Use online CSS and JS
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<title>Vibrations induced by the translation stage motion</title>
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/*]]>*/-->
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/*
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@licstart The following is the entire license notice for the
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JavaScript code in this tag.
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Copyright (C) 2012-2019 Free Software Foundation, Inc.
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The JavaScript code in this tag is free software: you can
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redistribute it and/or modify it under the terms of the GNU
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General Public License (GNU GPL) as published by the Free Software
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Foundation, either version 3 of the License, or (at your option)
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any later version. The code is distributed WITHOUT ANY WARRANTY;
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without even the implied warranty of MERCHANTABILITY or FITNESS
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FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
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As additional permission under GNU GPL version 3 section 7, you
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may distribute non-source (e.g., minimized or compacted) forms of
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that code without the copy of the GNU GPL normally required by
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section 4, provided you include this license notice and a URL
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through which recipients can access the Corresponding Source.
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@licend The above is the entire license notice
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for the JavaScript code in this tag.
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*/
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/*]]>*///-->
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<body>
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<div id="org-div-home-and-up">
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@@ -258,30 +22,30 @@ for the JavaScript code in this tag.
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#org810c300">1. Measurement description</a></li>
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<li><a href="#orge7c9591">2. Measurement Analysis</a>
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<li><a href="#org2aaea5a">1. Measurement description</a></li>
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<li><a href="#orgb83e4a0">2. Measurement Analysis</a>
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<ul>
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<li><a href="#orgec8ecca">2.1. Load data</a></li>
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<li><a href="#orgcd50803">2.2. Voltage to Velocity</a></li>
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<li><a href="#org1c8a0dc">2.3. Time domain plots</a></li>
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<li><a href="#org0d692f4">2.4. Frequency Domain</a></li>
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<li><a href="#orgd741d6b">2.5. Relative Motion</a></li>
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<li><a href="#org3ded48e">2.6. Save</a></li>
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<li><a href="#org4fbe75b">2.7. Position of the translation stage and Current</a>
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<li><a href="#orga4b0f90">2.1. Load data</a></li>
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<li><a href="#org08f7d3b">2.2. Voltage to Velocity</a></li>
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<li><a href="#orga7eb7f7">2.3. Time domain plots</a></li>
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<li><a href="#org7915079">2.4. Frequency Domain</a></li>
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||||
<li><a href="#org7197f2e">2.5. Relative Motion</a></li>
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<li><a href="#orgdef72b0">2.6. Save</a></li>
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||||
<li><a href="#org6e3ca4c">2.7. Position of the translation stage and Current</a>
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<ul>
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<li><a href="#orge07cd8f">2.7.1. Data pre-processing</a></li>
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<li><a href="#org851b639">2.7.2. Time domain data</a></li>
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||||
<li><a href="#org363d3eb">2.7.1. Data pre-processing</a></li>
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||||
<li><a href="#org7b14198">2.7.2. Time domain data</a></li>
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</ul>
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</li>
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||||
<li><a href="#org011cbae">2.8. Conclusion</a></li>
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<li><a href="#orge66d0f8">2.8. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org810c300" class="outline-2">
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<h2 id="org810c300"><span class="section-number-2">1</span> Measurement description</h2>
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||||
<div id="outline-container-org2aaea5a" class="outline-2">
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||||
<h2 id="org2aaea5a"><span class="section-number-2">1</span> Measurement description</h2>
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||||
<div class="outline-text-2" id="text-1">
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<p>
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<b>Setup</b>:
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||||
@@ -311,7 +75,7 @@ The scans are done with the ELMO software.
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</p>
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||||
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||||
<p>
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||||
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>).
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||||
The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure <a href="#org0e95dcd">1</a>).
|
||||
</p>
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||||
|
||||
<p>
|
||||
@@ -395,7 +159,7 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
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</table>
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||||
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||||
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||||
<div id="orgc5e9621" class="figure">
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||||
<div id="org0e95dcd" class="figure">
|
||||
<p><img src="./img/IMG_20190513_163032.jpg" alt="IMG_20190513_163032.jpg" width="500px" />
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||||
</p>
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||||
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
|
||||
@@ -408,13 +172,13 @@ The setup used for the measurement is described <a href="file:///home/thomas/Clo
|
||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-orge7c9591" class="outline-2">
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||||
<h2 id="orge7c9591"><span class="section-number-2">2</span> Measurement Analysis</h2>
|
||||
<div id="outline-container-orgb83e4a0" class="outline-2">
|
||||
<h2 id="orgb83e4a0"><span class="section-number-2">2</span> Measurement Analysis</h2>
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||||
<div class="outline-text-2" id="text-2">
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||||
<p>
|
||||
<a id="org8955a2d"></a>
|
||||
<a id="orgacbdcf3"></a>
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||||
</p>
|
||||
<div class="note">
|
||||
<div class="note" id="org3969b90">
|
||||
<p>
|
||||
All the files (data and Matlab scripts) are accessible <a href="data/disturbance_ty.zip">here</a>.
|
||||
</p>
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||||
@@ -422,18 +186,18 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
|
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</div>
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</div>
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||||
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||||
<div id="outline-container-orgec8ecca" class="outline-3">
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||||
<h3 id="orgec8ecca"><span class="section-number-3">2.1</span> Load data</h3>
|
||||
<div id="outline-container-orga4b0f90" class="outline-3">
|
||||
<h3 id="orga4b0f90"><span class="section-number-3">2.1</span> Load data</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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||||
<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 class="src src-matlab">z_ty = load(<span class="org-string">'mat/data_040.mat'</span>, <span class="org-string">'data'</span>); z_ty = z_ty.data;
|
||||
z_of = load(<span class="org-string">'mat/data_051.mat'</span>, <span class="org-string">'data'</span>); z_of = z_of.data;
|
||||
e_ty = load(<span class="org-string">'mat/data_041.mat'</span>, <span class="org-string">'data'</span>); e_ty = e_ty.data;
|
||||
e_of = load(<span class="org-string">'mat/data_042.mat'</span>, <span class="org-string">'data'</span>); e_of = e_of.data;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="warning">
|
||||
<div class="warning" id="orgd72d7d3">
|
||||
<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.
|
||||
@@ -442,70 +206,70 @@ The problem probably comes from the wiring in the Slip-Ring.
|
||||
</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 class="src src-matlab">z_ty(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>z_ty(<span class="org-type">:</span>, 2);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgcd50803" class="outline-3">
|
||||
<h3 id="orgcd50803"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
|
||||
<div id="outline-container-org08f7d3b" class="outline-3">
|
||||
<h3 id="org08f7d3b"><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/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>
|
||||
<pre class="src src-matlab">gain = 40; <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-type">:</span>, 1) = voltageToVelocityL22(z_ty(<span class="org-type">:</span>, 1), z_ty(<span class="org-type">:</span>, 3), gain);
|
||||
z_of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(z_of(<span class="org-type">:</span>, 1), z_of(<span class="org-type">:</span>, 3), gain);
|
||||
e_ty(<span class="org-type">:</span>, 1) = voltageToVelocityL22(e_ty(<span class="org-type">:</span>, 1), e_ty(<span class="org-type">:</span>, 3), gain);
|
||||
e_of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(e_of(<span class="org-type">:</span>, 1), e_of(<span class="org-type">:</span>, 3), gain);
|
||||
|
||||
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>;
|
||||
z_ty(<span class="org-type">:</span>, 2) = voltageToVelocityL22(z_ty(<span class="org-type">:</span>, 2), z_ty(<span class="org-type">:</span>, 3), gain);
|
||||
z_of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(z_of(<span class="org-type">:</span>, 2), z_of(<span class="org-type">:</span>, 3), gain);
|
||||
e_ty(<span class="org-type">:</span>, 2) = voltageToVelocityL22(e_ty(<span class="org-type">:</span>, 2), e_ty(<span class="org-type">:</span>, 3), gain);
|
||||
e_of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(e_of(<span class="org-type">:</span>, 2), e_of(<span class="org-type">:</span>, 3), gain);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1c8a0dc" class="outline-3">
|
||||
<h3 id="org1c8a0dc"><span class="section-number-3">2.3</span> Time domain plots</h3>
|
||||
<div id="outline-container-orga7eb7f7" class="outline-3">
|
||||
<h3 id="orga7eb7f7"><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="#org60b7c99">2</a>) and in the X direction (figure <a href="#orgc2eb360">3</a>).
|
||||
We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org2bf33b7">2</a>) and in the X direction (figure <a href="#orgfdb2237">3</a>).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
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).
|
||||
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgdf208c5">4</a> in the X direction and figure <a href="#org29f0aa7">5</a> in the Z direction).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org60b7c99" class="figure">
|
||||
<div id="org2bf33b7" 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 id="orgc2eb360" class="figure">
|
||||
<div id="orgfdb2237" 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 id="orgdcb90f2" class="figure">
|
||||
<div id="orgdf208c5" 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 id="orgd1edd4b" class="figure">
|
||||
<div id="org29f0aa7" 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>
|
||||
@@ -513,14 +277,14 @@ We also integrate the relative velocity to obtain the relative displacement (fig
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0d692f4" class="outline-3">
|
||||
<h3 id="org0d692f4"><span class="section-number-3">2.4</span> Frequency Domain</h3>
|
||||
<div id="outline-container-org7915079" class="outline-3">
|
||||
<h3 id="org7915079"><span class="section-number-3">2.4</span> Frequency Domain</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<p>
|
||||
We load measured ground motion at ID31 to compare with the velocities measured.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">gm = load(<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>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -528,11 +292,11 @@ We load measured ground motion at ID31 to compare with the velocities measured.
|
||||
We first compute some parameters that will be used for the PSD computation.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">dt = z_ty<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>z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">dt = z_ty(2, 3)<span class="org-type">-</span>z_ty(1, 3);
|
||||
|
||||
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
|
||||
Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
|
||||
|
||||
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
win = hanning(ceil(10<span class="org-type">*</span>Fs));
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -544,10 +308,10 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
|
||||
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 class="src src-matlab">[pxz_ty_m, f] = pwelch(z_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
[pxz_of_m, <span class="org-type">~</span>] = pwelch(z_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
[pxe_ty_m, <span class="org-type">~</span>] = pwelch(e_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
[pxe_of_m, <span class="org-type">~</span>] = pwelch(e_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -555,10 +319,10 @@ First for the geophone located on the marble
|
||||
And for the geophone located at the sample position.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>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 class="src src-matlab">[pxz_ty_s, <span class="org-type">~</span>] = pwelch(z_ty(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
|
||||
[pxz_of_s, <span class="org-type">~</span>] = pwelch(z_of(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
|
||||
[pxe_ty_s, <span class="org-type">~</span>] = pwelch(e_ty(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
|
||||
[pxe_of_s, <span class="org-type">~</span>] = pwelch(e_of(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
@@ -566,13 +330,13 @@ And for the geophone located at the sample position.
|
||||
And we plot the ASD of the measured velocities:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<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>
|
||||
<li>figure <a href="#orgca2c421">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
|
||||
<li>figure <a href="#org0dcea9c">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
|
||||
<li>figure <a href="#orgd07432f">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<div id="org888ff45" class="figure">
|
||||
<div id="orgca2c421" 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>
|
||||
@@ -580,7 +344,7 @@ And we plot the ASD of the measured velocities:
|
||||
|
||||
|
||||
|
||||
<div id="orgde2e042" class="figure">
|
||||
<div id="org0dcea9c" 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>
|
||||
@@ -588,14 +352,14 @@ And we plot the ASD of the measured velocities:
|
||||
|
||||
|
||||
|
||||
<div id="orga58a3f5" class="figure">
|
||||
<div id="orgd07432f" 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">
|
||||
<div id="org7ccf215" 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>
|
||||
@@ -603,39 +367,53 @@ And we plot the ASD of the measured velocities:
|
||||
</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 id="outline-container-org7197f2e" class="outline-3">
|
||||
<h3 id="org7197f2e"><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 class="src src-matlab">[pxz_ty_r, f] = pwelch(z_ty(<span class="org-type">:</span>, 2)<span class="org-type">-</span>z_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
[pxz_of_r, <span class="org-type">~</span>] = pwelch(z_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>z_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
[pxe_ty_r, <span class="org-type">~</span>] = pwelch(e_ty(<span class="org-type">:</span>, 2)<span class="org-type">-</span>e_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
[pxe_of_r, <span class="org-type">~</span>] = pwelch(e_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>e_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
|
||||
</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
|
||||
Fig. <a href="#org4172285">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>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>;
|
||||
plot(f, sqrt(pxz_of_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - Z'</span>);
|
||||
plot(f, sqrt(pxz_of_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - Z'</span>);
|
||||
plot(f, sqrt(pxz_of_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - Z'</span>);
|
||||
hold off;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'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>;
|
||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
|
||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
|
||||
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span>);
|
||||
xlim([0.1, 500]);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
hold on;
|
||||
plot(f, sqrt(pxz_of_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - Z'</span>);
|
||||
plot(f, sqrt(pxz_ty_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - Z'</span>);
|
||||
hold off;
|
||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
|
||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
|
||||
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span>);
|
||||
xlim([0.1, 500]);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org61c3a2e" class="figure">
|
||||
<div id="org0a0b6dc" class="figure">
|
||||
<p><img src="figs/asd_z_relative.png" alt="asd_z_relative.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
|
||||
@@ -644,19 +422,19 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
<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'</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>;
|
||||
plot(f, sqrt(pxe_of_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - E'</span>);
|
||||
plot(f, sqrt(pxe_ty_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - E'</span>);
|
||||
hold off;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'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>;
|
||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
|
||||
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
|
||||
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
|
||||
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span>);
|
||||
xlim([0.1, 500]);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7d4814e" class="figure">
|
||||
<div id="org4172285" class="figure">
|
||||
<p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
|
||||
@@ -664,108 +442,141 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3ded48e" class="outline-3">
|
||||
<h3 id="org3ded48e"><span class="section-number-3">2.6</span> Save</h3>
|
||||
<div id="outline-container-orgdef72b0" class="outline-3">
|
||||
<h3 id="orgdef72b0"><span class="section-number-3">2.6</span> Save</h3>
|
||||
<div class="outline-text-3" id="text-2-6">
|
||||
<p>
|
||||
The Power Spectral Density of the relative velocity is saved for further analysis.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/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 class="src src-matlab">save(<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-string">'pxz_ty_s'</span>);
|
||||
save(<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-string">'pxe_ty_s'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<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 id="outline-container-org6e3ca4c" class="outline-3">
|
||||
<h3 id="org6e3ca4c"><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-orge07cd8f" class="outline-4">
|
||||
<h4 id="orge07cd8f"><span class="section-number-4">2.7.1</span> Data pre-processing</h4>
|
||||
<div id="outline-container-org363d3eb" class="outline-4">
|
||||
<h4 id="org363d3eb"><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.
|
||||
Let’s look at at the start of the csv file.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-bash">sed -n <span class="org-highlight-numbers-number">1,30p</span> mat/sin_elmo.csv | nl -ba -
|
||||
<pre class="src src-bash">sed -n 1,30p mat/sin_elmo.csv | nl -ba -
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<pre class="example" id="org7539d3f">
|
||||
1 Elmo txt chart ver 2.0
|
||||
2
|
||||
3 [File Properties]
|
||||
4 Creation Time,2019-05-13 05:11:45
|
||||
5 Last Updated,2019-05-13 05:11:45
|
||||
6 Resolution,0.001
|
||||
7 Sampling Time,5E-05
|
||||
8 Recording Time,5.461
|
||||
9
|
||||
10 [Chart Properties]
|
||||
11 No.,Name,X Linear,X No.
|
||||
12 1,Chart #1,True,0
|
||||
13 2,Chart #2,True,0
|
||||
14
|
||||
15 [Chart Data]
|
||||
16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
|
||||
17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
|
||||
18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
|
||||
19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
|
||||
20
|
||||
21 [Signal Names]
|
||||
22 1,Time (sec)
|
||||
23 2,Position [cnt]
|
||||
24 3,Current Command [A]
|
||||
25 4,Total Current Command [A]
|
||||
26
|
||||
27 [Signals Data Group 1]
|
||||
28 1,2,3,4,
|
||||
29 0,1110769,-0.320872406596209,-0.320872406596209,
|
||||
30 0.001,1108743,-0.319658428261391,-0.319658428261391,
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
The real data starts at line 29.
|
||||
We then load this <code>cvs</code> file starting at line 29.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">data = csvread<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">"mat/sin_elmo.csv"</span>, <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<pre class="src src-matlab">data = csvread(<span class="org-string">"mat/sin_elmo.csv"</span>, 29, 0);
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<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 id="outline-container-org7b14198" class="outline-4">
|
||||
<h4 id="org7b14198"><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="#orgf3ec62f">12</a>.
|
||||
The result is shown on figure <a href="#org5fc3c58">12</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>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>;
|
||||
plot(data(<span class="org-type">:</span>, 1), data(<span class="org-type">:</span>, 2)<span class="org-type">/</span>200000);
|
||||
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-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>;
|
||||
xlim([0, 5]);
|
||||
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Position [mm]'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgf3ec62f" class="figure">
|
||||
<div id="org5fc3c58" 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="org501c879" class="figure">
|
||||
<div id="org8a1581f" 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="#orge486741">14</a>.
|
||||
We also plot the current as function of the time on figure <a href="#org43368d0">14</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
hold on;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>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>;
|
||||
plot(data(<span class="org-type">:</span>, 1), data(<span class="org-type">:</span>, 3));
|
||||
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-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>;
|
||||
xlim([0, 5]); ylim([<span class="org-type">-</span>10, 10]);
|
||||
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Current [A]'</span>);
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orge486741" class="figure">
|
||||
<div id="org43368d0" 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="org8b9bcbe" class="figure">
|
||||
<div id="org6a48bae" 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>
|
||||
@@ -774,10 +585,10 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org011cbae" class="outline-3">
|
||||
<h3 id="org011cbae"><span class="section-number-3">2.8</span> Conclusion</h3>
|
||||
<div id="outline-container-orge66d0f8" class="outline-3">
|
||||
<h3 id="orge66d0f8"><span class="section-number-3">2.8</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-8">
|
||||
<div class="important">
|
||||
<div class="important" id="org637452e">
|
||||
<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 value of the translation stage encoder can also be read with the speedgoat, this could permit to synchronize the measurements</li>
|
||||
@@ -790,8 +601,7 @@ 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: 2019-10-31 jeu. 18:00</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
<p class="date">Created: 2020-11-12 jeu. 10:27</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user