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Update old analysis: add zip and matlab file.

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Thomas Dehaeze
2019-07-05 11:35:40 +02:00
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@@ -3,12 +3,12 @@
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Measurement Analysis</title>
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<meta name="author" content="Dehaeze Thomas" />
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@@ -195,10 +195,11 @@
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<div id="content">
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<a accesskey="h" href="../index.html"> UP </a>
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</div><div id="content">
<h1 class="title">Measurement Analysis</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orga57c824">1. Measurement Description</a></li>
<li><a href="#orgac83bb1">2. Importation of the data</a></li>
<li><a href="#orge44c773">3. Variables for analysis</a></li>
<li><a href="#orgcb0a2db">4. Coherence between the two vertical geophones on the Tilt Stage</a></li>
<li><a href="#orgc619b39">5. Data Post Processing</a></li>
<li><a href="#org03ef418">6. Normalization</a></li>
<li><a href="#org8583637">7. Measurement 1 - Effect of Ty stage</a></li>
<li><a href="#org47192a7">8. Measurement 2 - Effect of Ry stage</a></li>
<li><a href="#org0c3a1d4">9. Measurement 3 - Effect of the Hexapod</a></li>
<li><a href="#org1529580">10. Measurement 4 - Effect of the Splip-Ring and Spindle</a></li>
<li><a href="#orga767d61">11. Measurement 5 - Transmission from ground to marble</a></li>
<li><a href="#org3a9a926">1. Measurement Description</a></li>
<li><a href="#orga751c46">2. Importation of the data</a></li>
<li><a href="#orgbb22f41">3. Variables for analysis</a></li>
<li><a href="#orgfad99e2">4. Coherence between the two vertical geophones on the Tilt Stage</a></li>
<li><a href="#org95ba164">5. Data Post Processing</a></li>
<li><a href="#org7ad093b">6. Normalization</a></li>
<li><a href="#org2a0c6af">7. Measurement 1 - Effect of Ty stage</a></li>
<li><a href="#orgc84b427">8. Measurement 2 - Effect of Ry stage</a></li>
<li><a href="#org735052a">9. Measurement 3 - Effect of the Hexapod</a></li>
<li><a href="#org567caf5">10. Measurement 4 - Effect of the Splip-Ring and Spindle</a></li>
<li><a href="#orgbd1a834">11. Measurement 5 - Transmission from ground to marble</a></li>
</ul>
</div>
</div>
<div class="note">
<p>
<a href="../index.html">Back to main page</a>.
All the files (data and Matlab scripts) are accessible <a href="data/meas_analysis_geophones.zip">here</a>.
</p>
<div id="outline-container-orga57c824" class="outline-2">
<h2 id="orga57c824"><span class="section-number-2">1</span> Measurement Description</h2>
</div>
<div id="outline-container-org3a9a926" class="outline-2">
<h2 id="org3a9a926"><span class="section-number-2">1</span> Measurement Description</h2>
<div class="outline-text-2" id="text-1">
<div id="orgc56bc67" class="figure">
<p><img src="./figs/setup_picture.png" alt="setup_picture.png" />
<div id="org842eee7" class="figure">
<p><img src="./figs/setup_picture.png" alt="setup_picture.png" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the setup for the measurement</p>
</div>
@@ -296,8 +304,8 @@ The goal is to see what noise is injected in the system due to the regulation lo
</div>
</div>
<div id="outline-container-orgac83bb1" class="outline-2">
<h2 id="orgac83bb1"><span class="section-number-2">2</span> Importation of the data</h2>
<div id="outline-container-orga751c46" class="outline-2">
<h2 id="orga751c46"><span class="section-number-2">2</span> Importation of the data</h2>
<div class="outline-text-2" id="text-2">
<p>
First, load all the measurement files:
@@ -322,10 +330,10 @@ meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highli
</div>
<p>
For the measurements 1 to 4, the measurement channels are shown table <a href="#org7e4418b">1</a>.
For the measurements 1 to 4, the measurement channels are shown table <a href="#orgf8d6e45">1</a>.
</p>
<table id="org7e4418b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgf8d6e45" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Channels for measurements 1 to 4</caption>
<colgroup>
@@ -378,9 +386,9 @@ For the measurements 1 to 4, the measurement channels are shown table <a href="#
<p>
For the measurement 5, the channels are shown table <a href="#org00892de">2</a>.
For the measurement 5, the channels are shown table <a href="#org5907f53">2</a>.
</p>
<table id="org00892de" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org5907f53" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Channels for measurement 5</caption>
<colgroup>
@@ -416,8 +424,8 @@ For the measurement 5, the channels are shown table <a href="#org00892de">2</a>.
</div>
</div>
<div id="outline-container-orge44c773" class="outline-2">
<h2 id="orge44c773"><span class="section-number-2">3</span> Variables for analysis</h2>
<div id="outline-container-orgbb22f41" class="outline-2">
<h2 id="orgbb22f41"><span class="section-number-2">3</span> Variables for analysis</h2>
<div class="outline-text-2" id="text-3">
<p>
We define the sampling frequency and the time vectors for the plots.
@@ -426,11 +434,11 @@ We define the sampling frequency and the time vectors for the plots.
<div class="org-src-container">
<pre class="src src-matlab">Fs = <span class="org-highlight-numbers-number">256</span>; <span class="org-comment">% [Hz]</span>
dt = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
t1 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">]</span>;
t2 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">]</span>;
t3 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">]</span>;
t4 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">]</span>;
t5 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">]</span>;
t1 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">)</span>;
t2 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">)</span>;
t3 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">)</span>;
t4 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">)</span>;
t5 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<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-1">)</span>;
</pre>
</div>
@@ -453,11 +461,11 @@ Then we define the windows that will be used to average the results.
</div>
</div>
<div id="outline-container-orgcb0a2db" class="outline-2">
<h2 id="orgcb0a2db"><span class="section-number-2">4</span> Coherence between the two vertical geophones on the Tilt Stage</h2>
<div id="outline-container-orgfad99e2" class="outline-2">
<h2 id="orgfad99e2"><span class="section-number-2">4</span> Coherence between the two vertical geophones on the Tilt Stage</h2>
<div class="outline-text-2" id="text-4">
<p>
We first compute the coherence between the two geophones located on the tilt stage. The result is shown on figure <a href="#org3d4d6fd">2</a>.
We first compute the coherence between the two geophones located on the tilt stage. The result is shown on figure <a href="#orgb80e1a5">2</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh, f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <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>;
@@ -465,14 +473,14 @@ We first compute the coherence between the two geophones located on the tilt sta
</div>
<div id="org3d4d6fd" class="figure">
<div id="orgb80e1a5" class="figure">
<p><img src="figs/coherence_vertical_tilt_sensors.png" alt="coherence_vertical_tilt_sensors.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Coherence between the two vertical sensors positionned on the Tilt Stage</p>
</div>
<p>
We then compute the transfer function from one sensor to the other (figure <a href="#org62100a4">3</a>).
We then compute the transfer function from one sensor to the other (figure <a href="#org9c39675">3</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>tf23, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <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>;
@@ -480,7 +488,7 @@ We then compute the transfer function from one sensor to the other (figure <a hr
</div>
<div id="org62100a4" class="figure">
<div id="org9c39675" class="figure">
<p><img src="figs/tf_vertical_tilt_sensors.png" alt="tf_vertical_tilt_sensors.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Transfer function from one vertical geophone on the tilt stage to the other vertical geophone on the tilt stage</p>
@@ -492,8 +500,8 @@ Even though the coherence is not very good, we observe no resonance between the
</div>
</div>
<div id="outline-container-orgc619b39" class="outline-2">
<h2 id="orgc619b39"><span class="section-number-2">5</span> Data Post Processing</h2>
<div id="outline-container-org95ba164" class="outline-2">
<h2 id="org95ba164"><span class="section-number-2">5</span> Data Post Processing</h2>
<div class="outline-text-2" id="text-5">
<p>
When using two geophone sensors on the same tilt stage (measurements 1 and 2), we post-process the data to obtain the z displacement and the rotation of the tilt stage:
@@ -523,12 +531,12 @@ meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highli
</div>
</div>
<div id="outline-container-org03ef418" class="outline-2">
<h2 id="org03ef418"><span class="section-number-2">6</span> Normalization</h2>
<div id="outline-container-org7ad093b" class="outline-2">
<h2 id="org7ad093b"><span class="section-number-2">6</span> Normalization</h2>
<div class="outline-text-2" id="text-6">
<p>
Parameters of the geophone are defined below.
The transfer function from geophone velocity to measured voltage is shown on figure <a href="#org47ba141">4</a>.
The transfer function from geophone velocity to measured voltage is shown on figure <a href="#org9f3edd8">4</a>.
</p>
<p>
@@ -539,12 +547,12 @@ Measurements will be normalized by the inverse of this transfer function in orde
<pre class="src src-matlab">L4C_w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
L4C_ksi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">28</span>;
L4C_G0 = <span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>; <span class="org-comment">% [V/(m/s)]</span>
[Omitted long matching line]
L4C_G = L4C_G0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span>L4C_w0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>L4C_w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>L4C_ksi<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>L4C_w0<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-1">)</span>;
</pre>
</div>
<div id="org47ba141" class="figure">
<div id="org9f3edd8" class="figure">
<p><img src="figs/L4C_bode_plot.png" alt="L4C_bode_plot.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Bode plot of the L4C Geophone</p>
@@ -600,14 +608,14 @@ meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highli
</div>
</div>
<div id="outline-container-org8583637" class="outline-2">
<h2 id="org8583637"><span class="section-number-2">7</span> Measurement 1 - Effect of Ty stage</h2>
<div id="outline-container-org2a0c6af" class="outline-2">
<h2 id="org2a0c6af"><span class="section-number-2">7</span> Measurement 1 - Effect of Ty stage</h2>
<div class="outline-text-2" id="text-7">
<p>
The configuration for this measurement is shown table <a href="#orgc1f3234">3</a>.
The configuration for this measurement is shown table <a href="#orgb2c9cfc">3</a>.
</p>
<table id="orgc1f3234" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgb2c9cfc" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Stages configuration - Measurement 1</caption>
<colgroup>
@@ -658,7 +666,7 @@ The configuration for this measurement is shown table <a href="#orgc1f3234">3</a
</table>
<p>
We then plot the measurements in time domain (figure <a href="#orgf931943">5</a>).
We then plot the measurements in time domain (figure <a href="#orge80ff30">5</a>).
</p>
<div class="important">
@@ -670,7 +678,7 @@ How can we explain that?
</div>
<div id="orgf931943" class="figure">
<div id="orge80ff30" class="figure">
<p><img src="figs/meas1.png" alt="meas1.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Time domain - measurement 1</p>
@@ -681,10 +689,10 @@ To understand what is going on, instead of looking at the velocity, we can look
</p>
<p>
Then we plot the position with respect to time (figure <a href="#orgb6bceab">6</a>).
Then we plot the position with respect to time (figure <a href="#orga73c9be">6</a>).
</p>
<div id="orgb6bceab" class="figure">
<div id="orga73c9be" class="figure">
<p><img src="figs/meas1_disp.png" alt="meas1_disp.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Y displacement of the Ty stage</p>
@@ -706,25 +714,25 @@ We when compute the power spectral density of each measurement before and after
</div>
<p>
We finally plot the power spectral density of each track (figures <a href="#org767e453">7</a>, <a href="#org8cd1899">8</a>, <a href="#org3030170">9</a>).
We finally plot the power spectral density of each track (figures <a href="#org612c087">7</a>, <a href="#org41d5f1b">8</a>, <a href="#orgc543ef7">9</a>).
</p>
<div id="org767e453" class="figure">
<div id="org612c087" class="figure">
<p><img src="figs/meas1_ry_z_psd.png" alt="meas1_ry_z_psd.png" />
</p>
<p><span class="figure-number">Figure 7: </span>PSD of the Z velocity of Ry stage - measurement 1</p>
</div>
<div id="org8cd1899" class="figure">
<div id="org41d5f1b" class="figure">
<p><img src="figs/meas1_ry_tilt_psd.png" alt="meas1_ry_tilt_psd.png" />
</p>
<p><span class="figure-number">Figure 8: </span>PSD of the Rotation of Ry Stage - measurement 1</p>
</div>
<div id="org3030170" class="figure">
<div id="orgc543ef7" class="figure">
<p><img src="figs/meas1_ty_y_psd.png" alt="meas1_ty_y_psd.png" />
</p>
<p><span class="figure-number">Figure 9: </span>PSD of the Ty velocity in the Y direction - measurement 1</p>
@@ -748,14 +756,14 @@ It does not seems to have any effect on the Z motion of the tilt stage.
</div>
</div>
<div id="outline-container-org47192a7" class="outline-2">
<h2 id="org47192a7"><span class="section-number-2">8</span> Measurement 2 - Effect of Ry stage</h2>
<div id="outline-container-orgc84b427" class="outline-2">
<h2 id="orgc84b427"><span class="section-number-2">8</span> Measurement 2 - Effect of Ry stage</h2>
<div class="outline-text-2" id="text-8">
<p>
The tilt stage is turned ON at around 326 seconds (table <a href="#orgba0882e">4</a>).
The tilt stage is turned ON at around 326 seconds (table <a href="#orgb1e5f86">4</a>).
</p>
<table id="orgba0882e" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="orgb1e5f86" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 4:</span> Stages configuration - Measurement 2</caption>
<colgroup>
@@ -806,25 +814,25 @@ The tilt stage is turned ON at around 326 seconds (table <a href="#orgba0882e">4
</table>
<p>
We plot the time domain (figure <a href="#org9bf6e90">10</a>) and we don't observe anything special in the time domain.
We plot the time domain (figure <a href="#orgd48d30c">10</a>) and we don't observe anything special in the time domain.
</p>
<div id="org9bf6e90" class="figure">
<div id="orgd48d30c" class="figure">
<p><img src="figs/meas2.png" alt="meas2.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Time domain - measurement 2</p>
</div>
<div id="org767f834" class="figure">
<div id="org603b8af" class="figure">
<p><img src="figs/meas2_disp.png" alt="meas2_disp.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Time domain - measurement 2</p>
</div>
<p>
We compute the PSD of each track and we plot them (figures <a href="#org23fbfb4">12</a>, <a href="#org7a18c86">13</a> and <a href="#orgdcf33e8">14</a> ).
We compute the PSD of each track and we plot them (figures <a href="#orge84422e">12</a>, <a href="#orga5f41c7">13</a> and <a href="#org7c30a4f">14</a> ).
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx211, f21<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">326</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <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>;
@@ -839,21 +847,21 @@ We compute the PSD of each track and we plot them (figures <a href="#org23fbfb4"
</div>
<div id="org23fbfb4" class="figure">
<div id="orge84422e" class="figure">
<p><img src="figs/meas2_ry_z_psd.png" alt="meas2_ry_z_psd.png" />
</p>
<p><span class="figure-number">Figure 12: </span>PSD of the Z velocity of Ry Stage - measurement 2</p>
</div>
<div id="org7a18c86" class="figure">
<div id="orga5f41c7" class="figure">
<p><img src="figs/meas2_ry_tilt_psd.png" alt="meas2_ry_tilt_psd.png" />
</p>
<p><span class="figure-number">Figure 13: </span>PSD of the Rotation motion of Ry Stage - measurement 2</p>
</div>
<div id="orgdcf33e8" class="figure">
<div id="org7c30a4f" class="figure">
<p><img src="figs/meas2_ty_y_psd.png" alt="meas2_ty_y_psd.png" />
</p>
<p><span class="figure-number">Figure 14: </span>PSD of the Ty velocity in the Y direction - measurement 2</p>
@@ -868,14 +876,14 @@ We observe no noticeable difference when the Tilt-stage is turned ON expect a sm
</div>
</div>
<div id="outline-container-org0c3a1d4" class="outline-2">
<h2 id="org0c3a1d4"><span class="section-number-2">9</span> Measurement 3 - Effect of the Hexapod</h2>
<div id="outline-container-org735052a" class="outline-2">
<h2 id="org735052a"><span class="section-number-2">9</span> Measurement 3 - Effect of the Hexapod</h2>
<div class="outline-text-2" id="text-9">
<p>
The hexapod is turned off after 406 seconds (table <a href="#org8b4187d">5</a>).
The hexapod is turned off after 406 seconds (table <a href="#org173876d">5</a>).
</p>
<table id="org8b4187d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org173876d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 5:</span> Stages configuration - Measurement 3</caption>
<colgroup>
@@ -926,25 +934,25 @@ The hexapod is turned off after 406 seconds (table <a href="#org8b4187d">5</a>).
</table>
<p>
The time domain result is shown figure <a href="#org08fc17d">15</a>.
The time domain result is shown figure <a href="#orgf7e79c3">15</a>.
</p>
<div id="org08fc17d" class="figure">
<div id="orgf7e79c3" class="figure">
<p><img src="figs/meas3.png" alt="meas3.png" />
</p>
<p><span class="figure-number">Figure 15: </span>Time domain - measurement 3</p>
</div>
<div id="org4ae7ca4" class="figure">
<div id="org5206570" class="figure">
<p><img src="figs/meas3_disp.png" alt="meas3_disp.png" />
</p>
<p><span class="figure-number">Figure 16: </span>Time domain - measurement 3</p>
</div>
<p>
We then compute the PSD of each track before and after turning off the hexapod and plot the results in the figures <a href="#org0c4287e">17</a>, <a href="#org899151a">18</a> and <a href="#org0fc8e31">19</a>.
We then compute the PSD of each track before and after turning off the hexapod and plot the results in the figures <a href="#orgb6df1c9">17</a>, <a href="#org0169c44">18</a> and <a href="#org02dedc8">19</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx311, f31<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">400</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <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>;
@@ -959,21 +967,21 @@ We then compute the PSD of each track before and after turning off the hexapod a
</div>
<div id="org0c4287e" class="figure">
<div id="orgb6df1c9" class="figure">
<p><img src="figs/meas3_hexa_z_psd.png" alt="meas3_hexa_z_psd.png" />
</p>
<p><span class="figure-number">Figure 17: </span>PSD of the Z velocity of the Hexapod - measurement 3</p>
</div>
<div id="org899151a" class="figure">
<div id="org0169c44" class="figure">
<p><img src="figs/meas3_ry_z_psd.png" alt="meas3_ry_z_psd.png" />
</p>
<p><span class="figure-number">Figure 18: </span>PSD of the Z velocity of the Ry stage - measurement 3</p>
</div>
<div id="org0fc8e31" class="figure">
<div id="org02dedc8" class="figure">
<p><img src="figs/meas3_ty_y_psd.png" alt="meas3_ty_y_psd.png" />
</p>
<p><span class="figure-number">Figure 19: </span>PSD of the Ty velocity in the Y direction - measurement 3</p>
@@ -981,7 +989,7 @@ We then compute the PSD of each track before and after turning off the hexapod a
<div class="important">
<p>
Turning ON induces some motion on the hexapod in the z direction (figure <a href="#org0c4287e">17</a>), on the tilt stage in the z direction (figure <a href="#org899151a">18</a>) and on the y motion of the Ty stage (figure <a href="#org0fc8e31">19</a>):
Turning ON induces some motion on the hexapod in the z direction (figure <a href="#orgb6df1c9">17</a>), on the tilt stage in the z direction (figure <a href="#org0169c44">18</a>) and on the y motion of the Ty stage (figure <a href="#org02dedc8">19</a>):
</p>
<ul class="org-ul">
<li>at 17Hz</li>
@@ -992,14 +1000,14 @@ Turning ON induces some motion on the hexapod in the z direction (figure <a href
</div>
</div>
<div id="outline-container-org1529580" class="outline-2">
<h2 id="org1529580"><span class="section-number-2">10</span> Measurement 4 - Effect of the Splip-Ring and Spindle</h2>
<div id="outline-container-org567caf5" class="outline-2">
<h2 id="org567caf5"><span class="section-number-2">10</span> Measurement 4 - Effect of the Splip-Ring and Spindle</h2>
<div class="outline-text-2" id="text-10">
<p>
The slip ring is turned on at 300s, then the spindle is turned on at 620s (table <a href="#org274f078">6</a>). The time domain signals are shown figure <a href="#orgf0966f9">20</a>.
The slip ring is turned on at 300s, then the spindle is turned on at 620s (table <a href="#org3b56920">6</a>). The time domain signals are shown figure <a href="#org2d96c98">20</a>.
</p>
<table id="org274f078" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org3b56920" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 6:</span> Stages configuration - Measurement 4</caption>
<colgroup>
@@ -1058,18 +1066,18 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
</table>
<div id="orgf0966f9" class="figure">
<div id="org2d96c98" class="figure">
<p><img src="figs/meas4.png" alt="meas4.png" />
</p>
<p><span class="figure-number">Figure 20: </span>Time domain - measurement 4</p>
</div>
<p>
If we integrate this signal, we obtain Figure <a href="#org62b5bdf">21</a>.
If we integrate this signal, we obtain Figure <a href="#org3420b14">21</a>.
</p>
<div id="org62b5bdf" class="figure">
<div id="org3420b14" class="figure">
<p><img src="figs/meas4_int.png" alt="meas4_int.png" />
</p>
<p><span class="figure-number">Figure 21: </span>Time domain - measurement 4</p>
@@ -1079,7 +1087,7 @@ If we integrate this signal, we obtain Figure <a href="#org62b5bdf">21</a>.
The PSD of each track are computed using the code below.
</p>
<div id="orgfd7f8ce" class="figure">
<div id="orgd9a5a57" class="figure">
<p><img src="figs/meas4_hexa_z_psd.png" alt="meas4_hexa_z_psd.png" />
</p>
<p><span class="figure-number">Figure 22: </span>PSD of the Z velocity of the Hexapod - measurement 4</p>
@@ -1089,7 +1097,7 @@ The PSD of each track are computed using the code below.
We plot the PSD of the displacement.
</p>
<div id="org917dbdc" class="figure">
<div id="org13210e8" class="figure">
<p><img src="figs/meas4_hexa_z_psd_int.png" alt="meas4_hexa_z_psd_int.png" />
</p>
<p><span class="figure-number">Figure 23: </span>PSD<sub>INT</sub> of the Z velocity of the Hexapod - measurement 4</p>
@@ -1099,7 +1107,7 @@ We plot the PSD of the displacement.
And we compute the Cumulative amplitude spectrum.
</p>
<div id="orge4b6d59" class="figure">
<div id="orga20c0b8" class="figure">
<p><img src="figs/meas4_ry_z_psd.png" alt="meas4_ry_z_psd.png" />
</p>
<p><span class="figure-number">Figure 24: </span>PSD of the Ry rotation in the Y direction - measurement 4</p>
@@ -1107,7 +1115,7 @@ And we compute the Cumulative amplitude spectrum.
<div id="org08ad3dc" class="figure">
<div id="orgde0719f" class="figure">
<p><img src="figs/meas4_ty_y_psd.png" alt="meas4_ty_y_psd.png" />
</p>
<p><span class="figure-number">Figure 25: </span>PSD of the Ty velocity in the Y direction - measurement 4</p>
@@ -1117,7 +1125,7 @@ And we compute the Cumulative amplitude spectrum.
<div class="important">
<p>
Turning ON the splipring seems to not add motions on the stages measured.
It even seems to lower the motion of the Ty stage (figure <a href="#org08ad3dc">25</a>): does that make any sense?
It even seems to lower the motion of the Ty stage (figure <a href="#orgde0719f">25</a>): does that make any sense?
</p>
<p>
@@ -1133,26 +1141,26 @@ Turning ON the spindle induces motions:
</div>
</div>
<div id="outline-container-orga767d61" class="outline-2">
<h2 id="orga767d61"><span class="section-number-2">11</span> Measurement 5 - Transmission from ground to marble</h2>
<div id="outline-container-orgbd1a834" class="outline-2">
<h2 id="orgbd1a834"><span class="section-number-2">11</span> Measurement 5 - Transmission from ground to marble</h2>
<div class="outline-text-2" id="text-11">
<p>
This measurement just consists of measurement of Y-Z motion of the ground and the marble.
</p>
<p>
The time domain signals are shown on figure <a href="#orgc513617">26</a>.
The time domain signals are shown on figure <a href="#org3d00bca">26</a>.
</p>
<div id="orgc513617" class="figure">
<div id="org3d00bca" class="figure">
<p><img src="figs/meas5.png" alt="meas5.png" />
</p>
<p><span class="figure-number">Figure 26: </span>Time domain - measurement 5</p>
</div>
<p>
We compute the PSD of each track and we plot the PSD of the Z motion for the ground and marble on figure <a href="#org28b0b94">27</a> and for the Y motion on figure <a href="#orgf797eae">28</a>.
We compute the PSD of each track and we plot the PSD of the Z motion for the ground and marble on figure <a href="#orgc4070a5">27</a> and for the Y motion on figure <a href="#org9f35e98">28</a>.
</p>
<div class="org-src-container">
@@ -1164,14 +1172,14 @@ We compute the PSD of each track and we plot the PSD of the Z motion for the gro
</div>
<div id="org28b0b94" class="figure">
<div id="orgc4070a5" class="figure">
<p><img src="figs/meas5_z_psd.png" alt="meas5_z_psd.png" />
</p>
<p><span class="figure-number">Figure 27: </span>PSD of the ground and marble in the Z direction</p>
</div>
<div id="orgf797eae" class="figure">
<div id="org9f35e98" class="figure">
<p><img src="figs/meas5_y_psd.png" alt="meas5_y_psd.png" />
</p>
<p><span class="figure-number">Figure 28: </span>PSD of the ground and marble in the Y direction</p>
@@ -1179,7 +1187,7 @@ We compute the PSD of each track and we plot the PSD of the Z motion for the gro
<p>
Then, instead of looking at the Power Spectral Density, we can try to estimate the transfer function from a ground motion to the motion of the marble.
The transfer functions are shown on figure <a href="#orgbb283a9">29</a> and the coherence on figure <a href="#orga357e58">30</a>.
The transfer functions are shown on figure <a href="#org30b772d">29</a> and the coherence on figure <a href="#orgd6d1e80">30</a>.
</p>
<div class="org-src-container">
@@ -1189,7 +1197,7 @@ The transfer functions are shown on figure <a href="#orgbb283a9">29</a> and the
</div>
<div id="orgbb283a9" class="figure">
<div id="org30b772d" class="figure">
<p><img src="figs/meas5_tf.png" alt="meas5_tf.png" />
</p>
<p><span class="figure-number">Figure 29: </span>Transfer function estimation - measurement 5</p>
@@ -1202,7 +1210,7 @@ The transfer functions are shown on figure <a href="#orgbb283a9">29</a> and the
</div>
<div id="orga357e58" class="figure">
<div id="orgd6d1e80" class="figure">
<p><img src="figs/meas5_coh.png" alt="meas5_coh.png" />
</p>
<p><span class="figure-number">Figure 30: </span>Coherence - measurement 5</p>
@@ -1219,8 +1227,8 @@ But the coherence is not good above 20Hz, so it is difficult to estimate resonan
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-04-02 mar. 10:39</p>
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-07-05 ven. 11:35</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>