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Thomas Dehaeze
2020-04-27 11:35:57 +02:00
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@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-06-19 mer. 11:12 -->
<!-- 2019-10-31 jeu. 18:00 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by the translation stage motion</title>
@@ -258,29 +258,30 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org39f8fb3">1. Measurement description</a></li>
<li><a href="#org9c1c4dc">2. Measurement Analysis</a>
<li><a href="#org810c300">1. Measurement description</a></li>
<li><a href="#orge7c9591">2. Measurement Analysis</a>
<ul>
<li><a href="#org83beca6">2.1. Load data</a></li>
<li><a href="#org6739365">2.2. Voltage to Velocity</a></li>
<li><a href="#org0e76d60">2.3. Time domain plots</a></li>
<li><a href="#orgae02709">2.4. Frequency Domain analysis</a></li>
<li><a href="#org86d8525">2.5. Transfer function from marble motion in the East direction to sample motion in the East direction</a></li>
<li><a href="#orgfdf507c">2.6. Position of the translation stage and Current</a>
<li><a href="#orgec8ecca">2.1. Load data</a></li>
<li><a href="#orgcd50803">2.2. Voltage to Velocity</a></li>
<li><a href="#org1c8a0dc">2.3. Time domain plots</a></li>
<li><a href="#org0d692f4">2.4. Frequency Domain</a></li>
<li><a href="#orgd741d6b">2.5. Relative Motion</a></li>
<li><a href="#org3ded48e">2.6. Save</a></li>
<li><a href="#org4fbe75b">2.7. Position of the translation stage and Current</a>
<ul>
<li><a href="#orgc57aee0">2.6.1. Data pre-processing</a></li>
<li><a href="#orgb39f0c9">2.6.2. Time domain data</a></li>
<li><a href="#orge07cd8f">2.7.1. Data pre-processing</a></li>
<li><a href="#org851b639">2.7.2. Time domain data</a></li>
</ul>
</li>
<li><a href="#org7881c9d">2.7. Conclusion</a></li>
<li><a href="#org011cbae">2.8. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org39f8fb3" class="outline-2">
<h2 id="org39f8fb3"><span class="section-number-2">1</span> Measurement description</h2>
<div id="outline-container-org810c300" class="outline-2">
<h2 id="org810c300"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1">
<p>
<b>Setup</b>:
@@ -295,7 +296,7 @@ Two geophone are use:
Two voltage amplifiers are used, their setup is:
</p>
<ul class="org-ul">
<li>gain of 40dB (the gain at the be lowered from 60dB to 40dB to not saturate the voltage amplifiers)</li>
<li>gain of 40dB (the gain had to be lowered from 60dB to 40dB in order to not saturate the voltage amplifiers)</li>
<li>AC/DC switch on AC</li>
<li>Low pass filter at 1kHz</li>
</ul>
@@ -310,7 +311,7 @@ The scans are done with the ELMO software.
</p>
<p>
The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure <a href="#orgf0c462e">1</a>).
The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure <a href="#orgc5e9621">1</a>).
</p>
<p>
@@ -394,19 +395,24 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table>
<div id="orgf0c462e" class="figure">
<div id="orgc5e9621" class="figure">
<p><img src="./img/IMG_20190513_163032.jpg" alt="IMG_20190513_163032.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
</div>
<p>
We also use the file <code>mat/data_051.mat</code> when we measure the z direction when everything is off.
The setup used for the measurement is described <a href="file:///home/thomas/Cloud/thesis/matlab/meas/disturbance-ty-sr/index.html">here</a>.
</p>
</div>
</div>
<div id="outline-container-org9c1c4dc" class="outline-2">
<h2 id="org9c1c4dc"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div id="outline-container-orge7c9591" class="outline-2">
<h2 id="orge7c9591"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="orgd482cbe"></a>
<a id="org8955a2d"></a>
</p>
<div class="note">
<p>
@@ -416,33 +422,49 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div>
</div>
<div id="outline-container-org83beca6" class="outline-3">
<h3 id="org83beca6"><span class="section-number-3">2.1</span> Load data</h3>
<div id="outline-container-orgec8ecca" class="outline-3">
<h3 id="orgec8ecca"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">z_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_040.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_ty = z_ty.data;
e_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_041.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_ty = e_ty.data;
e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_042.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_of = e_of.data;
<pre class="src src-matlab">z_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_040.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_ty = z_ty.data;
z_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_of = z_of.data;
e_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_041.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_ty = e_ty.data;
e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_042.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_of = e_of.data;
</pre>
</div>
<div class="warning">
<p>
There is probably a sign error for the Geophone located on top of the Hexapod (only for the z direction).
The problem probably comes from the wiring in the Slip-Ring.
</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab">z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org6739365" class="outline-3">
<h3 id="org6739365"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div id="outline-container-orgcd50803" class="outline-3">
<h3 id="orgcd50803"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/These/meas/src/index.html">here</a>).
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">40</span>; <span class="org-comment">% [dB]</span>
z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
z_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
z_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
@@ -450,80 +472,40 @@ e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">
</div>
</div>
<div id="outline-container-org0e76d60" class="outline-3">
<h3 id="org0e76d60"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div id="outline-container-org1c8a0dc" class="outline-3">
<h3 id="org1c8a0dc"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org34814fe">2</a>) and in the X direction (figure <a href="#org8e9b7b5">3</a>).
We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org60b7c99">2</a>) and in the X direction (figure <a href="#orgc2eb360">3</a>).
</p>
<p>
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgd86ada1">4</a> in the X direction and figure <a href="#org3e96a6b">5</a> in the Z direction).
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgdcb90f2">4</a> in the X direction and figure <a href="#orgd1edd4b">5</a> in the Z direction).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org34814fe" class="figure">
<div id="org60b7c99" class="figure">
<p><img src="figs/ty_z_time.png" alt="ty_z_time.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Z velocity of the sample and marble when scanning with the translation stage</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org8e9b7b5" class="figure">
<div id="orgc2eb360" class="figure">
<p><img src="figs/ty_e_time.png" alt="ty_e_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1e6</span><span class="org-type">*</span>lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, e_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>e_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, e_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>X Relative Displacement <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgd86ada1" class="figure">
<div id="orgdcb90f2" class="figure">
<p><img src="figs/x_relative_disp.png" alt="x_relative_disp.png" />
</p>
<p><span class="figure-number">Figure 4: </span>X relative displacement of the sample with respect to the marble</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1e6</span><span class="org-type">*</span>lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, z_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, z_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Z Relative Displacement <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org3e96a6b" class="figure">
<div id="orgd1edd4b" class="figure">
<p><img src="figs/z_relative_disp.png" alt="z_relative_disp.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Z relative disp of the sample with respect to the marble</p>
@@ -531,14 +513,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div>
</div>
<div id="outline-container-orgae02709" class="outline-3">
<h3 id="orgae02709"><span class="section-number-3">2.4</span> Frequency Domain analysis</h3>
<div id="outline-container-org0d692f4" class="outline-3">
<h3 id="org0d692f4"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We get the typical ground velocity to compare with the velocities measured.
We load measured ground motion at ID31 to compare with the velocities measured.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx_gm, f_gm<span class="org-rainbow-delimiters-depth-1">]</span> = getPSDGroundVelocity<span class="org-rainbow-delimiters-depth-1">()</span>;
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
@@ -563,6 +545,7 @@ First for the geophone located on the marble
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
@@ -573,190 +556,139 @@ And for the geophone located at the sample position.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And finally for the relative velocity between the sample and the marble.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
And we plot the ASD of the measured velocities:
</p>
<ul class="org-ul">
<li>figure <a href="#org94d27c9">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgb11f07e">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgaefec33">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
<li>figure <a href="#org0099071">9</a> shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz</li>
<li>figure <a href="#org888ff45">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgde2e042">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orga58a3f5">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Marble <span class="org-type">-</span> X'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF - Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f_gm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx_gm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k--', 'DisplayName', 'Ground Motion'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org94d27c9" class="figure">
<div id="org888ff45" class="figure">
<p><img src="figs/asd_east_marble.png" alt="asd_east_marble.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located on the marble when the translation stage is OFF and when it is scanning at 1Hz</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Sample <span class="org-type">-</span> X'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF - Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f_gm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx_gm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k--', 'DisplayName', 'Ground Motion'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgb11f07e" class="figure">
<div id="orgde2e042" class="figure">
<p><img src="figs/asd_east_sample.png" alt="asd_east_sample.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located at the sample location when the translation stage is OFF and when it is scanning at 1Hz</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_ty_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Marble <span class="org-type">-</span> Z'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_ty_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Sample <span class="org-type">-</span> Z'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f_gm, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx_gm<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k--', 'DisplayName', 'Ground Motion'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgaefec33" class="figure">
<div id="orga58a3f5" class="figure">
<p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p>
</div>
<div id="org1dd835a" class="figure">
<p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p>
</div>
</div>
</div>
<div id="outline-container-orgd741d6b" class="outline-3">
<h3 id="orgd741d6b"><span class="section-number-3">2.5</span> Relative Motion</h3>
<div class="outline-text-3" id="text-2-5">
<p>
And finally for the relative velocity between the sample and the marble.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_r, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Fig. <a href="#org7d4814e">11</a> shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF - Relative - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> E'<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> Z<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org0099071" class="figure">
<p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" />
<div id="org61c3a2e" class="figure">
<p><img src="figs/asd_z_relative.png" alt="asd_z_relative.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
<p><span class="figure-number">Figure 10: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
</div>
</div>
</div>
<div id="outline-container-org86d8525" class="outline-3">
<h3 id="org86d8525"><span class="section-number-3">2.5</span> Transfer function from marble motion in the East direction to sample motion in the East direction</h3>
<div class="outline-text-3" id="text-2-5">
<p>
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.
</p>
<p>
We first plot the time domain motions when every stage is off (figure <a href="#orgb0f7dd4">10</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> E<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgb0f7dd4" class="figure">
<p><img src="figs/east_marble_sample.png" alt="east_marble_sample.png" />
<div id="org7d4814e" class="figure">
<p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Velocity in the east direction of the marble and sample when all the stages are OFF</p>
<p><span class="figure-number">Figure 11: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
</div>
</div>
</div>
<div id="outline-container-org3ded48e" class="outline-3">
<h3 id="org3ded48e"><span class="section-number-3">2.6</span> Save</h3>
<div class="outline-text-3" id="text-2-6">
<p>
We then compute the transfer function using <code>tfestimate</code>.
The Power Spectral Density of the relative velocity is saved for further analysis.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>T, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxz_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxz_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxe_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxe_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
The result is shown on figure <a href="#orgc32127e">11</a>.
</p>
<div id="orgc32127e" class="figure">
<p><img src="figs/tf_east_marble_sample.png" alt="tf_east_marble_sample.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction</p>
</div>
</div>
</div>
<div id="outline-container-orgfdf507c" class="outline-3">
<h3 id="orgfdf507c"><span class="section-number-3">2.6</span> Position of the translation stage and Current</h3>
<div class="outline-text-3" id="text-2-6">
<div id="outline-container-org4fbe75b" class="outline-3">
<h3 id="org4fbe75b"><span class="section-number-3">2.7</span> Position of the translation stage and Current</h3>
<div class="outline-text-3" id="text-2-7">
<p>
The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file.
</p>
</div>
<div id="outline-container-orgc57aee0" class="outline-4">
<h4 id="orgc57aee0"><span class="section-number-4">2.6.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-6-1">
<div id="outline-container-orge07cd8f" class="outline-4">
<h4 id="orge07cd8f"><span class="section-number-4">2.7.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-7-1">
<p>
Let's look at at the start of the csv file.
</p>
@@ -778,13 +710,13 @@ We then load this <code>cvs</code> file starting at line 29.
</div>
</div>
<div id="outline-container-orgb39f0c9" class="outline-4">
<h4 id="orgb39f0c9"><span class="section-number-4">2.6.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-6-2">
<div id="outline-container-org851b639" class="outline-4">
<h4 id="org851b639"><span class="section-number-4">2.7.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-7-2">
<p>
We plot the position of the translation stage measured by the encoders.
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
The result is shown on figure <a href="#org3c042ab">12</a>.
The result is shown on figure <a href="#orgf3ec62f">12</a>.
</p>
<div class="org-src-container">
@@ -793,26 +725,26 @@ hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="org3c042ab" class="figure">
<div id="orgf3ec62f" class="figure">
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Y position of the translation stage measured by the encoders</p>
</div>
<div id="orgac4a46b" class="figure">
<div id="org501c879" class="figure">
<p><img src="figs/ty_position_time_zoom.png" alt="ty_position_time_zoom.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Y position of the translation stage measured by the encoders - Zoom</p>
</div>
<p>
We also plot the current as function of the time on figure <a href="#orgc686f17">14</a>.
We also plot the current as function of the time on figure <a href="#orge486741">14</a>.
</p>
<div class="org-src-container">
@@ -821,19 +753,19 @@ hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgc686f17" class="figure">
<div id="orge486741" class="figure">
<p><img src="figs/current_time.png" alt="current_time.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Current going through the actuator of the translation stage</p>
</div>
<div id="org3b181bb" class="figure">
<div id="org8b9bcbe" class="figure">
<p><img src="figs/current_time_zoom.png" alt="current_time_zoom.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Current going through the actuator of the translation stage - Zoom</p>
@@ -842,9 +774,9 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
</div>
<div id="outline-container-org7881c9d" class="outline-3">
<h3 id="org7881c9d"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-7">
<div id="outline-container-org011cbae" class="outline-3">
<h3 id="org011cbae"><span class="section-number-3">2.8</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-8">
<div class="important">
<ul class="org-ul">
<li>The acquisition is done using the Speedgoat as well as using ELMO. The two acquisition are <b>not</b> synchronize</li>
@@ -858,7 +790,7 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-06-19 mer. 11:12</p>
<p class="date">Created: 2019-10-31 jeu. 18:00</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

160
disturbance-ty/index.org
View File

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

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