776 lines
68 KiB
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776 lines
68 KiB
HTML
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<title>Vibrations induced by simultaneous scans of the translation stage and of the slip-ring</title>
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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">Vibrations induced by simultaneous scans of the translation stage and of the slip-ring</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="#orge303e87">1. Measurement description</a></li>
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<li><a href="#orgc23d6dc">2. Data Analysis</a>
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<ul>
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<li><a href="#org629d4b4">2.1. Load data</a></li>
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<li><a href="#org79a2c27">2.2. Voltage to Velocity</a></li>
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<li><a href="#org1bafa09">2.3. Time domain plots</a></li>
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<li><a href="#org05973bc">2.4. Frequency Domain</a></li>
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<li><a href="#org57188a5">2.5. Ty motion and current</a>
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<ul>
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<li><a href="#org07bb77c">2.5.1. Data pre-processing</a></li>
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<li><a href="#org8bcb0f7">2.5.2. Time domain data</a></li>
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</ul>
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</li>
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<li><a href="#org005d22e">2.6. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orge303e87" class="outline-2">
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<h2 id="orge303e87"><span class="section-number-2">1</span> Measurement description</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<b>Setup</b>:
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All the stages are OFF except the translation stage and the Slip-Ring.
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</p>
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<p>
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Each of the signal is amplified by voltage amplifiers with the following settings:
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</p>
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<ul class="org-ul">
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<li>Gain: 40dB</li>
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<li>AC/DC option: AC</li>
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<li>Low pass filter: 1kHz</li>
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</ul>
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<p>
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The slip-ring is rotating at 60rpm. At the same time, scans with the translation stage are done at 1Hz with an amplitude of 600000cnt (= 3mm).
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</p>
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<p>
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Two geophones are used to measure the motion in the vertical direction of the marble and of the sample.
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</p>
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<p>
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<b>Goal</b>:
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</p>
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<ul class="org-ul">
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<li>The goal is to estimate the vibrations induced by the simultaneous scans of the spindle (here the slip-ring is used as the spindle is not fully functional yet) and of the translation stage</li>
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</ul>
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<p>
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<b>Measurements</b>:
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</p>
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<p>
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Three measurements are done:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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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">Measurement File</th>
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<th scope="col" class="org-left">Description</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"><code>mat/data_050.mat</code></td>
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<td class="org-left">Slip-Ring at 1Hz, Ty OFF</td>
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</tr>
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<tr>
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<td class="org-left"><code>mat/data_051.mat</code></td>
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<td class="org-left">Slip-Ring at 1Hz, Ty ON (The current and cnt error of Ty is also registered)</td>
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</tr>
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<tr>
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<td class="org-left"><code>mat/data_052.mat</code></td>
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<td class="org-left">Slip-Ring at 1Hz, Ty 1Hz 600000cnt</td>
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</tr>
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</tbody>
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</table>
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<p>
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Each of the measurement <code>mat</code> file contains one <code>data</code> array with 3 columns:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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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-right">Column number</th>
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<th scope="col" class="org-left">Description</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-right">1</td>
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<td class="org-left">Geophone on the marble</td>
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</tr>
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<tr>
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<td class="org-right">2</td>
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<td class="org-left">Geophone at the sample location</td>
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</tr>
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<tr>
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<td class="org-right">3</td>
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<td class="org-left">Time</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-orgc23d6dc" class="outline-2">
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<h2 id="orgc23d6dc"><span class="section-number-2">2</span> Data Analysis</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org4563c51"></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/disturbance_ty_sr.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-org629d4b4" class="outline-3">
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<h3 id="org629d4b4"><span class="section-number-3">2.1</span> Load data</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab">ty_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_050.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_of = ty_of.data;
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ty_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_on = ty_on.data;
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ty_1h = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_052.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_1h = ty_1h.data;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org79a2c27" class="outline-3">
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<h3 id="org79a2c27"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
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<div class="outline-text-3" id="text-2-2">
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<p>
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We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/These/meas/src/index.html">here</a>).
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">40</span>; <span class="org-comment">% [dB]</span>
|
|
|
|
ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
ty_on<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
ty_1h<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
ty_on<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
ty_1h<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1bafa09" class="outline-3">
|
|
<h3 id="org1bafa09"><span class="section-number-3">2.3</span> Time domain plots</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<p>
|
|
We plot the measured velocity of the marble (figure <a href="#org53f1c30">1</a>), sample (figure <a href="#org6938117">2</a>) and the relative velocity of the sample with respect to the marble (figure <a href="#orgfd8af3e">3</a>).
|
|
</p>
|
|
|
|
<p>
|
|
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#org425e005">4</a>).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org53f1c30" class="figure">
|
|
<p><img src="figs/ty_marble_time.png" alt="ty_marble_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 1: </span>Velocity of the marble in the vertical direction</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org6938117" class="figure">
|
|
<p><img src="figs/ty_sample_time.png" alt="ty_sample_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Velocity of the sample in the vertical direction</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative Velocity <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Velocity - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Velocity - Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgfd8af3e" class="figure">
|
|
<p><img src="figs/ty_relative_time.png" alt="ty_relative_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Relative velocity of the sample with respect to the marble</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative Displacement<span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Displacement- Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Displacement- Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Displacement </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org425e005" class="figure">
|
|
<p><img src="figs/ty_relative_disp_time.png" alt="ty_relative_disp_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Relative Displacement of the sample with respect to the marble</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org05973bc" class="outline-3">
|
|
<h3 id="org05973bc"><span class="section-number-3">2.4</span> Frequency Domain</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<p>
|
|
We first compute some parameters that will be used for the PSD computation.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
|
|
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then we compute the Power Spectral Density using <code>pwelch</code> function.
|
|
</p>
|
|
|
|
<p>
|
|
First for the geophone located on the marble
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And for the geophone located at the sample position.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Finally, for the relative velocity.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we plot the ASD of the measured velocities:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>figure <a href="#org00eb9e9">5</a> for the geophone located on the marble</li>
|
|
<li>figure <a href="#org192c441">6</a> for the geophone at the sample position</li>
|
|
<li>figure <a href="#org1b88cd2">7</a> for the relative velocity</li>
|
|
</ul>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org00eb9e9" class="figure">
|
|
<p><img src="figs/psd_marble_compare.png" alt="psd_marble_compare.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org192c441" class="figure">
|
|
<p><img src="figs/psd_sample_compare.png" alt="psd_sample_compare.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org1b88cd2" class="figure">
|
|
<p><img src="figs/psd_relative_compare.png" alt="psd_relative_compare.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Comparison of the ASD of the relative velocity</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org57188a5" class="outline-3">
|
|
<h3 id="org57188a5"><span class="section-number-3">2.5</span> Ty motion and current</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<p>
|
|
The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org07bb77c" class="outline-4">
|
|
<h4 id="org07bb77c"><span class="section-number-4">2.5.1</span> Data pre-processing</h4>
|
|
<div class="outline-text-4" id="text-2-5-1">
|
|
<p>
|
|
Let's look at at the start of the csv file.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-bash">sed -n <span class="org-highlight-numbers-number">1,30p</span> mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
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</pre>
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</div>
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<p>
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The real data starts at line 29.
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We then load this <code>cvs</code> file starting at line 29.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">tye_on = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
tye_1h = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span><span class="org-type">-</span>and<span class="org-type">-</span>Ty<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org8bcb0f7" class="outline-4">
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<h4 id="org8bcb0f7"><span class="section-number-4">2.5.2</span> Time domain data</h4>
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<div class="outline-text-4" id="text-2-5-2">
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<p>
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We plot the position of the translation stage measured by the encoders.
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</p>
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<p>
|
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There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
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</p>
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<p>
|
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The result is shown on figure <a href="#orgfeb408e">8</a>.
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</p>
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|
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<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">(</span>tye_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_on<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">(</span>tye_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_1h<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgfeb408e" class="figure">
|
|
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Y position of the translation stage measured by the encoders</p>
|
|
</div>
|
|
|
|
|
|
<p>
|
|
We also plot the current as function of the time on figure <a href="#orgbd294dc">9</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orgbd294dc" class="figure">
|
|
<p><img src="figs/ty_current_time.png" alt="ty_current_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Current going through the actuator of the translation stage</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org005d22e" class="outline-3">
|
|
<h3 id="org005d22e"><span class="section-number-3">2.6</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-6">
|
|
<div class="important">
|
|
<ul class="org-ul">
|
|
<li></li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2019-05-15 mer. 15:49</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|