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<title>Effect on the control system of each stages on the vibration of the station</title>
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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">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
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<li><a href="#org51d7a3e">1. Effect of all the control systems on the Sample vibrations</a>
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<ul>
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<li><a href="#org053d9fe">1.1. Experimental Setup</a></li>
<li><a href="#orgcb36bc1">1.2. Load data</a></li>
<li><a href="#org5895a96">1.3. Analysis - Time Domain</a></li>
<li><a href="#org390bba0">1.4. Analysis - Frequency Domain</a>
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<ul>
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<li><a href="#org3a4a488">1.4.1. Vibrations at the sample location</a></li>
<li><a href="#org49d7279">1.4.2. Vibrations on the marble</a></li>
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</ul>
</li>
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<li><a href="#org9b2f5fd">1.5. Conclusion</a></li>
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</ul>
</li>
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<li><a href="#org4eafed3">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="#org4addbe8">2.1. Experimental Setup</a></li>
<li><a href="#orgb60aa2f">2.2. Load data</a></li>
<li><a href="#org68831ee">2.3. Voltage to Velocity</a></li>
<li><a href="#orgbbb370a">2.4. Analysis - Time Domain</a></li>
<li><a href="#orgd436876">2.5. Analysis - Frequency Domain</a>
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<ul>
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<li><a href="#org2e1f962">2.5.1. Vibrations at the sample location</a></li>
<li><a href="#org8f33a44">2.5.2. Vibrations on the marble</a></li>
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</ul>
</li>
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<li><a href="#org381e6c2">2.6. Conclusion</a></li>
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</ul>
</li>
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<li><a href="#orgce5eef9">3. Effect of the Symetrie Driver</a>
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<ul>
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<li><a href="#org6e62fbe">3.1. Experimental Setup</a></li>
<li><a href="#orgd0c4704">3.2. Load data</a></li>
<li><a href="#org30686ba">3.3. Analysis - Time Domain</a></li>
<li><a href="#orgd922ea4">3.4. Analysis - Frequency Domain</a>
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<ul>
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<li><a href="#orgd49e7c3">3.4.1. Vibrations at the sample location</a></li>
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</ul>
</li>
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<li><a href="#org031a084">3.5. Conclusion</a></li>
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</ul>
</li>
</ul>
</div>
</div>
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<p>
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This file is organized as follow:
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</p>
<ul class="org-ul">
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<li>Section <a href="#org3b0d32c">1</a>:
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<ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one by one</li>
</ul></li>
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<li>Section <a href="#org757823f">2</a>:
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<ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one at a time</li>
</ul></li>
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<li>Section <a href="#orgd9c378b">3</a>:
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<ul class="org-ul">
<li>We check if the Symetrie driver induces some vibrations when placed on the marble</li>
</ul></li>
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</ul>
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<div id="outline-container-org51d7a3e" class="outline-2">
<h2 id="org51d7a3e"><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">
<p>
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<a id="org3b0d32c"></a>
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</p>
<div class="note">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/effect_control_all.zip">here</a>.
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</p>
</div>
</div>
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<div id="outline-container-org053d9fe" class="outline-3">
<h3 id="org053d9fe"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<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 L22 geophones:
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</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>
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<p>
The signals are amplified with voltage amplifiers with the following settings:
</p>
<ul class="org-ul">
<li>gain of 60dB</li>
<li>AC/DC option set on AC</li>
<li>Low pass filter set at 1kHz</li>
</ul>
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<p>
The signal from the top geophone does not go trought the slip-ring.
</p>
<p>
First, all the control systems are turned ON, then, they are turned one by one.
Each measurement are done during 50s.
</p>
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<table id="org8234ce1" 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>
<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"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><code>meas_003.mat</code></td>
</tr>
<tr>
<td class="org-left">OFF</td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><code>meas_004.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"><b>ON</b></td>
<td class="org-left"><b>ON</b></td>
<td class="org-left"><code>meas_005.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"><b>ON</b></td>
<td class="org-left"><code>meas_006.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_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>
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<div id="outline-container-orgcb36bc1" class="outline-3">
<h3 id="orgcb36bc1"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2">
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<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('mat/data_003.mat', 'data'); d3 = d3.data;
d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
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</pre>
</div>
</div>
</div>
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<div id="outline-container-org5895a96" class="outline-3">
<h3 id="org5895a96"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-1-3">
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<p>
First, we can look at the time domain data and compare all the measurements:
</p>
<ul class="org-ul">
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<li>comparison for the geophone at the sample location (figure <a href="#org2c7f590">1</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org51a2672">2</a>)</li>
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</ul>
<div class="org-src-container">
<pre class="src src-matlab">figure;
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hold on;
plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF');
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hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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</pre>
</div>
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<div id="org2c7f590" class="figure">
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<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>
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</div>
<div class="org-src-container">
<pre class="src src-matlab">figure;
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hold on;
plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR');
plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz');
plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa');
plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF');
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hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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</pre>
</div>
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<div id="org51a2672" class="figure">
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<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>
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</div>
</div>
</div>
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<div id="outline-container-org390bba0" class="outline-3">
<h3 id="org390bba0"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4">
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<div class="org-src-container">
<pre class="src src-matlab">dt = d3(2, 3) - d3(1, 3);
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Fs = 1/dt;
win = hanning(ceil(10*Fs));
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</pre>
</div>
</div>
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<div id="outline-container-org3a4a488" class="outline-4">
<h4 id="org3a4a488"><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">
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<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">[px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);
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</pre>
</div>
<p>
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And we compare all the signals (figures <a href="#org939f58a">3</a> and <a href="#orgf26e845">4</a>).
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</p>
<div class="org-src-container">
<pre class="src src-matlab">figure;
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hold on;
plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
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hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'southwest');
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</pre>
</div>
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<div id="org939f58a" class="figure">
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<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>
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</div>
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<div id="orgf26e845" class="figure">
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<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>
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</div>
</div>
</div>
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<div id="outline-container-org49d7279" class="outline-4">
<h4 id="org49d7279"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-1-4-2">
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<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">[px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);
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</pre>
</div>
<p>
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And we compare the Amplitude Spectral Densities (figures <a href="#org3fd93c6">5</a> and <a href="#org2185be4">6</a>)
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</p>
<div class="org-src-container">
<pre class="src src-matlab">figure;
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hold on;
plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
plot(f, sqrt(px7), 'DisplayName', 'Hexa');
plot(f, sqrt(px8), 'DisplayName', 'All OFF');
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hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'northeast');
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</pre>
</div>
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<div id="org3fd93c6" class="figure">
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<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>
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</div>
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<div id="org2185be4" class="figure">
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<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>
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</div>
</div>
</div>
</div>
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<div id="outline-container-org9b2f5fd" class="outline-3">
<h3 id="org9b2f5fd"><span class="section-number-3">1.5</span> Conclusion</h3>
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<div class="outline-text-3" id="text-1-5">
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<div class="important">
<ul class="org-ul">
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<li>The control system of the Ty stage induces a lot of vibrations of the marble above 100Hz</li>
<li>The hexapod control system add vibrations of the sample only above 200Hz</li>
<li>When the Slip-Ring is ON, white noise appears at high frequencies. This is studied <a href="../slip-ring-electrical-noise/index.html">here</a></li>
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</ul>
</div>
</div>
</div>
</div>
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<div id="outline-container-org4eafed3" class="outline-2">
<h2 id="org4eafed3"><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>
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<a id="org757823f"></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>
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</div>
</div>
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<div id="outline-container-org4addbe8" class="outline-3">
<h3 id="org4addbe8"><span class="section-number-3">2.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-2-1">
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<p>
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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>
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The settings of the voltage amplifier are shown on figure <a href="#orgeb410b4">7</a>:
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</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>
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A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
</p>
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<table id="orgb3e54be" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<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>
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<div id="orgeb410b4" class="figure">
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<p><img src="./img/IMG_20190507_101459.jpg" alt="IMG_20190507_101459.jpg" width="500px" />
</p>
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<p><span class="figure-number">Figure 7: </span>Voltage amplifier settings for the measurement</p>
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</div>
</div>
</div>
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<div id="outline-container-orgb60aa2f" class="outline-3">
<h3 id="orgb60aa2f"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2">
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<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('mat/data_013.mat', 'data'); d_of = d_of.data;
d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
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</pre>
</div>
</div>
</div>
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<div id="outline-container-org68831ee" class="outline-3">
<h3 id="org68831ee"><span class="section-number-3">2.3</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-3">
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<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>).
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</p>
<div class="org-src-container">
<pre class="src src-matlab">gain = 60; % [dB]
d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
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</pre>
</div>
</div>
</div>
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<div id="outline-container-orgbbb370a" class="outline-3">
<h3 id="orgbbb370a"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3>
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<div class="outline-text-3" id="text-2-4">
<p>
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First, we can look at the time domain data and compare all the measurements:
</p>
<ul class="org-ul">
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<li>comparison for the geophone at the sample location (figure <a href="#org03fb45e">8</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#orgc177b3a">9</a>)</li>
<li>relative displacement of the sample with respect to the marble (figure <a href="#orgc177b3a">9</a>)</li>
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</ul>
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<div id="org03fb45e" class="figure">
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<p><img src="figs/time_domain_sample_lpf.png" alt="time_domain_sample_lpf.png" />
</p>
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<p><span class="figure-number">Figure 8: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
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</div>
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<div id="orgc177b3a" class="figure">
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<p><img src="figs/time_domain_marble_lpf.png" alt="time_domain_marble_lpf.png" />
</p>
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<p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
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</div>
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<div id="orgb57231f" class="figure">
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<p><img src="figs/time_domain_relative_disp.png" alt="time_domain_relative_disp.png" />
</p>
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<p><span class="figure-number">Figure 10: </span>Relative displacement of the sample with respect to the marble</p>
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</div>
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</div>
</div>
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<div id="outline-container-orgd436876" class="outline-3">
<h3 id="orgd436876"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3>
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<div class="outline-text-3" id="text-2-5">
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<div class="org-src-container">
<pre class="src src-matlab">dt = d_of(2, 3) - d_of(1, 3);
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Fs = 1/dt;
win = hanning(ceil(10*Fs));
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</pre>
</div>
</div>
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<div id="outline-container-org2e1f962" class="outline-4">
<h4 id="org2e1f962"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4>
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<div class="outline-text-4" id="text-2-5-1">
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<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">[px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
[px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
[px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
[px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
[px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
[px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);
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</pre>
</div>
<p>
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And we compare all the signals (figures <a href="#orgb661144">11</a> and <a href="#orgd36a2b1">12</a>).
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</p>
<div class="org-src-container">
<pre class="src src-matlab">figure;
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hold on;
plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
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hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'southwest');
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</pre>
</div>
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<div id="orgb661144" class="figure">
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<p><img src="figs/psd_sample_comp_lpf.png" alt="psd_sample_comp_lpf.png" />
</p>
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<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the sample velocity</p>
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</div>
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<div id="orgd36a2b1" class="figure">
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<p><img src="figs/psd_sample_comp_high_freq_lpf.png" alt="psd_sample_comp_high_freq_lpf.png" />
</p>
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<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the sample velocity (zoom at high frequencies)</p>
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</div>
</div>
</div>
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<div id="outline-container-org8f33a44" class="outline-4">
<h4 id="org8f33a44"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4>
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<div class="outline-text-4" id="text-2-5-2">
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<p>
Now we plot the same curves for the geophone located on the marble.
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And we compare the Amplitude Spectral Densities (figures <a href="#org57f110f">13</a> and <a href="#orgcbf8e87">14</a>)
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</p>
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<div id="org57f110f" class="figure">
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<p><img src="figs/psd_marble_comp_lpf.png" alt="psd_marble_comp_lpf.png" />
</p>
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<p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the marble velocity</p>
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</div>
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<div id="orgcbf8e87" class="figure">
<p><img src="figs/psd_marble_lpf_high_freq.png" alt="psd_marble_lpf_high_freq.png" />
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</p>
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<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the marble velocity (zoom at high frequencies)</p>
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</div>
</div>
</div>
</div>
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<div id="outline-container-org381e6c2" class="outline-3">
<h3 id="org381e6c2"><span class="section-number-3">2.6</span> Conclusion</h3>
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<div class="outline-text-3" id="text-2-6">
<div class="important">
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<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>
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</div>
</div>
</div>
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<div id="outline-container-orgce5eef9" class="outline-2">
<h2 id="orgce5eef9"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2>
<div class="outline-text-2" id="text-3">
<p>
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<a id="orgd9c378b"></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>
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</div>
</div>
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<div id="outline-container-org6e62fbe" class="outline-3">
<h3 id="org6e62fbe"><span class="section-number-3">3.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-3-1">
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<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">
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<li>gain of 60dB</li>
<li>AC/DC option set on DC</li>
<li>Low pass filter set at 1kHz</li>
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</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&rsquo;s driver on the granite</li>
<li><code>meas_019.mat</code>: Hexapod&rsquo;s driver on the ground</li>
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</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>
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<div id="outline-container-orgd0c4704" class="outline-3">
<h3 id="orgd0c4704"><span class="section-number-3">3.2</span> Load data</h3>
<div class="outline-text-3" id="text-3-2">
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<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('mat/data_018.mat', 'data'); d_18 = d_18.data;
d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data;
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</pre>
</div>
</div>
</div>
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<div id="outline-container-org30686ba" class="outline-3">
<h3 id="org30686ba"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-3-3">
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<div class="org-src-container">
<pre class="src src-matlab">figure;
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hold on;
plot(d_19(:, 3), d_19(:, 1), 'DisplayName', 'Driver - Ground');
plot(d_18(:, 3), d_18(:, 1), 'DisplayName', 'Driver - Granite');
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hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 50]);
legend('Location', 'bestoutside');
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</pre>
</div>
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<div id="orgd0329f8" class="figure">
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<p><img src="figs/time_domain_hexa_driver.png" alt="time_domain_hexa_driver.png" />
</p>
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<p><span class="figure-number">Figure 15: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
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</div>
</div>
</div>
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<div id="outline-container-orgd922ea4" class="outline-3">
<h3 id="orgd922ea4"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-3-4">
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<div class="org-src-container">
<pre class="src src-matlab">dt = d_18(2, 3) - d_18(1, 3);
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Fs = 1/dt;
win = hanning(ceil(10*Fs));
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</pre>
</div>
</div>
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<div id="outline-container-orgd49e7c3" class="outline-4">
<h4 id="orgd49e7c3"><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">
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<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">[px_18, f] = pwelch(d_18(:, 1), win, [], [], Fs);
[px_19, ~] = pwelch(d_19(:, 1), win, [], [], Fs);
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</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">figure;
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hold on;
plot(f, sqrt(px_19), 'DisplayName', 'Driver - Ground');
plot(f, sqrt(px_18), 'DisplayName', 'Driver - Granite');
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hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);
legend('Location', 'southwest');
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</pre>
</div>
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<div id="org474aa6e" class="figure">
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<p><img src="figs/psd_hexa_driver.png" alt="psd_hexa_driver.png" />
</p>
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<p><span class="figure-number">Figure 16: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
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</div>
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<div id="org01ebad8" class="figure">
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<p><img src="figs/psd_hexa_driver_high_freq.png" alt="psd_hexa_driver_high_freq.png" />
</p>
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<p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
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</div>
</div>
</div>
</div>
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<div id="outline-container-org031a084" class="outline-3">
<h3 id="org031a084"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5">
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<div class="important">
<p>
Even tough the Hexapod&rsquo;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.
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</p>
</div>
</div>
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</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2020-04-27 lun. 10:18</p>
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