1411 lines
130 KiB
HTML
1411 lines
130 KiB
HTML
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Effect on the control system of each stages on the vibration of the station</h1>
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<div id="table-of-contents">
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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="#orgbbaaa98">1. Effect of all the control systems on the Sample vibrations</a>
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<ul>
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<li><a href="#org06b693f">1.1. Experimental Setup</a></li>
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<li><a href="#orgd47a227">1.2. Load data</a></li>
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<li><a href="#orgef1cef2">1.3. Analysis - Time Domain</a></li>
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<li><a href="#orgab71525">1.4. Analysis - Frequency Domain</a>
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<ul>
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<li><a href="#org93314dd">1.4.1. Vibrations at the sample location</a></li>
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<li><a href="#org39db171">1.4.2. Vibrations on the marble</a></li>
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</ul>
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</li>
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<li><a href="#org8f07d2e">1.5. Effect of the control system on the transmissibility from ground to sample</a></li>
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<li><a href="#org47a7f4c">1.6. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org96b6d66">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a>
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<ul>
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<li><a href="#org21aea52">2.1. Experimental Setup</a></li>
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<li><a href="#orgf9fa5d1">2.2. Load data</a></li>
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<li><a href="#orgb1aceca">2.3. Voltage to Velocity</a></li>
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<li><a href="#org9deea89">2.4. Analysis - Time Domain</a></li>
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<li><a href="#orga52ae70">2.5. Analysis - Frequency Domain</a>
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<ul>
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<li><a href="#orgc044b46">2.5.1. Vibrations at the sample location</a></li>
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<li><a href="#orgff12b0a">2.5.2. Vibrations on the marble</a></li>
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</ul>
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</li>
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<li><a href="#orgf832269">2.6. Conclusion</a></li>
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</ul>
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</li>
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<li><a href="#org76bb785">3. Effect of the Symetrie Driver</a>
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<ul>
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<li><a href="#org3e3d670">3.1. Experimental Setup</a></li>
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<li><a href="#org2c5eb48">3.2. Load data</a></li>
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<li><a href="#org7b92812">3.3. Analysis - Time Domain</a></li>
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<li><a href="#orgd042971">3.4. Analysis - Frequency Domain</a>
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<ul>
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<li><a href="#orgdc25bb2">3.4.1. Vibrations at the sample location</a></li>
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</ul>
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</li>
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<li><a href="#org2a573c2">3.5. 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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<p>
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For all the measurements shown here:
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</p>
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<ul class="org-ul">
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<li>geophones used are L22 with a resonance frequency of 1Hz</li>
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<li>the signals are amplified with voltage amplifiers with a gain of 60dB</li>
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<li>the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz</li>
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</ul>
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<div id="outline-container-orgbbaaa98" class="outline-2">
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<h2 id="orgbbaaa98"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="orgdddc824"></a>
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</p>
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<div class="note">
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<p>
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All the files (data and Matlab scripts) are accessible <a href="data/effect_control_all.zip">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-org06b693f" class="outline-3">
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<h3 id="org06b693f"><span class="section-number-3">1.1</span> Experimental Setup</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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We here measure the signals of two geophones:
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</p>
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<ul class="org-ul">
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<li>One is located on top of the Sample platform</li>
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<li>One is located on the marble</li>
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</ul>
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<p>
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The signal from the top geophone does not go trought the slip-ring.
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</p>
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<p>
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First, all the control systems are turned ON, then, they are turned one by one.
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Each measurement are done during 50s.
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</p>
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<table id="org3dc1795" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption>
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<colgroup>
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left">Ty</th>
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<th scope="col" class="org-left">Ry</th>
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<th scope="col" class="org-left">Slip Ring</th>
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<th scope="col" class="org-left">Spindle</th>
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<th scope="col" class="org-left">Hexapod</th>
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<th scope="col" class="org-left">Meas. file</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><code>meas_003.mat</code></td>
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</tr>
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<tr>
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<td class="org-left">OFF</td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><code>meas_004.mat</code></td>
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</tr>
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<tr>
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<td class="org-left">OFF</td>
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<td class="org-left">OFF</td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><code>meas_005.mat</code></td>
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</tr>
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<tr>
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<td class="org-left">OFF</td>
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<td class="org-left">OFF</td>
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<td class="org-left">OFF</td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><b>ON</b></td>
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<td class="org-left"><code>meas_006.mat</code></td>
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</tr>
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<tr>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left"><code>meas_007.mat</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><code>meas_008.mat</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Each of the <code>mat</code> file contains one array <code>data</code> with 3 columns:
|
|
</p>
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-right">Column number</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">1</td>
|
|
<td class="org-left">Geophone - Marble</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">2</td>
|
|
<td class="org-left">Geophone - Sample</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">3</td>
|
|
<td class="org-left">Time</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd47a227" class="outline-3">
|
|
<h3 id="orgd47a227"><span class="section-number-3">1.2</span> Load data</h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
<p>
|
|
We load the data of the z axis of two geophones.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">d3 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_003.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d3 = d3.data;
|
|
d4 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_004.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d4 = d4.data;
|
|
d5 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_005.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d5 = d5.data;
|
|
d6 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_006.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d6 = d6.data;
|
|
d7 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_007.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d7 = d7.data;
|
|
d8 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_008.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d8 = d8.data;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgef1cef2" class="outline-3">
|
|
<h3 id="orgef1cef2"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
|
|
<div class="outline-text-3" id="text-1-3">
|
|
<p>
|
|
First, we can look at the time domain data and compare all the measurements:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>comparison for the geophone at the sample location (figure <a href="#orge122156">1</a>)</li>
|
|
<li>comparison for the geophone on the granite (figure <a href="#org812d3e0">2</a>)</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>d3<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>, d3<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', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<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>, d4<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', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<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>, d5<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', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<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>, d6<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', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<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>, d7<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', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<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>, d8<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', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</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', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orge122156" class="figure">
|
|
<p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
|
|
</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>d3<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>, d3<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', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<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>, d4<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', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<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>, d5<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', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<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>, d6<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', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<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>, d7<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', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<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>, d8<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', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</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', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org812d3e0" class="figure">
|
|
<p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgab71525" class="outline-3">
|
|
<h3 id="orgab71525"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
|
|
<div class="outline-text-3" id="text-1-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = d3<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> d3<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;
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org93314dd" class="outline-4">
|
|
<h4 id="org93314dd"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4>
|
|
<div class="outline-text-4" id="text-1-4-1">
|
|
<p>
|
|
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px3, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d3<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>px4, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d4<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>px5, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d5<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>px6, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d6<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>px7, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d7<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>px8, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we compare all the signals (figures <a href="#org7432b3d">3</a> and <a href="#orgefd2377">4</a>).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
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>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org7432b3d" class="figure">
|
|
<p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgefd2377" class="figure">
|
|
<p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org39db171" class="outline-4">
|
|
<h4 id="org39db171"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4>
|
|
<div class="outline-text-4" id="text-1-4-2">
|
|
<p>
|
|
Now we plot the same curves for the geophone located on the marble.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px3, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d3<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>px4, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d4<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>px5, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d5<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>px6, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d6<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>px7, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d7<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>px8, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d8<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 compare the Amplitude Spectral Densities (figures <a href="#orga0ae73f">5</a> and <a href="#orgcfb23f8">6</a>)
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
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>;
|
|
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="orga0ae73f" class="figure">
|
|
<p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgcfb23f8" class="figure">
|
|
<p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org8f07d2e" class="outline-3">
|
|
<h3 id="org8f07d2e"><span class="section-number-3">1.5</span> Effect of the control system on the transmissibility from ground to sample</h3>
|
|
<div class="outline-text-3" id="text-1-5">
|
|
<p>
|
|
As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure <a href="#orgd9f2aae">7</a>).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = d3<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> d3<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;
|
|
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">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T3, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d3<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>, d3<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>T4, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d4<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>, d4<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>T5, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d5<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>, d5<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>T6, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d6<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>, d6<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>T7, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d7<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>, d7<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>T8, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d8<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>, d8<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>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</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>;
|
|
|
|
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T3<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T4<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T5<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T6<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T7<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T8<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</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>;
|
|
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">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
yticks<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">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</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">'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">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgd9f2aae" class="figure">
|
|
<p><img src="figs/trans_comp.png" alt="trans_comp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Comparison of the transfer function from the geophone on the marble to the geophone at the sample location</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="outline-container-org47a7f4c" class="outline-3">
|
|
<h3 id="org47a7f4c"><span class="section-number-3">1.6</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-1-6">
|
|
<div class="important">
|
|
<ul class="org-ul">
|
|
<li>The control system of the Ty stage induces a lot of vibrations of the marble</li>
|
|
</ul>
|
|
|
|
</div>
|
|
|
|
<div class="note">
|
|
<ul class="org-ul">
|
|
<li>Why it seems that the measurement noise at high frequency is the limiting factor when the slip ring is ON but not when it is OFF?</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org96b6d66" class="outline-2">
|
|
<h2 id="org96b6d66"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
<a id="org0b65553"></a>
|
|
</p>
|
|
<div class="note">
|
|
<p>
|
|
All the files (data and Matlab scripts) are accessible <a href="data/effect_control_one.zip">here</a>.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org21aea52" class="outline-3">
|
|
<h3 id="org21aea52"><span class="section-number-3">2.1</span> Experimental Setup</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<p>
|
|
We here measure the signals of two geophones:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>One is located on top of the Sample platform</li>
|
|
<li>One is located on the marble</li>
|
|
</ul>
|
|
|
|
<p>
|
|
The signal from the top geophone does go trought the slip-ring.
|
|
</p>
|
|
|
|
<p>
|
|
All the control systems are turned OFF, then, they are turned on one at a time.
|
|
</p>
|
|
|
|
<p>
|
|
Each measurement are done during 100s.
|
|
</p>
|
|
|
|
<p>
|
|
The settings of the voltage amplifier are shown on figure <a href="#orga2e0c1e">8</a>:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>gain of 60dB</li>
|
|
<li>AC/DC option set on DC</li>
|
|
<li>Low pass filter set at 1kHz</li>
|
|
</ul>
|
|
|
|
<p>
|
|
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
|
|
</p>
|
|
|
|
<table id="org879a5e4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
<caption class="t-above"><span class="table-number">Table 2:</span> Summary of the measurements and the states of the control systems</caption>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Ty</th>
|
|
<th scope="col" class="org-left">Ry</th>
|
|
<th scope="col" class="org-left">Slip Ring</th>
|
|
<th scope="col" class="org-left">Spindle</th>
|
|
<th scope="col" class="org-left">Hexapod</th>
|
|
<th scope="col" class="org-left">Meas. file</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><code>meas_013.mat</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><code>meas_014.mat</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><code>meas_015.mat</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><code>meas_016.mat</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><code>meas_017.mat</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left"><code>meas_018.mat</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Each of the <code>mat</code> file contains one array <code>data</code> with 3 columns:
|
|
</p>
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-right">Column number</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">1</td>
|
|
<td class="org-left">Geophone - Marble</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">2</td>
|
|
<td class="org-left">Geophone - Sample</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">3</td>
|
|
<td class="org-left">Time</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
|
|
<div id="orga2e0c1e" class="figure">
|
|
<p><img src="./img/IMG_20190507_101459.jpg" alt="IMG_20190507_101459.jpg" width="500px" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Voltage amplifier settings for the measurement</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf9fa5d1" class="outline-3">
|
|
<h3 id="orgf9fa5d1"><span class="section-number-3">2.2</span> Load data</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<p>
|
|
We load the data of the z axis of two geophones.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">d_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_013.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_of = d_of.data;
|
|
d_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_014.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_ty = d_ty.data;
|
|
d_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_015.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_ry = d_ry.data;
|
|
d_sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_016.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_sr = d_sr.data;
|
|
d_rz = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_017.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_rz = d_rz.data;
|
|
d_he = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_018.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_he = d_he.data;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb1aceca" class="outline-3">
|
|
<h3 id="orgb1aceca"><span class="section-number-3">2.3</span> Voltage to Velocity</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<p>
|
|
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/MEGA/These/meas/src/index.html">here</a>).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
|
|
|
|
d_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>d_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>, d_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>;
|
|
d_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>d_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>, d_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>;
|
|
d_ry<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>d_ry<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>, d_ry<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>;
|
|
d_sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
d_rz<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>d_rz<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>, d_rz<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>;
|
|
d_he<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>d_he<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>, d_he<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>;
|
|
|
|
d_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>d_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>, d_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>;
|
|
d_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>d_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>, d_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>;
|
|
d_ry<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>d_ry<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>, d_ry<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>;
|
|
d_sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
d_rz<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>d_rz<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>, d_rz<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>;
|
|
d_he<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>d_he<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>, d_he<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org9deea89" class="outline-3">
|
|
<h3 id="org9deea89"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<p>
|
|
First, we can look at the time domain data and compare all the measurements:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>comparison for the geophone at the sample location (figure <a href="#org0c06ee9">9</a>)</li>
|
|
<li>comparison for the geophone on the granite (figure <a href="#org45a64e1">10</a>)</li>
|
|
<li>relative displacement of the sample with respect to the marble (figure <a href="#org45a64e1">10</a>)</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>d_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>, d_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', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_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>, d_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', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<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>, d_ry<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', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<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>, d_rz<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', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_he<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>, d_he<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', 'Hexa ON'</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">50</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', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org0c06ee9" class="figure">
|
|
<p><img src="figs/time_domain_sample_lpf.png" alt="time_domain_sample_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
|
|
</div>
|
|
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_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>, d_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', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_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>, d_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', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<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>, d_ry<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', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<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>, d_rz<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', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_he<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>, d_he<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', 'Hexa ON'</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">50</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', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org45a64e1" class="figure">
|
|
<p><img src="figs/time_domain_marble_lpf.png" alt="time_domain_marble_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">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><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>d_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_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><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_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>d_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>, d_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-string">'DisplayName', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<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><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_ry<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>d_ry<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>, d_ry<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <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><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_sr<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>d_sr<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>, d_sr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<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><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_rz<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>d_rz<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>, d_rz<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_he<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><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_he<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>d_he<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>, d_he<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa ON'</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">'</span>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">50</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', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgbad8646" class="figure">
|
|
<p><img src="figs/time_domain_relative_disp.png" alt="time_domain_relative_disp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Relative displacement of the sample with respect to the marble</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga52ae70" class="outline-3">
|
|
<h3 id="orga52ae70"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = d_of<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> d_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;
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc044b46" class="outline-4">
|
|
<h4 id="orgc044b46"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4>
|
|
<div class="outline-text-4" id="text-2-5-1">
|
|
<p>
|
|
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_of, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_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>px_ty, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_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>px_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<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>px_sr, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px_rz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<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>px_he, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_he<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we compare all the signals (figures <a href="#org87295b7">12</a> and <a href="#orgd42d7db">13</a>).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_of<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ty<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_rz<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_he<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa ON'</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>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
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>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org87295b7" class="figure">
|
|
<p><img src="figs/psd_sample_comp_lpf.png" alt="psd_sample_comp_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the sample velocity</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgd42d7db" class="figure">
|
|
<p><img src="figs/psd_sample_comp_high_freq_lpf.png" alt="psd_sample_comp_high_freq_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the sample velocity (zoom at high frequencies)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgff12b0a" class="outline-4">
|
|
<h4 id="orgff12b0a"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4>
|
|
<div class="outline-text-4" id="text-2-5-2">
|
|
<p>
|
|
Now we plot the same curves for the geophone located on the marble.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_of, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_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>px_ty, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_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>px_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<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>px_sr, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px_rz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<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>px_he, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_he<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 compare the Amplitude Spectral Densities (figures <a href="#org7f25560">14</a> and <a href="#orgc96b599">15</a>)
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_of<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ty<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_rz<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_he<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa ON'</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>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
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>;
|
|
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="org7f25560" class="figure">
|
|
<p><img src="figs/psd_marble_comp_lpf.png" alt="psd_marble_comp_lpf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the marble velocity</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgc96b599" class="figure">
|
|
<p><img src="figs/psd_marble_comp_lpf_high_freq.png" alt="psd_marble_comp_lpf_high_freq.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the marble velocity (zoom at high frequencies)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf832269" class="outline-3">
|
|
<h3 id="orgf832269"><span class="section-number-3">2.6</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-6">
|
|
<div class="important">
|
|
<ul class="org-ul">
|
|
<li>The Ty stage induces vibrations of the marble and at the sample location above 100Hz</li>
|
|
<li>The hexapod stage induces vibrations at the sample position above 220Hz</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org76bb785" class="outline-2">
|
|
<h2 id="org76bb785"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
<a id="orga49b7fb"></a>
|
|
</p>
|
|
<div class="note">
|
|
<p>
|
|
All the files (data and Matlab scripts) are accessible <a href="data/effect_symetrie_driver.zip">here</a>.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3e3d670" class="outline-3">
|
|
<h3 id="org3e3d670"><span class="section-number-3">3.1</span> Experimental Setup</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<p>
|
|
We here measure the signals of two geophones:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>One is located on top of the Sample platform</li>
|
|
<li>One is located on the marble</li>
|
|
</ul>
|
|
|
|
<p>
|
|
The signal from the top geophone does go trought the slip-ring.
|
|
</p>
|
|
|
|
<p>
|
|
All the control systems are turned OFF except the Hexapod one.
|
|
</p>
|
|
|
|
<p>
|
|
Each measurement are done during 100s.
|
|
</p>
|
|
|
|
<p>
|
|
The settings of the voltage amplifier are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>DC</li>
|
|
<li>60dB</li>
|
|
<li>1kHz</li>
|
|
</ul>
|
|
|
|
<p>
|
|
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
|
|
</p>
|
|
|
|
<p>
|
|
The measurements are:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li><code>meas_018.mat</code>: Hexapod's driver on the granite</li>
|
|
<li><code>meas_019.mat</code>: Hexapod's driver on the ground</li>
|
|
</ul>
|
|
|
|
<p>
|
|
Each of the <code>mat</code> file contains one array <code>data</code> with 3 columns:
|
|
</p>
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-right">Column number</th>
|
|
<th scope="col" class="org-left">Description</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">1</td>
|
|
<td class="org-left">Geophone - Marble</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">2</td>
|
|
<td class="org-left">Geophone - Sample</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-right">3</td>
|
|
<td class="org-left">Time</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2c5eb48" class="outline-3">
|
|
<h3 id="org2c5eb48"><span class="section-number-3">3.2</span> Load data</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<p>
|
|
We load the data of the z axis of two geophones.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">d_18 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_018.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_18 = d_18.data;
|
|
d_19 = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_019.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_19 = d_19.data;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7b92812" class="outline-3">
|
|
<h3 id="org7b92812"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_19<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>, d_19<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', 'Driver - Ground'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>d_18<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>, d_18<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', 'Driver - Granite'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</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', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org6d6c3ee" class="figure">
|
|
<p><img src="figs/time_domain_hexa_driver.png" alt="time_domain_hexa_driver.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd042971" class="outline-3">
|
|
<h3 id="orgd042971"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
|
|
<div class="outline-text-3" id="text-3-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = d_18<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> d_18<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;
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdc25bb2" class="outline-4">
|
|
<h4 id="orgdc25bb2"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4>
|
|
<div class="outline-text-4" id="text-3-4-1">
|
|
<p>
|
|
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_18, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_18<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>px_19, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_19<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>
|
|
|
|
<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>px_19<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Driver - Ground'</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>px_18<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Driver - Granite'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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|
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>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
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>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgb3d2af2" class="figure">
|
|
<p><img src="figs/psd_hexa_driver.png" alt="psd_hexa_driver.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="orgdf358e8" class="figure">
|
|
<p><img src="figs/psd_hexa_driver_high_freq.png" alt="psd_hexa_driver_high_freq.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org2a573c2" class="outline-3">
|
|
<h3 id="org2a573c2"><span class="section-number-3">3.5</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-3-5">
|
|
<div class="important">
|
|
<p>
|
|
Even tough the Hexapod's driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2019-05-15 mer. 17:24</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
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</body>
|
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</html>
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