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Reworked the analysis for the Ty stage motion

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Thomas Dehaeze 2019-05-14 17:55:59 +02:00
parent de8bf8eae9
commit 00614b2ef3
15 changed files with 324 additions and 138 deletions
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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. 14:09 --> <!-- 2019-05-14 mar. 17:20 -->
<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>
@ -258,28 +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="#org9a632ab">1. Measurement description</a></li> <li><a href="#org9de4889">1. Measurement description</a></li>
<li><a href="#orgbcb8a15">2. Measurement Analysis</a> <li><a href="#org670b06e">2. Measurement Analysis</a>
<ul> <ul>
<li><a href="#org41bad02">2.1. Load data</a></li> <li><a href="#org5b7e46e">2.1. Load data</a></li>
<li><a href="#orgb5c8af2">2.2. Time domain plots</a></li> <li><a href="#org755854a">2.2. Voltage to Velocity</a></li>
<li><a href="#org1ada52f">2.3. Frequency Domain analysis</a></li> <li><a href="#orgea114d1">2.3. Time domain plots</a></li>
<li><a href="#org9c3b00c">2.4. Transfer function from marble motion in the East direction to sample motion in the East direction</a></li> <li><a href="#orgbbc14c0">2.4. Frequency Domain analysis</a></li>
<li><a href="#org1512497">2.5. Position of the translation stage and Current</a> <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="#org577441f">2.6. Position of the translation stage and Current</a>
<ul> <ul>
<li><a href="#org1f1e19b">2.5.1. Data pre-processing</a></li> <li><a href="#orgc9e7589">2.6.1. Data pre-processing</a></li>
<li><a href="#org7b8bb62">2.5.2. Time domain data</a></li> <li><a href="#org424f5e2">2.6.2. Time domain data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org066b822">2.6. Conclusion</a></li> <li><a href="#orgcb24d9f">2.7. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org9a632ab" class="outline-2"> <div id="outline-container-org9de4889" class="outline-2">
<h2 id="org9a632ab"><span class="section-number-2">1</span> Measurement description</h2> <h2 id="org9de4889"><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>:
@ -309,7 +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="#org453b1ae">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="#org6ee74f8">1</a>).
</p> </p>
<p> <p>
@ -393,7 +394,7 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<div id="org453b1ae" class="figure"> <div id="org6ee74f8" 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>
@ -401,11 +402,11 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-orgbcb8a15" class="outline-2"> <div id="outline-container-org670b06e" class="outline-2">
<h2 id="orgbcb8a15"><span class="section-number-2">2</span> Measurement Analysis</h2> <h2 id="org670b06e"><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="orgdadf778"></a> <a id="org1302a91"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -415,8 +416,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div> </div>
</div> </div>
<div id="outline-container-org41bad02" class="outline-3"> <div id="outline-container-org5b7e46e" class="outline-3">
<h3 id="org41bad02"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org5b7e46e"><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;
@ -427,33 +428,53 @@ e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org
</div> </div>
</div> </div>
<div id="outline-container-orgb5c8af2" class="outline-3"> <div id="outline-container-org755854a" class="outline-3">
<h3 id="orgb5c8af2"><span class="section-number-3">2.2</span> Time domain plots</h3> <h3 id="org755854a"><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">z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">40</span><span class="org-rainbow-delimiters-depth-1">)</span>;
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">40</span><span class="org-rainbow-delimiters-depth-1">)</span>;
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">40</span><span class="org-rainbow-delimiters-depth-1">)</span>;
z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">40</span><span class="org-rainbow-delimiters-depth-1">)</span>;
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">40</span><span class="org-rainbow-delimiters-depth-1">)</span>;
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">40</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgea114d1" class="outline-3">
<h3 id="orgea114d1"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <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>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off; 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">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="org97f088a" class="figure"> <div id="org753fe23" 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 motion 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="org33a0b96" class="figure"> <div id="org58a4bf6" 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 motion 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>
</div> </div>
@ -463,31 +484,31 @@ hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off; 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">10</span>, <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="orgd31998f" class="figure"> <div id="org97063fa" 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>Motion 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="org2346a47" class="figure"> <div id="org660b28c" 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>Motion 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>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1ada52f" class="outline-3"> <div id="outline-container-orgbbc14c0" class="outline-3">
<h3 id="org1ada52f"><span class="section-number-3">2.3</span> Frequency Domain analysis</h3> <h3 id="orgbbc14c0"><span class="section-number-3">2.4</span> Frequency Domain analysis</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-4">
<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>
@ -525,12 +546,12 @@ And for the geophone located at the sample position.
</div> </div>
<p> <p>
And we plot the ASD of the measured signals: And we plot the ASD of the measured velocities:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>figure <a href="#orgcdc360c">6</a> compares the marble motion in the east direction when scanning and when Ty is OFF</li> <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="#org7a15478">7</a> compares the sample motion 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="#orge54908e">8</a> shows the marble and sample motion in the Z direction when scanning with the translation stage</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>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
@ -541,17 +562,17 @@ plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org
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>; 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="orgcdc360c" class="figure"> <div id="org07479f1" 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 measure voltage 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>
</div> </div>
@ -563,17 +584,17 @@ plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org
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>; 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>; 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>;
</pre> </pre>
</div> </div>
<div id="org7a15478" class="figure"> <div id="orgfe0db70" 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 measure voltage 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>
</div> </div>
@ -587,12 +608,12 @@ 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">'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 Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', '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="orge54908e" class="figure"> <div id="org36cae29" 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 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>
@ -600,15 +621,15 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org9c3b00c" class="outline-3"> <div id="outline-container-orgae3e2d3" class="outline-3">
<h3 id="org9c3b00c"><span class="section-number-3">2.4</span> Transfer function from marble motion in the East direction to sample motion in the East direction</h3> <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>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-5">
<p> <p>
Let's compute the transfer function for the marble motion in the east direction to the sample motion 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="#orge1584e0">9</a>). We first plot the time domain motions when every stage is off (figure <a href="#orge1188dc">9</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -617,17 +638,17 @@ hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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">1</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>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', '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="orge1584e0" class="figure"> <div id="orge1188dc" 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>East motion 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>
</div> </div>
@ -645,28 +666,28 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
<p> <p>
The result is shown on figure <a href="#org2a92c0e">10</a>. The result is shown on figure <a href="#org919ea41">10</a>.
</p> </p>
<div id="org2a92c0e" class="figure"> <div id="org919ea41" 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 motion in the east direction to sample motion 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>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1512497" class="outline-3"> <div id="outline-container-org577441f" class="outline-3">
<h3 id="org1512497"><span class="section-number-3">2.5</span> Position of the translation stage and Current</h3> <h3 id="org577441f"><span class="section-number-3">2.6</span> Position of the translation stage and Current</h3>
<div class="outline-text-3" id="text-2-5"> <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-org1f1e19b" class="outline-4"> <div id="outline-container-orgc9e7589" class="outline-4">
<h4 id="org1f1e19b"><span class="section-number-4">2.5.1</span> Data pre-processing</h4> <h4 id="orgc9e7589"><span class="section-number-4">2.6.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-5-1"> <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.
</p> </p>
@ -688,13 +709,13 @@ We then load this <code>cvs</code> file starting at line 29.
</div> </div>
</div> </div>
<div id="outline-container-org7b8bb62" class="outline-4"> <div id="outline-container-org424f5e2" class="outline-4">
<h4 id="org7b8bb62"><span class="section-number-4">2.5.2</span> Time domain data</h4> <h4 id="org424f5e2"><span class="section-number-4">2.6.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-5-2"> <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="#orgbfc9bb3">11</a>. The result is shown on figure <a href="#org706ebc4">11</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -708,21 +729,21 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="orgbfc9bb3" class="figure"> <div id="org706ebc4" 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="orgef12336" class="figure"> <div id="orge94268a" 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="#org4606174">13</a>. We also plot the current as function of the time on figure <a href="#org4b3d2c9">13</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -736,14 +757,14 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org4606174" class="figure"> <div id="org4b3d2c9" 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="org677343d" class="figure"> <div id="orgdd07d0a" 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>
@ -752,9 +773,9 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org066b822" class="outline-3"> <div id="outline-container-orgcb24d9f" class="outline-3">
<h3 id="org066b822"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="orgcb24d9f"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-7">
<div class="important"> <div class="important">
<ul class="org-ul"> <ul class="org-ul">
<li>The acquisition is done using the Speedgoat as well as using ELMO. The two acquisition are <b>not</b> synchronize</li> <li>The acquisition is done using the Speedgoat as well as using ELMO. The two acquisition are <b>not</b> synchronize</li>
@ -768,7 +789,7 @@ 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. 14:09</p> <p class="date">Created: 2019-05-14 mar. 17:20</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>

77
disturbance-ty/index.org
View File

@ -102,11 +102,11 @@ 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>>
#+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
@ -116,6 +116,19 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
e_of = load('mat/data_042.mat', 'data'); e_of = e_of.data; e_of = load('mat/data_042.mat', 'data'); e_of = e_of.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
z_ty(:, 1) = voltageToVelocityL22(z_ty(:, 1), z_ty(:, 3), 40);
e_ty(:, 1) = voltageToVelocityL22(e_ty(:, 1), e_ty(:, 3), 40);
e_of(:, 1) = voltageToVelocityL22(e_of(:, 1), e_of(:, 3), 40);
z_ty(:, 2) = voltageToVelocityL22(z_ty(:, 2), z_ty(:, 3), 40);
e_ty(:, 2) = voltageToVelocityL22(e_ty(:, 2), e_ty(:, 3), 40);
e_of(:, 2) = voltageToVelocityL22(e_of(:, 2), e_of(:, 3), 40);
#+end_src
** Time domain plots ** Time domain plots
#+begin_src matlab #+begin_src matlab
figure; figure;
@ -123,8 +136,8 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z'); plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z');
plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z'); plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
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, 100]);
legend('Location', 'northeast'); legend('Location', 'northeast');
#+end_src #+end_src
@ -135,12 +148,12 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
#+end_src #+end_src
#+NAME: fig:ty_z_time #+NAME: fig:ty_z_time
#+CAPTION: Z motion of the sample and marble when scanning with the translation stage #+CAPTION: Z velocity of the sample and marble when scanning with the translation stage
#+RESULTS: fig:ty_z_time #+RESULTS: fig:ty_z_time
[[file:figs/ty_z_time.png]] [[file:figs/ty_z_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_z_time_zoom #+NAME: fig:ty_z_time_zoom
@ -150,7 +163,7 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
#+end_src #+end_src
#+NAME: fig:ty_z_time_zoom #+NAME: fig:ty_z_time_zoom
#+CAPTION: Z motion of the sample and marble when scanning with the translation stage - Zoom #+CAPTION: Z velocity of the sample and marble when scanning with the translation stage - Zoom
#+RESULTS: fig:ty_z_time_zoom #+RESULTS: fig:ty_z_time_zoom
[[file:figs/ty_z_time_zoom.png]] [[file:figs/ty_z_time_zoom.png]]
@ -161,8 +174,8 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X'); plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X');
plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X'); plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
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
@ -173,7 +186,7 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
#+end_src #+end_src
#+NAME: fig:ty_e_time #+NAME: fig:ty_e_time
#+CAPTION: Motion of the sample and marble in the east direction when scanning with the translation stage #+CAPTION: Velocity of the sample and marble in the east direction when scanning with the translation stage
#+RESULTS: fig:ty_e_time #+RESULTS: fig:ty_e_time
[[file:figs/ty_e_time.png]] [[file:figs/ty_e_time.png]]
@ -188,11 +201,16 @@ Each of the measurement =mat= file contains one =data= array with 3 columns:
#+end_src #+end_src
#+NAME: fig:ty_e_time_zoom #+NAME: fig:ty_e_time_zoom
#+CAPTION: Motion of the sample and marble in the east direction when scanning with the translation stage - Zoom #+CAPTION: Velocity of the sample and marble in the east direction when scanning with the translation stage - Zoom
#+RESULTS: fig:ty_e_time_zoom #+RESULTS: fig:ty_e_time_zoom
[[file:figs/ty_e_time_zoom.png]] [[file:figs/ty_e_time_zoom.png]]
** Frequency Domain analysis ** Frequency Domain analysis
We get the typical ground velocity to compare with the velocities measured.
#+begin_src matlab
[pxx_gm, f_gm] = getPSDGroundVelocity();
#+end_src
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.
#+begin_src matlab #+begin_src matlab
dt = z_ty(2, 3)-z_ty(1, 3); dt = z_ty(2, 3)-z_ty(1, 3);
@ -218,22 +236,23 @@ And for the geophone located at the sample position.
[pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs); [pxe_of_s, ~] = pwelch(e_of(:, 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:asd_east_marble]] compares the marble motion in the east direction when scanning and when Ty is OFF - figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_east_sample]] compares the sample motion in the east direction when scanning and when Ty is OFF - figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_z_direction]] shows the marble and sample motion in the Z direction when scanning with the translation stage - figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
#+begin_src matlab #+begin_src matlab
figure; figure;
hold on; hold on;
plot(f, sqrt(pxe_ty_m), 'DisplayName', 'Ty 1Hz - Marble - X'); plot(f, sqrt(pxe_ty_m), 'DisplayName', 'Ty 1Hz - Marble - X');
plot(f, sqrt(pxe_of_m), 'DisplayName', 'Ty OFF - Marble - X'); plot(f, sqrt(pxe_of_m), 'DisplayName', 'Ty OFF - Marble - X');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
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]); ylim([1e-5, 1e1]); xlim([0.1, 500]);
#+end_src #+end_src
#+NAME: fig:asd_east_marble #+NAME: fig:asd_east_marble
@ -243,7 +262,7 @@ And we plot the ASD of the measured signals:
#+end_src #+end_src
#+NAME: fig:asd_east_marble #+NAME: fig:asd_east_marble
#+CAPTION: Amplitude spectral density of the measure voltage 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 #+CAPTION: 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
#+RESULTS: fig:asd_east_marble #+RESULTS: fig:asd_east_marble
[[file:figs/asd_east_marble.png]] [[file:figs/asd_east_marble.png]]
@ -253,12 +272,13 @@ And we plot the ASD of the measured signals:
hold on; hold on;
plot(f, sqrt(pxe_ty_s), 'DisplayName', 'Ty 1Hz - Sample - X'); plot(f, sqrt(pxe_ty_s), 'DisplayName', 'Ty 1Hz - Sample - X');
plot(f, sqrt(pxe_of_s), 'DisplayName', 'Ty OFF - Sample - X'); plot(f, sqrt(pxe_of_s), 'DisplayName', 'Ty OFF - Sample - X');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
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]); ylim([1e-5, 1e1]); xlim([0.1, 500]);
#+end_src #+end_src
#+NAME: fig:asd_east_sample #+NAME: fig:asd_east_sample
@ -268,7 +288,7 @@ And we plot the ASD of the measured signals:
#+end_src #+end_src
#+NAME: fig:asd_east_sample #+NAME: fig:asd_east_sample
#+CAPTION: Amplitude spectral density of the measure voltage 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 #+CAPTION: 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
#+RESULTS: fig:asd_east_sample #+RESULTS: fig:asd_east_sample
[[file:figs/asd_east_sample.png]] [[file:figs/asd_east_sample.png]]
@ -278,12 +298,13 @@ And we plot the ASD of the measured signals:
hold on; hold on;
plot(f, sqrt(pxz_ty_m), 'DisplayName', 'Ty 1Hz - Marble - Z'); plot(f, sqrt(pxz_ty_m), 'DisplayName', 'Ty 1Hz - Marble - Z');
plot(f, sqrt(pxz_ty_s), 'DisplayName', 'Ty 1Hz - Sample - Z'); plot(f, sqrt(pxz_ty_s), 'DisplayName', 'Ty 1Hz - Sample - Z');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
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 Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest'); legend('Location', 'northwest');
xlim([0.1, 500]); ylim([1e-5, 1e1]); xlim([0.1, 500]);
#+end_src #+end_src
#+NAME: fig:asd_z_direction #+NAME: fig:asd_z_direction
@ -298,7 +319,7 @@ And we plot the ASD of the measured signals:
[[file:figs/asd_z_direction.png]] [[file:figs/asd_z_direction.png]]
** Transfer function from marble motion in the East direction to sample motion in the East direction ** Transfer function from marble motion in the East direction to sample motion in the East direction
Let's compute the transfer function for the marble motion in the east direction to the sample motion 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.
We first plot the time domain motions when every stage is off (figure [[fig:east_marble_sample]]). We first plot the time domain motions when every stage is off (figure [[fig:east_marble_sample]]).
@ -308,9 +329,9 @@ We first plot the time domain motions when every stage is off (figure [[fig:east
plot(e_of(:, 3), e_of(:, 2), 'DisplayName', 'Sample - X'); plot(e_of(:, 3), e_of(:, 2), 'DisplayName', 'Sample - X');
plot(e_of(:, 3), e_of(:, 1), 'DisplayName', 'Marble - X'); plot(e_of(:, 3), e_of(:, 1), 'DisplayName', 'Marble - X');
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); ylim([-1, 1]); xlim([0, 100]);
legend('Location', 'northeast'); legend('Location', 'southwest');
#+end_src #+end_src
#+NAME: fig:east_marble_sample #+NAME: fig:east_marble_sample
@ -320,7 +341,7 @@ We first plot the time domain motions when every stage is off (figure [[fig:east
#+end_src #+end_src
#+NAME: fig:east_marble_sample #+NAME: fig:east_marble_sample
#+CAPTION: East motion of the marble and sample when all the stages are OFF #+CAPTION: Velocity in the east direction of the marble and sample when all the stages are OFF
#+RESULTS: fig:east_marble_sample #+RESULTS: fig:east_marble_sample
[[file:figs/east_marble_sample.png]] [[file:figs/east_marble_sample.png]]
@ -366,7 +387,7 @@ The result is shown on figure [[fig:tf_east_marble_sample]].
#+end_src #+end_src
#+NAME: fig:tf_east_marble_sample #+NAME: fig:tf_east_marble_sample
#+CAPTION: Estimation of the transfer function from marble motion in the east direction to sample motion in the east direction #+CAPTION: Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction
#+RESULTS: fig:tf_east_marble_sample #+RESULTS: fig:tf_east_marble_sample
[[file:figs/tf_east_marble_sample.png]] [[file:figs/tf_east_marble_sample.png]]

69
disturbance-ty/matlab/disturbance_ty.m
View File

@ -10,6 +10,18 @@ z_ty = load('mat/data_040.mat', 'data'); z_ty = z_ty.data;
e_ty = load('mat/data_041.mat', 'data'); e_ty = e_ty.data; e_ty = load('mat/data_041.mat', 'data'); e_ty = e_ty.data;
e_of = load('mat/data_042.mat', 'data'); e_of = e_of.data; e_of = load('mat/data_042.mat', 'data'); e_of = e_of.data;
% Voltage to Velocity
% We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
z_ty(:, 1) = voltageToVelocityL22(z_ty(:, 1), z_ty(:, 3), 40);
e_ty(:, 1) = voltageToVelocityL22(e_ty(:, 1), e_ty(:, 3), 40);
e_of(:, 1) = voltageToVelocityL22(e_of(:, 1), e_of(:, 3), 40);
z_ty(:, 2) = voltageToVelocityL22(z_ty(:, 2), z_ty(:, 3), 40);
e_ty(:, 2) = voltageToVelocityL22(e_ty(:, 2), e_ty(:, 3), 40);
e_of(:, 2) = voltageToVelocityL22(e_of(:, 2), e_of(:, 3), 40);
% Time domain plots % Time domain plots
figure; figure;
@ -17,24 +29,24 @@ hold on;
plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z'); plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z');
plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z'); plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
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, 100]);
legend('Location', 'northeast'); legend('Location', 'northeast');
% #+NAME: fig:ty_z_time % #+NAME: fig:ty_z_time
% #+CAPTION: Z motion of the sample and marble when scanning with the translation stage % #+CAPTION: Z velocity of the sample and marble when scanning with the translation stage
% #+RESULTS: fig:ty_z_time % #+RESULTS: fig:ty_z_time
% [[file:figs/ty_z_time.png]] % [[file:figs/ty_z_time.png]]
xlim([0, 1]) xlim([0, 1]);
% #+NAME: fig:ty_z_time_zoom % #+NAME: fig:ty_z_time_zoom
% #+CAPTION: Z motion of the sample and marble when scanning with the translation stage - Zoom % #+CAPTION: Z velocity of the sample and marble when scanning with the translation stage - Zoom
% #+RESULTS: fig:ty_z_time_zoom % #+RESULTS: fig:ty_z_time_zoom
% [[file:figs/ty_z_time_zoom.png]] % [[file:figs/ty_z_time_zoom.png]]
@ -45,14 +57,14 @@ hold on;
plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X'); plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X');
plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X'); plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
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');
% #+NAME: fig:ty_e_time % #+NAME: fig:ty_e_time
% #+CAPTION: Motion of the sample and marble in the east direction when scanning with the translation stage % #+CAPTION: Velocity of the sample and marble in the east direction when scanning with the translation stage
% #+RESULTS: fig:ty_e_time % #+RESULTS: fig:ty_e_time
% [[file:figs/ty_e_time.png]] % [[file:figs/ty_e_time.png]]
@ -60,6 +72,12 @@ legend('Location', 'northeast');
xlim([0, 1]) xlim([0, 1])
% Frequency Domain analysis % Frequency Domain analysis
% We get the typical ground velocity to compare with the velocities measured.
[pxx_gm, f_gm] = getPSDGroundVelocity();
% 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.
dt = z_ty(2, 3)-z_ty(1, 3); dt = z_ty(2, 3)-z_ty(1, 3);
@ -88,27 +106,28 @@ win = hanning(ceil(10*Fs));
% And we plot the ASD of the measured signals: % And we plot the ASD of the measured velocities:
% - figure [[fig:asd_east_marble]] compares the marble motion in the east direction when scanning and when Ty is OFF % - figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
% - figure [[fig:asd_east_sample]] compares the sample motion in the east direction when scanning and when Ty is OFF % - figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
% - figure [[fig:asd_z_direction]] shows the marble and sample motion in the Z direction when scanning with the translation stage % - figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
figure; figure;
hold on; hold on;
plot(f, sqrt(pxe_ty_m), 'DisplayName', 'Ty 1Hz - Marble - X'); plot(f, sqrt(pxe_ty_m), 'DisplayName', 'Ty 1Hz - Marble - X');
plot(f, sqrt(pxe_of_m), 'DisplayName', 'Ty OFF - Marble - X'); plot(f, sqrt(pxe_of_m), 'DisplayName', 'Ty OFF - Marble - X');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
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]); ylim([1e-5, 1e1]); xlim([0.1, 500]);
% #+NAME: fig:asd_east_marble % #+NAME: fig:asd_east_marble
% #+CAPTION: Amplitude spectral density of the measure voltage 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 % #+CAPTION: 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
% #+RESULTS: fig:asd_east_marble % #+RESULTS: fig:asd_east_marble
% [[file:figs/asd_east_marble.png]] % [[file:figs/asd_east_marble.png]]
@ -118,17 +137,18 @@ figure;
hold on; hold on;
plot(f, sqrt(pxe_ty_s), 'DisplayName', 'Ty 1Hz - Sample - X'); plot(f, sqrt(pxe_ty_s), 'DisplayName', 'Ty 1Hz - Sample - X');
plot(f, sqrt(pxe_of_s), 'DisplayName', 'Ty OFF - Sample - X'); plot(f, sqrt(pxe_of_s), 'DisplayName', 'Ty OFF - Sample - X');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
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]); ylim([1e-5, 1e1]); xlim([0.1, 500]);
% #+NAME: fig:asd_east_sample % #+NAME: fig:asd_east_sample
% #+CAPTION: Amplitude spectral density of the measure voltage 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 % #+CAPTION: 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
% #+RESULTS: fig:asd_east_sample % #+RESULTS: fig:asd_east_sample
% [[file:figs/asd_east_sample.png]] % [[file:figs/asd_east_sample.png]]
@ -138,15 +158,16 @@ figure;
hold on; hold on;
plot(f, sqrt(pxz_ty_m), 'DisplayName', 'Ty 1Hz - Marble - Z'); plot(f, sqrt(pxz_ty_m), 'DisplayName', 'Ty 1Hz - Marble - Z');
plot(f, sqrt(pxz_ty_s), 'DisplayName', 'Ty 1Hz - Sample - Z'); plot(f, sqrt(pxz_ty_s), 'DisplayName', 'Ty 1Hz - Sample - Z');
plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
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 Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest'); legend('Location', 'northwest');
xlim([0.1, 500]); ylim([1e-5, 1e1]); xlim([0.1, 500]);
% Transfer function from marble motion in the East direction to sample motion in the East direction % Transfer function from marble motion in the East direction to sample motion in the East direction
% Let's compute the transfer function for the marble motion in the east direction to the sample motion 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.
% We first plot the time domain motions when every stage is off (figure [[fig:east_marble_sample]]). % We first plot the time domain motions when every stage is off (figure [[fig:east_marble_sample]]).
@ -156,14 +177,14 @@ hold on;
plot(e_of(:, 3), e_of(:, 2), 'DisplayName', 'Sample - X'); plot(e_of(:, 3), e_of(:, 2), 'DisplayName', 'Sample - X');
plot(e_of(:, 3), e_of(:, 1), 'DisplayName', 'Marble - X'); plot(e_of(:, 3), e_of(:, 1), 'DisplayName', 'Marble - X');
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); ylim([-1, 1]); xlim([0, 100]);
legend('Location', 'northeast'); legend('Location', 'southwest');
% #+NAME: fig:east_marble_sample % #+NAME: fig:east_marble_sample
% #+CAPTION: East motion of the marble and sample when all the stages are OFF % #+CAPTION: Velocity in the east direction of the marble and sample when all the stages are OFF
% #+RESULTS: fig:east_marble_sample % #+RESULTS: fig:east_marble_sample
% [[file:figs/east_marble_sample.png]] % [[file:figs/east_marble_sample.png]]

127
src/index.org
View File

@ -36,6 +36,10 @@ This Matlab function is accessible [[file:voltageToVelocityL22.m][here]].
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0); S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
#+end_src #+end_src
#+begin_src matlab
voltage = detrend(voltage);
#+end_src
#+begin_src matlab #+begin_src matlab
velocity = lsim((S*10^(gain/20))\1, voltage, time); velocity = lsim((S*10^(gain/20))\1, voltage, time);
#+end_src #+end_src
@ -70,9 +74,128 @@ This Matlab function is accessible [[file:voltageToDisplacementL22.m][here]].
#+end_src #+end_src
#+begin_src matlab #+begin_src matlab
voltage = voltage - mean(voltage);
velocity = voltageToVelocityL22(voltage, time, gain); velocity = voltageToVelocityL22(voltage, time, gain);
disp = lsim(1/s, velocity, time); disp = lsim(1/s, velocity, time);
#+end_src #+end_src
* getGroundVelocity
:PROPERTIES:
:header-args:matlab+: :tangle getGroundVelocity.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:getGroundVelocity>>
This Matlab function is accessible [[file:getGroundVelocity.m][here]].
#+begin_src matlab
function [time, velocity] = getGroundVelocity()
% getGroundVelocity -
%
% Syntax: [time, velocity] = voltageToVelocityL22()
%
% Inputs:
% - -
%
% Outputs:
% - time - in [s]
% - velocity - in [m/s]
current_dir = pwd;
src_dir = mfilename('fullpath');
src_dir = strsplit(src_dir, '/');
src_dir = strjoin(src_dir(1:end-1), '/');
cd(src_dir);
data = load('mat/data_028.mat', 'data'); data = data.data;
time = data(:, 3);
[velocity] = voltageToVelocityL22(data(:, 1), time, 60);
cd(current_dir);
end
#+end_src
* getGroundDisplacement
:PROPERTIES:
:header-args:matlab+: :tangle getGroundDisplacement.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:getGroundDisplacement>>
This Matlab function is accessible [[file:getGroundDisplacement.m][here]].
#+begin_src matlab
function [time, displacement] = getGroundDisplacement()
% getGroundDisplacement -
%
% Syntax: [time, displacement] = voltageToVelocityL22()
%
% Inputs:
% - -
%
% Outputs:
% - time - in [s]
% - displacement - in [m]
s = zpk('s');
[time, velocity] = getGroundVelocity();
displacement = lsim(1/s, velocity, time);
end
#+end_src
* getPSDGroundVelocity
:PROPERTIES:
:header-args:matlab+: :tangle getPSDGroundVelocity.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:getPSDGroundVelocity>>
This Matlab function is accessible [[file:getPSDGroundVelocity.m][here]].
#+begin_src matlab
function [pxx, f] = getPSDGroundVelocity()
% getPSDGroundVelocity -
%
% Syntax: [pxx, f] = voltageToVelocityL22(in_data)
%
% Outputs:
% - psd -
% - f -
[time, velocity] = getGroundVelocity();
dt = time(2) - time(1);
Fs = 1/dt;
win = hanning(ceil(10*Fs));
[pxx, f] = pwelch(velocity, win, [], [], Fs);
#+end_src
* getPSDGroundDisplacement
:PROPERTIES:
:header-args:matlab+: :tangle getPSDGroundDisplacement.m
:header-args:matlab+: :comments org :mkdirp yes
:header-args:matlab+: :eval no :results none
:END:
<<sec:getPSDGroundDisplacement>>
This Matlab function is accessible [[file:getPSDGroundDisplacement.m][here]].
#+begin_src matlab
function [pxx, f] = getPSDGroundDisplacement()
% getPSDGroundDisplacement -
%
% Syntax: [pxx, f] = voltageToVelocityL22(in_data)
%
% Outputs:
% - pxx -
% - f -
[pxx, f] = getPSDGroundVelocity();
pxx = (sqrt(pxx)./(2*pi*f)).^2;
#+end_src

2
src/voltageToDisplacementL22.m
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@ -13,8 +13,6 @@ function [disp] = voltageToDisplacementL22(voltage, time, gain)
s = zpk('s'); s = zpk('s');
voltage = voltage - mean(voltage);
velocity = voltageToVelocityL22(voltage, time, gain); velocity = voltageToVelocityL22(voltage, time, gain);
disp = lsim(1/s, velocity, time); disp = lsim(1/s, velocity, time);

2
src/voltageToVelocityL22.m
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@ -18,4 +18,6 @@ f0 = 2; % Cut-off frequnecy [Hz]
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0); S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
voltage = detrend(voltage);
velocity = lsim((S*10^(gain/20))\1, voltage, time); velocity = lsim((S*10^(gain/20))\1, voltage, time);