain plots</a></li> <li><a href="#org79a2c27">2.2. Voltage to Velocity</a></li>
<li><a href="#org1bafa09">2.3. Time domain plots</a></li>
<li><a href="#org05973bc">2.4. Frequency Domain</a></li>
<li><a href="#org57188a5">2.5. Ty motion and current</a>
<ul>
<li><a href="#org07bb77c">2.5.1. Data pre-processing</a></li>
<li><a href="#org8bcb0f7">2.5.2. Time domain data</a></li>
</ul>
</li>
<li><a href="#org005d22e">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org8a17ec6" class="outline-2"> <div id="outline-container-orge303e87" class="outline-2">
<h2 id="org8a17ec6"><span class="section-number-2">1</span> Measurement description</h2> <h2 id="orge303e87"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
@ -375,11 +384,11 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-orgf15470a" class="outline-2"> <div id="outline-container-orgc23d6dc" class="outline-2">
<h2 id="orgf15470a"><span class="section-number-2">2</span> Data Analysis</h2> <h2 id="orgc23d6dc"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="orgd07fa1b"></a> <a id="org4563c51"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -389,63 +398,377 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div> </div>
</div> </div>
<div id="outline-container-org2066778" class="outline-3"> <div id="outline-container-org629d4b4" class="outline-3">
<h3 id="org2066778"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org629d4b4"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">ty_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_050.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_off = ty_off.data; <pre class="src src-matlab">ty_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_050.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_of = ty_of.data;
ty_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_on = ty_on.data; ty_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_on = ty_on.data;
ty_1hz = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_052.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_1hz = ty_1hz.data; ty_1h = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_052.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_1h = ty_1h.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org5bdcb1d" class="outline-3"> <div id="outline-container-org79a2c27" class="outline-3">
<h3 id="org5bdcb1d"><span class="section-number-3">2.2</span> Time domain plots</h3> <h3 id="org79a2c27"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2"> <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/MEGA/These/meas/src/index.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>
ty_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>ty_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>, ty_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>;
ty_on<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>ty_on<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>, ty_on<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>;
ty_1h<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>ty_1h<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>, ty_1h<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>;
ty_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>ty_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>, ty_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>;
ty_on<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>ty_on<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>, ty_on<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>;
ty_1h<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>ty_1h<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>, ty_1h<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-org1bafa09" class="outline-3">
<h3 id="org1bafa09"><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 (figure <a href="#org53f1c30">1</a>), sample (figure <a href="#org6938117">2</a>) and the relative velocity of the sample with respect to the marble (figure <a href="#orgfd8af3e">3</a>).
</p>
<p>
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#org425e005">4</a>).
</p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1hz<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>, ty_1hz<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>ty_1h<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>, ty_1h<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', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>, ty_on<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>ty_on<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>, ty_on<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 - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_off<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>, ty_off<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>ty_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>, ty_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 - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off; 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>; 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>; 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">5</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>; 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>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div class="org-src-container">
<pre class="src src-matlab">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-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <div id="org53f1c30" class="figure">
</pre> <p><img src="figs/ty_marble_time.png" alt="ty_marble_time.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Velocity of the marble in the vertical direction</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1hz<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>, ty_1hz<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', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<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>, ty_1h<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>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>, ty_on<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', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>, ty_on<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 - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_off<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>, ty_off<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', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_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>, ty_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 - Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off; 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>; 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>; 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">5</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>; 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>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="org6938117" class="figure">
<p><img src="figs/ty_sample_time.png" alt="ty_sample_time.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Velocity of the sample in the vertical direction</p>
</div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">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-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<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>, ty_1h<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>ty_1h<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', 'Relative Velocity <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>, ty_on<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>ty_on<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', 'Relative Velocity - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_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>, ty_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>ty_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', 'Relative Velocity - Ty - 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">'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', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="orgfd8af3e" class="figure">
<p><img src="figs/ty_relative_time.png" alt="ty_relative_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Relative velocity 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>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<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>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_1h<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>ty_1h<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>, ty_1h<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>, 'DisplayName', 'Relative Displacement<span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_on<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>ty_on<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>, ty_on<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-string">'DisplayName', 'Relative Displacement- Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_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>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_of<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>ty_of<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>, ty_of<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-string">'DisplayName', 'Relative Displacement- Ty - 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">'Displacement </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m</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', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org425e005" class="figure">
<p><img src="figs/ty_relative_disp_time.png" alt="ty_relative_disp_time.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Relative Displacement of the sample with respect to the marble</p>
</div>
</div>
</div>
<div id="outline-container-org05973bc" class="outline-3">
<h3 id="org05973bc"><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 = ty_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>ty_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>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<p>
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>pxof_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_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>pxon_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>px1h_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<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 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>ty_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>pxon_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>px1h_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<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>
Finally, for the relative velocity.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_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>ty_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>pxon_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<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>ty_on<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>px1h_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<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>ty_1h<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="#org00eb9e9">5</a> for the geophone located on the marble</li>
<li>figure <a href="#org192c441">6</a> for the geophone at the sample position</li>
<li>figure <a href="#org1b88cd2">7</a> for the relative velocity</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>px1h_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</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>pxon_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty ON'</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', 'Marble - Ty 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 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', '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">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="org00eb9e9" class="figure">
<p><img src="figs/psd_marble_compare.png" alt="psd_marble_compare.png" />
</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>px1h_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</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>pxon_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty ON'</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', 'Sample - Ty 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 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', '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">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="org192c441" class="figure">
<p><img src="figs/psd_sample_compare.png" alt="psd_sample_compare.png" />
</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>
<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>px1h_r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</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>pxon_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative - Ty ON'</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', 'Relative - Ty 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 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', '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">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="org1b88cd2" class="figure">
<p><img src="figs/psd_relative_compare.png" alt="psd_relative_compare.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Comparison of the ASD of the relative velocity</p>
</div>
</div>
</div>
<div id="outline-container-org57188a5" class="outline-3">
<h3 id="org57188a5"><span class="section-number-3">2.5</span> Ty motion and current</h3>
<div class="outline-text-3" id="text-2-5">
<p>
The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
</p>
</div>
<div id="outline-container-org07bb77c" class="outline-4">
<h4 id="org07bb77c"><span class="section-number-4">2.5.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-5-1">
<p>
Let's look at at the start of the csv file.
</p>
<div class="org-src-container">
<pre class="src src-bash">sed -n <span class="org-highlight-numbers-number">1,30p</span> mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
</pre>
</div>
<p>
The real data starts at line 29.
We then load this <code>cvs</code> file starting at line 29.
</p>
<div class="org-src-container">
<pre class="src src-matlab">tye_on = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
tye_1h = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span><span class="org-type">-</span>and<span class="org-type">-</span>Ty<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org8bcb0f7" class="outline-4">
<h4 id="org8bcb0f7"><span class="section-number-4">2.5.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-5-2">
<p>
We plot the position of the translation stage measured by the encoders.
</p>
<p>
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
</p>
<p>
The result is shown on figure <a href="#orgfeb408e">8</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<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-rainbow-delimiters-depth-2">(</span>tye_on<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>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_on<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</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-type">/</span><span class="org-highlight-numbers-number">200000</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">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>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<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-rainbow-delimiters-depth-2">(</span>tye_1h<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>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_1h<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</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-type">/</span><span class="org-highlight-numbers-number">200000</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">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>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgfeb408e" class="figure">
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Y position of the translation stage measured by the encoders</p>
</div>
<p>
We also plot the current as function of the time on figure <a href="#orgbd294dc">9</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<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>, tye_on<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-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_on<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>;
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">'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>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<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>, tye_1h<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-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_1h<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>;
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">'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>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgbd294dc" class="figure">
<p><img src="figs/ty_current_time.png" alt="ty_current_time.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Current going through the actuator of the translation stage</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org005d22e" class="outline-3">
<h3 id="org005d22e"><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">
<li></li>
</ul>
</div>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-15 mer. 08:38</p> <p class="date">Created: 2019-05-15 mer. 15:49</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>

362
disturbance-ty-sr/index.org
View File

@ -93,6 +93,7 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
addpath('../src');
#+end_src #+end_src
#+begin_src matlab :exports none :results silent :noweb yes #+begin_src matlab :exports none :results silent :noweb yes
@ -101,40 +102,351 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
** Load data ** Load data
#+begin_src matlab #+begin_src matlab
ty_off = load('mat/data_050.mat', 'data'); ty_off = ty_off.data; ty_of = load('mat/data_050.mat', 'data'); ty_of = ty_of.data;
ty_on = load('mat/data_051.mat', 'data'); ty_on = ty_on.data; ty_on = load('mat/data_051.mat', 'data'); ty_on = ty_on.data;
ty_1hz = load('mat/data_052.mat', 'data'); ty_1hz = ty_1hz.data; ty_1h = load('mat/data_052.mat', 'data'); ty_1h = ty_1h.data;
#+end_src
** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
#+begin_src matlab
gain = 40; % [dB]
ty_of(:, 1) = voltageToVelocityL22(ty_of(:, 1), ty_of(:, 3), gain);
ty_on(:, 1) = voltageToVelocityL22(ty_on(:, 1), ty_on(:, 3), gain);
ty_1h(:, 1) = voltageToVelocityL22(ty_1h(:, 1), ty_1h(:, 3), gain);
ty_of(:, 2) = voltageToVelocityL22(ty_of(:, 2), ty_of(:, 3), gain);
ty_on(:, 2) = voltageToVelocityL22(ty_on(:, 2), ty_on(:, 3), gain);
ty_1h(:, 2) = voltageToVelocityL22(ty_1h(:, 2), ty_1h(:, 3), gain);
#+end_src #+end_src
** Time domain plots ** Time domain plots
#+begin_src matlab We plot the measured velocity of the marble (figure [[fig:ty_marble_time]]), sample (figure [[fig:ty_sample_time]]) and the relative velocity of the sample with respect to the marble (figure [[fig:ty_relative_time]]).
figure;
hold on;
plot(ty_1hz(:, 3), ty_1hz(:, 1), 'DisplayName', 'Marble - Z');
plot(ty_on(:, 3), ty_on(:, 1), 'DisplayName', 'Marble - Z');
plot(ty_off(:, 3), ty_off(:, 1), 'DisplayName', 'Marble - Z');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-5, 5]);
legend('Location', 'northeast');
#+end_src
#+begin_src matlab We also integrate the relative velocity to obtain the relative displacement (figure [[fig:ty_relative_disp_time]]).
xlim([0, 1]);
#+end_src
#+begin_src matlab #+begin_src matlab
figure; figure;
hold on; hold on;
plot(ty_1hz(:, 3), ty_1hz(:, 2), 'DisplayName', 'Marble - Z'); plot(ty_1h(:, 3), ty_1h(:, 1), 'DisplayName', 'Marble - Ty 1Hz');
plot(ty_on(:, 3), ty_on(:, 2), 'DisplayName', 'Marble - Z'); plot(ty_on(:, 3), ty_on(:, 1), 'DisplayName', 'Marble - Ty ON');
plot(ty_off(:, 3), ty_off(:, 2), 'DisplayName', 'Marble - Z'); plot(ty_of(:, 3), ty_of(:, 1), 'DisplayName', 'Marble - Ty OFF');
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); ylim([-5, 5]); xlim([0, 2]);
legend('Location', 'northeast'); legend('Location', 'southwest');
#+end_src #+end_src
#+begin_src matlab #+NAME: fig:ty_marble_time
xlim([0, 1]); #+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_marble_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src #+end_src
#+NAME: fig:ty_marble_time
#+CAPTION: Velocity of the marble in the vertical direction
#+RESULTS: fig:ty_marble_time
[[file:figs/ty_marble_time.png]]
#+begin_src matlab
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2), 'DisplayName', 'Sample - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2), 'DisplayName', 'Sample - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2), 'DisplayName', 'Sample - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 2]);
legend('Location', 'southwest');
#+end_src
#+NAME: fig:ty_sample_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_sample_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_sample_time
#+CAPTION: Velocity of the sample in the vertical direction
#+RESULTS: fig:ty_sample_time
[[file:figs/ty_sample_time.png]]
#+begin_src matlab
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2)-ty_1h(:, 1), 'DisplayName', 'Relative Velocity - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2)-ty_on(:, 1), 'DisplayName', 'Relative Velocity - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2)-ty_of(:, 1), 'DisplayName', 'Relative Velocity - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 2]);
legend('Location', 'southwest');
#+end_src
#+NAME: fig:ty_relative_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_relative_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_relative_time
#+CAPTION: Relative velocity of the sample with respect to the marble
#+RESULTS: fig:ty_relative_time
[[file:figs/ty_relative_time.png]]
#+begin_src matlab
figure;
hold on;
plot(ty_1h(:, 3), lsim(1/s, ty_1h(:, 2)-ty_1h(:, 1), ty_1h(:, 3)), 'DisplayName', 'Relative Displacement- Ty - 1Hz');
plot(ty_on(:, 3), lsim(1/s, ty_on(:, 2)-ty_on(:, 1), ty_on(:, 3)), 'DisplayName', 'Relative Displacement- Ty - ON');
plot(ty_of(:, 3), lsim(1/s, ty_of(:, 2)-ty_of(:, 1), ty_of(:, 3)), 'DisplayName', 'Relative Displacement- Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Displacement [m]');
xlim([0, 2]);
legend('Location', 'southwest');
#+end_src
#+NAME: fig:ty_relative_disp_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_relative_disp_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_relative_disp_time
#+CAPTION: Relative Displacement of the sample with respect to the marble
#+RESULTS: fig:ty_relative_disp_time
[[file:figs/ty_relative_disp_time.png]]
** Frequency Domain
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
dt = ty_of(2, 3)-ty_of(1, 3);
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
#+end_src
Then we compute the Power Spectral Density using =pwelch= function.
First for the geophone located on the marble
#+begin_src matlab
[pxof_m, f] = pwelch(ty_of(:, 1), win, [], [], Fs);
[pxon_m, ~] = pwelch(ty_on(:, 1), win, [], [], Fs);
[px1h_m, ~] = pwelch(ty_1h(:, 1), win, [], [], Fs);
#+end_src
And for the geophone located at the sample position.
#+begin_src matlab
[pxof_s, f] = pwelch(ty_of(:, 2), win, [], [], Fs);
[pxon_s, ~] = pwelch(ty_on(:, 2), win, [], [], Fs);
[px1h_s, ~] = pwelch(ty_1h(:, 2), win, [], [], Fs);
#+end_src
Finally, for the relative velocity.
#+begin_src matlab
[pxof_r, f] = pwelch(ty_of(:, 2)-ty_of(:, 1), win, [], [], Fs);
[pxon_r, ~] = pwelch(ty_on(:, 2)-ty_on(:, 1), win, [], [], Fs);
[px1h_r, ~] = pwelch(ty_1h(:, 2)-ty_1h(:, 1), win, [], [], Fs);
#+end_src
And we plot the ASD of the measured velocities:
- figure [[fig:psd_marble_compare]] for the geophone located on the marble
- figure [[fig:psd_sample_compare]] for the geophone at the sample position
- figure [[fig:psd_relative_compare]] for the relative velocity
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px1h_m), 'DisplayName', 'Marble - Ty 1Hz');
plot(f, sqrt(pxon_m), 'DisplayName', 'Marble - Ty ON');
plot(f, sqrt(pxof_m), 'DisplayName', 'Marble - Ty OFF');
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([1, 500]);
#+end_src
#+NAME: fig:psd_marble_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_marble_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_marble_compare
#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone on the marble
#+RESULTS: fig:psd_marble_compare
[[file:figs/psd_marble_compare.png]]
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px1h_s), 'DisplayName', 'Sample - Ty 1Hz');
plot(f, sqrt(pxon_s), 'DisplayName', 'Sample - Ty ON');
plot(f, sqrt(pxof_s), 'DisplayName', 'Sample - Ty OFF');
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([1, 500]);
#+end_src
#+NAME: fig:psd_sample_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_sample_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_sample_compare
#+CAPTION: Comparison of the ASD of the measured velocities from the Geophone at the sample location
#+RESULTS: fig:psd_sample_compare
[[file:figs/psd_sample_compare.png]]
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(px1h_r), 'DisplayName', 'Relative - Ty 1Hz');
plot(f, sqrt(pxon_r), 'DisplayName', 'Relative - Ty ON');
plot(f, sqrt(pxof_r), 'DisplayName', 'Relative - Ty OFF');
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([1, 500]);
#+end_src
#+NAME: fig:psd_relative_compare
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_relative_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_relative_compare
#+CAPTION: Comparison of the ASD of the relative velocity
#+RESULTS: fig:psd_relative_compare
[[file:figs/psd_relative_compare.png]]
** Ty motion and current
The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
*** Data pre-processing
Let's look at at the start of the csv file.
#+begin_src bash :results output
sed -n 1,30p mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
#+end_src
#+RESULTS:
#+begin_example
1 Elmo txt chart ver 2.0
2
3 [File Properties]
4 Creation Time,2019-05-13 05:33:43
5 Last Updated,2019-05-13 05:33:43
6 Resolution,0.001
7 Sampling Time,5E-05
8 Recording Time,5.461
9
10 [Chart Properties]
11 No.,Name,X Linear,X No.
12 1,Chart #1,True,0
13 2,Chart #2,True,0
14
15 [Chart Data]
16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
20
21 [Signal Names]
22 1,Time (sec)
23 2,Position [cnt]
24 3,Current Command [A]
25 4,Total Current Command [A]
26
27 [Signals Data Group 1]
28 1,2,3,4,
29 0,-141044,-0.537239575086517,-0.537239575086517,
30 0.001,-143127,-0.530803752974691,-0.530803752974691,
#+end_example
The real data starts at line 29.
We then load this =cvs= file starting at line 29.
#+begin_src matlab
tye_on = csvread("mat/Ty-when-Rz-1Hz.csv", 29, 0);
tye_1h = csvread("mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv", 29, 0);
#+end_src
*** Time domain data
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 [[fig:ty_position_time]].
#+begin_src matlab
figure;
subplot(1, 2, 1);
plot(tye_on(:, 1), (tye_on(:, 2)-mean(tye_on(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(tye_1h(:, 1), (tye_1h(:, 2)-mean(tye_1h(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');
#+end_src
#+NAME: fig:ty_position_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_position_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_position_time
#+CAPTION: Y position of the translation stage measured by the encoders
#+RESULTS: fig:ty_position_time
[[file:figs/ty_position_time.png]]
We also plot the current as function of the time on figure [[fig:ty_current_time]].
#+begin_src matlab
figure;
subplot(1, 2, 1);
plot(tye_on(:, 1), tye_on(:, 3)-mean(tye_on(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(tye_1h(:, 1), tye_1h(:, 3)-mean(tye_1h(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');
#+end_src
#+NAME: fig:ty_current_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_current_time.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_current_time
#+CAPTION: Current going through the actuator of the translation stage
#+RESULTS: fig:ty_current_time
[[file:figs/ty_current_time.png]]
** Conclusion
#+begin_important
-
#+end_important

250
disturbance-ty-sr/matlab/disturbance_ty_sr.m Normal file
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@ -0,0 +1,250 @@
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
% Load data
ty_of = load('mat/data_050.mat', 'data'); ty_of = ty_of.data;
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]]).
gain = 40; % [dB]
ty_of(:, 1) = voltageToVelocityL22(ty_of(:, 1), ty_of(:, 3), gain);
ty_on(:, 1) = voltageToVelocityL22(ty_on(:, 1), ty_on(:, 3), gain);
ty_1h(:, 1) = voltageToVelocityL22(ty_1h(:, 1), ty_1h(:, 3), gain);
ty_of(:, 2) = voltageToVelocityL22(ty_of(:, 2), ty_of(:, 3), gain);
ty_on(:, 2) = voltageToVelocityL22(ty_on(:, 2), ty_on(:, 3), gain);
ty_1h(:, 2) = voltageToVelocityL22(ty_1h(:, 2), ty_1h(:, 3), gain);
% Time domain plots
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 1), 'DisplayName', 'Marble - Ty 1Hz');
plot(ty_on(:, 3), ty_on(:, 1), 'DisplayName', 'Marble - Ty ON');
plot(ty_of(:, 3), ty_of(:, 1), 'DisplayName', 'Marble - Ty OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]);
legend('Location', 'southwest');
% #+NAME: fig:ty_marble_time_zoom
% #+CAPTION: caption
% #+RESULTS: fig:ty_marble_time_zoom
% [[file:figs/ty_marble_time_zoom.png]]
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2), 'DisplayName', 'Sample - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2), 'DisplayName', 'Sample - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2), 'DisplayName', 'Sample - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]);
legend('Location', 'southwest');
% Relative Velocity
figure;
hold on;
plot(ty_1h(:, 3), ty_1h(:, 2)-ty_1h(:, 1), 'DisplayName', 'Relative Velocity - Ty - 1Hz');
plot(ty_on(:, 3), ty_on(:, 2)-ty_on(:, 1), 'DisplayName', 'Relative Velocity - Ty - ON');
plot(ty_of(:, 3), ty_of(:, 2)-ty_of(:, 1), 'DisplayName', 'Relative Velocity - Ty - OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]);
legend('Location', 'southwest');
% Frequency Domain
% We first compute some parameters that will be used for the PSD computation.
dt = ty_of(2, 3)-ty_of(1, 3);
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
% Then we compute the Power Spectral Density using =pwelch= function.
% First for the geophone located on the marble
[pxof_m, f] = pwelch(ty_of(:, 1), win, [], [], Fs);
[pxon_m, ~] = pwelch(ty_on(:, 1), win, [], [], Fs);
[px1h_m, ~] = pwelch(ty_1h(:, 1), win, [], [], Fs);
% And for the geophone located at the sample position.
[pxof_s, f] = pwelch(ty_of(:, 2), win, [], [], Fs);
[pxon_s, ~] = pwelch(ty_on(:, 2), win, [], [], Fs);
[px1h_s, ~] = pwelch(ty_1h(:, 2), win, [], [], Fs);
% Finally, for the relative velocity.
[pxof_r, f] = pwelch(ty_of(:, 2)-ty_of(:, 1), win, [], [], Fs);
[pxon_r, ~] = pwelch(ty_on(:, 2)-ty_on(:, 1), win, [], [], Fs);
[px1h_r, ~] = pwelch(ty_1h(:, 2)-ty_1h(:, 1), win, [], [], Fs);
% And we plot the ASD of the measured velocities:
% - figure [[fig:psd_marble_compare]] for the geophone located on the marble
% - figure [[fig:psd_sample_compare]] for the geophone at the sample position
% - figure [[fig:psd_relative_compare]] for the relative velocity
figure;
hold on;
plot(f, sqrt(px1h_m), 'DisplayName', 'Marble - Ty 1Hz');
plot(f, sqrt(pxon_m), 'DisplayName', 'Marble - Ty ON');
plot(f, sqrt(pxof_m), 'DisplayName', 'Marble - Ty OFF');
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([1, 500]);
% #+NAME: fig:psd_marble_compare
% #+CAPTION: Comparison of the ASD of the measured velocities from the Geophone on the marble
% #+RESULTS: fig:psd_marble_compare
% [[file:figs/psd_marble_compare.png]]
figure;
hold on;
plot(f, sqrt(px1h_s), 'DisplayName', 'Sample - Ty 1Hz');
plot(f, sqrt(pxon_s), 'DisplayName', 'Sample - Ty ON');
plot(f, sqrt(pxof_s), 'DisplayName', 'Sample - Ty OFF');
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]);
% #+NAME: fig:psd_sample_compare
% #+CAPTION: Comparison of the ASD of the measured velocities from the Geophone at the sample location
% #+RESULTS: fig:psd_sample_compare
% [[file:figs/psd_sample_compare.png]]
figure;
hold on;
plot(f, sqrt(px1h_r), 'DisplayName', 'Relative - Ty 1Hz');
plot(f, sqrt(pxon_r), 'DisplayName', 'Relative - Ty ON');
plot(f, sqrt(pxof_r), 'DisplayName', 'Relative - Ty OFF');
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]);
% #+RESULTS:
% #+begin_example
% 1 Elmo txt chart ver 2.0
% 2
% 3 [File Properties]
% 4 Creation Time,2019-05-13 05:33:43
% 5 Last Updated,2019-05-13 05:33:43
% 6 Resolution,0.001
% 7 Sampling Time,5E-05
% 8 Recording Time,5.461
% 9
% 10 [Chart Properties]
% 11 No.,Name,X Linear,X No.
% 12 1,Chart #1,True,0
% 13 2,Chart #2,True,0
% 14
% 15 [Chart Data]
% 16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
% 17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
% 18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
% 19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
% 20
% 21 [Signal Names]
% 22 1,Time (sec)
% 23 2,Position [cnt]
% 24 3,Current Command [A]
% 25 4,Total Current Command [A]
% 26
% 27 [Signals Data Group 1]
% 28 1,2,3,4,
% 29 0,-141044,-0.537239575086517,-0.537239575086517,
% 30 0.001,-143127,-0.530803752974691,-0.530803752974691,
% #+end_example
% The real data starts at line 29.
% We then load this =cvs= file starting at line 29.
ty_on = csvread("mat/Ty-when-Rz-1Hz.csv", 29, 0);
ty_1h = csvread("mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv", 29, 0);
% Time domain data
% 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 [[fig:ty_position_time]].
figure;
subplot(1, 2, 1);
plot(ty_on(:, 1), (ty_on(:, 2)-mean(ty_on(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(ty_1h(:, 1), (ty_1h(:, 2)-mean(ty_1h(:, 2)))/200000);
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Position [mm]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');
% #+NAME: fig:ty_position_time
% #+CAPTION: Y position of the translation stage measured by the encoders
% #+RESULTS: fig:ty_position_time
% [[file:figs/ty_position_time.png]]
% We also plot the current as function of the time on figure [[fig:ty_current_time]].
figure;
subplot(1, 2, 1);
plot(ty_on(:, 1), ty_on(:, 3)-mean(ty_on(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - ON'}, 'Location', 'northeast');
subplot(1, 2, 2);
plot(ty_1h(:, 1), ty_1h(:, 3)-mean(ty_1h(:, 3)));
xlim([0, 5]);
xlabel('Time [s]'); ylabel('Current [A]');
legend({'Ty - 1Hz'}, 'Location', 'northeast');

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@ -0,0 +1 @@
\relax

133
disturbance-ty/index.html
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2019-05-14 mar. 17:20 --> <!-- 2019-05-15 mer. 14:37 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by the translation stage motion</title> <title>Vibrations induced by the translation stage motion</title>
@ -258,29 +258,29 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org9de4889">1. Measurement description</a></li> <li><a href="#orgf453937">1. Measurement description</a></li>
<li><a href="#org670b06e">2. Measurement Analysis</a> <li><a href="#org0d0d44a">2. Measurement Analysis</a>
<ul> <ul>
<li><a href="#org5b7e46e">2.1. Load data</a></li> <li><a href="#org8623e83">2.1. Load data</a></li>
<li><a href="#org755854a">2.2. Voltage to Velocity</a></li> <li><a href="#org29ed1af">2.2. Voltage to Velocity</a></li>
<li><a href="#orgea114d1">2.3. Time domain plots</a></li> <li><a href="#orgc0653a4">2.3. Time domain plots</a></li>
<li><a href="#orgbbc14c0">2.4. Frequency Domain analysis</a></li> <li><a href="#orgaa04452">2.4. Frequency Domain analysis</a></li>
<li><a href="#orgae3e2d3">2.5. Transfer function from marble motion in the East direction to sample motion in the East direction</a></li> <li><a href="#org0579205">2.5. Transfer function from marble motion in the East direction to sample motion in the East direction</a></li>
<li><a href="#org577441f">2.6. Position of the translation stage and Current</a> <li><a href="#org540379b">2.6. Position of the translation stage and Current</a>
<ul> <ul>
<li><a href="#orgc9e7589">2.6.1. Data pre-processing</a></li> <li><a href="#orgf590ed7">2.6.1. Data pre-processing</a></li>
<li><a href="#org424f5e2">2.6.2. Time domain data</a></li> <li><a href="#org0f186e6">2.6.2. Time domain data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgcb24d9f">2.7. Conclusion</a></li> <li><a href="#org4f5f98f">2.7. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org9de4889" class="outline-2"> <div id="outline-container-orgf453937" class="outline-2">
<h2 id="org9de4889"><span class="section-number-2">1</span> Measurement description</h2> <h2 id="orgf453937"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
@ -310,7 +310,7 @@ The scans are done with the ELMO software.
</p> </p>
<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="#org6ee74f8">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="#org8f10353">1</a>).
</p> </p>
<p> <p>
@ -394,7 +394,7 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<div id="org6ee74f8" class="figure"> <div id="org8f10353" class="figure">
<p><img src="./img/IMG_20190513_163032.jpg" alt="IMG_20190513_163032.jpg" width="500px" /> <p><img src="./img/IMG_20190513_163032.jpg" alt="IMG_20190513_163032.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p> <p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
@ -402,11 +402,11 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-org670b06e" class="outline-2"> <div id="outline-container-org0d0d44a" class="outline-2">
<h2 id="org670b06e"><span class="section-number-2">2</span> Measurement Analysis</h2> <h2 id="org0d0d44a"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org1302a91"></a> <a id="org65b415b"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -416,8 +416,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div> </div>
</div> </div>
<div id="outline-container-org5b7e46e" class="outline-3"> <div id="outline-container-org8623e83" class="outline-3">
<h3 id="org5b7e46e"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org8623e83"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <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; <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;
@ -428,8 +428,8 @@ e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org
</div> </div>
</div> </div>
<div id="outline-container-org755854a" class="outline-3"> <div id="outline-container-org29ed1af" class="outline-3">
<h3 id="org755854a"><span class="section-number-3">2.2</span> Voltage to Velocity</h3> <h3 id="org29ed1af"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/MEGA/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/MEGA/These/meas/src/index.html">here</a>).
@ -448,8 +448,8 @@ e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">
</div> </div>
</div> </div>
<div id="outline-container-orgea114d1" class="outline-3"> <div id="outline-container-orgc0653a4" class="outline-3">
<h3 id="orgea114d1"><span class="section-number-3">2.3</span> Time domain plots</h3> <h3 id="orgc0653a4"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -464,14 +464,14 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org753fe23" class="figure"> <div id="org66c8a67" class="figure">
<p><img src="figs/ty_z_time.png" alt="ty_z_time.png" /> <p><img src="figs/ty_z_time.png" alt="ty_z_time.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Z velocity of the sample and marble when scanning with the translation stage</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>
<div id="org58a4bf6" class="figure"> <div id="orgde211b5" class="figure">
<p><img src="figs/ty_z_time_zoom.png" alt="ty_z_time_zoom.png" /> <p><img src="figs/ty_z_time_zoom.png" alt="ty_z_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Z velocity of the sample and marble when scanning with the translation stage - Zoom</p> <p><span class="figure-number">Figure 3: </span>Z velocity of the sample and marble when scanning with the translation stage - Zoom</p>
@ -491,14 +491,14 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org97063fa" class="figure"> <div id="orgc1e7b3a" class="figure">
<p><img src="figs/ty_e_time.png" alt="ty_e_time.png" /> <p><img src="figs/ty_e_time.png" alt="ty_e_time.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage</p> <p><span class="figure-number">Figure 4: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage</p>
</div> </div>
<div id="org660b28c" class="figure"> <div id="orgff260b2" class="figure">
<p><img src="figs/ty_e_time_zoom.png" alt="ty_e_time_zoom.png" /> <p><img src="figs/ty_e_time_zoom.png" alt="ty_e_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage - Zoom</p> <p><span class="figure-number">Figure 5: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage - Zoom</p>
@ -506,9 +506,17 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-orgbbc14c0" class="outline-3"> <div id="outline-container-orgaa04452" class="outline-3">
<h3 id="orgbbc14c0"><span class="section-number-3">2.4</span> Frequency Domain analysis</h3> <h3 id="orgaa04452"><span class="section-number-3">2.4</span> Frequency Domain analysis</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p>
We get the typical ground velocity 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>
</div>
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
@ -549,9 +557,9 @@ And for the geophone located at the sample position.
And we plot the ASD of the measured velocities: And we plot the ASD of the measured velocities:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>figure <a href="#org07479f1">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li> <li>figure <a href="#org5fbea6a">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgfe0db70">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li> <li>figure <a href="#org2010bd4">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#org36cae29">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li> <li>figure <a href="#org40d5824">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
@ -559,6 +567,7 @@ And we plot the ASD of the measured velocities:
hold on; 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_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, 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; 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">'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>; <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>;
@ -569,7 +578,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org07479f1" class="figure"> <div id="org5fbea6a" class="figure">
<p><img src="figs/asd_east_marble.png" alt="asd_east_marble.png" /> <p><img src="figs/asd_east_marble.png" alt="asd_east_marble.png" />
</p> </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> <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>
@ -581,17 +590,18 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
hold on; 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_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, 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; 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">'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>; <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> 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>; 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>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">5</span>, <span class="org-highlight-numbers-number">1e1</span><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">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> </pre>
</div> </div>
<div id="orgfe0db70" class="figure"> <div id="org2010bd4" class="figure">
<p><img src="figs/asd_east_sample.png" alt="asd_east_sample.png" /> <p><img src="figs/asd_east_sample.png" alt="asd_east_sample.png" />
</p> </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> <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>
@ -603,33 +613,34 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
hold on; 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_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, 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; 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">'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>; <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> 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>; 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>; 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> </pre>
</div> </div>
<div id="org36cae29" class="figure"> <div id="org40d5824" class="figure">
<p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" /> <p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Amplitude spectral density of the measure voltage 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> <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>
</div> </div>
</div> </div>
<div id="outline-container-orgae3e2d3" class="outline-3"> <div id="outline-container-org0579205" class="outline-3">
<h3 id="orgae3e2d3"><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> <h3 id="org0579205"><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"> <div class="outline-text-3" id="text-2-5">
<p> <p>
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction. Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.
</p> </p>
<p> <p>
We first plot the time domain motions when every stage is off (figure <a href="#orge1188dc">9</a>). We first plot the time domain motions when every stage is off (figure <a href="#org8d02455">9</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -645,7 +656,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="orge1188dc" class="figure"> <div id="org8d02455" class="figure">
<p><img src="figs/east_marble_sample.png" alt="east_marble_sample.png" /> <p><img src="figs/east_marble_sample.png" alt="east_marble_sample.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Velocity in the east direction of the marble and sample when all the stages are OFF</p> <p><span class="figure-number">Figure 9: </span>Velocity in the east direction of the marble and sample when all the stages are OFF</p>
@ -666,10 +677,10 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
<p> <p>
The result is shown on figure <a href="#org919ea41">10</a>. The result is shown on figure <a href="#org1b6386e">10</a>.
</p> </p>
<div id="org919ea41" class="figure"> <div id="org1b6386e" class="figure">
<p><img src="figs/tf_east_marble_sample.png" alt="tf_east_marble_sample.png" /> <p><img src="figs/tf_east_marble_sample.png" alt="tf_east_marble_sample.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction</p> <p><span class="figure-number">Figure 10: </span>Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction</p>
@ -677,16 +688,16 @@ The result is shown on figure <a href="#org919ea41">10</a>.
</div> </div>
</div> </div>
<div id="outline-container-org577441f" class="outline-3"> <div id="outline-container-org540379b" class="outline-3">
<h3 id="org577441f"><span class="section-number-3">2.6</span> Position of the translation stage and Current</h3> <h3 id="org540379b"><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 class="outline-text-3" id="text-2-6">
<p> <p>
The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file. The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file.
</p> </p>
</div> </div>
<div id="outline-container-orgc9e7589" class="outline-4"> <div id="outline-container-orgf590ed7" class="outline-4">
<h4 id="orgc9e7589"><span class="section-number-4">2.6.1</span> Data pre-processing</h4> <h4 id="orgf590ed7"><span class="section-number-4">2.6.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-6-1"> <div class="outline-text-4" id="text-2-6-1">
<p> <p>
Let's look at at the start of the csv file. Let's look at at the start of the csv file.
@ -709,13 +720,13 @@ We then load this <code>cvs</code> file starting at line 29.
</div> </div>
</div> </div>
<div id="outline-container-org424f5e2" class="outline-4"> <div id="outline-container-org0f186e6" class="outline-4">
<h4 id="org424f5e2"><span class="section-number-4">2.6.2</span> Time domain data</h4> <h4 id="org0f186e6"><span class="section-number-4">2.6.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-6-2"> <div class="outline-text-4" id="text-2-6-2">
<p> <p>
We plot the position of the translation stage measured by the encoders. 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. There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
The result is shown on figure <a href="#org706ebc4">11</a>. The result is shown on figure <a href="#org064acde">11</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -729,21 +740,21 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org706ebc4" class="figure"> <div id="org064acde" class="figure">
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" /> <p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Y position of the translation stage measured by the encoders</p> <p><span class="figure-number">Figure 11: </span>Y position of the translation stage measured by the encoders</p>
</div> </div>
<div id="orge94268a" class="figure"> <div id="org33956fc" class="figure">
<p><img src="figs/ty_position_time_zoom.png" alt="ty_position_time_zoom.png" /> <p><img src="figs/ty_position_time_zoom.png" alt="ty_position_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Y position of the translation stage measured by the encoders - Zoom</p> <p><span class="figure-number">Figure 12: </span>Y position of the translation stage measured by the encoders - Zoom</p>
</div> </div>
<p> <p>
We also plot the current as function of the time on figure <a href="#org4b3d2c9">13</a>. We also plot the current as function of the time on figure <a href="#org436454e">13</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -757,14 +768,14 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org4b3d2c9" class="figure"> <div id="org436454e" class="figure">
<p><img src="figs/current_time.png" alt="current_time.png" /> <p><img src="figs/current_time.png" alt="current_time.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Current going through the actuator of the translation stage</p> <p><span class="figure-number">Figure 13: </span>Current going through the actuator of the translation stage</p>
</div> </div>
<div id="orgdd07d0a" class="figure"> <div id="org9e37388" class="figure">
<p><img src="figs/current_time_zoom.png" alt="current_time_zoom.png" /> <p><img src="figs/current_time_zoom.png" alt="current_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Current going through the actuator of the translation stage - Zoom</p> <p><span class="figure-number">Figure 14: </span>Current going through the actuator of the translation stage - Zoom</p>
@ -773,8 +784,8 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-orgcb24d9f" class="outline-3"> <div id="outline-container-org4f5f98f" class="outline-3">
<h3 id="orgcb24d9f"><span class="section-number-3">2.7</span> Conclusion</h3> <h3 id="org4f5f98f"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<div class="important"> <div class="important">
<ul class="org-ul"> <ul class="org-ul">
@ -789,7 +800,7 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 17:20</p> <p class="date">Created: 2019-05-15 mer. 14:37</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>

7
disturbance-ty/index.org
View File

@ -103,6 +103,7 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
** Matlab Init :noexport:ignore: ** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
addpath('../src');
#+end_src #+end_src
#+begin_src matlab :exports none :results silent :noweb yes #+begin_src matlab :exports none :results silent :noweb yes
@ -191,7 +192,7 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
[[file:figs/ty_e_time.png]] [[file:figs/ty_e_time.png]]
#+begin_src matlab :exports none #+begin_src matlab :exports none
xlim([0, 1]) xlim([0, 1]);
#+end_src #+end_src
#+NAME: fig:ty_e_time_zoom #+NAME: fig:ty_e_time_zoom
@ -302,7 +303,7 @@ And we plot the ASD of the measured velocities:
hold off; hold off;
set(gca, 'xscale', 'log'); set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$') xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest'); legend('Location', 'northwest');
xlim([0.1, 500]); xlim([0.1, 500]);
#+end_src #+end_src
@ -314,7 +315,7 @@ And we plot the ASD of the measured velocities:
#+end_src #+end_src
#+NAME: fig:asd_z_direction #+NAME: fig:asd_z_direction
#+CAPTION: Amplitude spectral density of the measure voltage 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 #+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 #+RESULTS: fig:asd_z_direction
[[file:figs/asd_z_direction.png]] [[file:figs/asd_z_direction.png]]