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<title>Measurement Analysis</title> <title>Measurement Analysis</title>
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<h1 class="title">Measurement Analysis</h1> <h1 class="title">Measurement Analysis</h1>
<div id="table-of-contents"> <div id="table-of-contents">
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orga57c824">1. Measurement Description</a></li> <li><a href="#org3a9a926">1. Measurement Description</a></li>
<li><a href="#orgac83bb1">2. Importation of the data</a></li> <li><a href="#orga751c46">2. Importation of the data</a></li>
<li><a href="#orge44c773">3. Variables for analysis</a></li> <li><a href="#orgbb22f41">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="#orgfad99e2">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="#org95ba164">5. Data Post Processing</a></li>
<li><a href="#org03ef418">6. Normalization</a></li> <li><a href="#org7ad093b">6. Normalization</a></li>
<li><a href="#org8583637">7. Measurement 1 - Effect of Ty stage</a></li> <li><a href="#org2a0c6af">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="#orgc84b427">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="#org735052a">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="#org567caf5">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="#orgbd1a834">11. Measurement 5 - Transmission from ground to marble</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div class="note">
<p> <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> </p>
<div id="outline-container-orga57c824" class="outline-2"> </div>
<h2 id="orga57c824"><span class="section-number-2">1</span> Measurement Description</h2>
<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 class="outline-text-2" id="text-1">
<div id="orgc56bc67" class="figure"> <div id="org842eee7" class="figure">
<p><img src="./figs/setup_picture.png" alt="setup_picture.png" /> <p><img src="./figs/setup_picture.png" alt="setup_picture.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the setup for the measurement</p> <p><span class="figure-number">Figure 1: </span>Picture of the setup for the measurement</p>
</div> </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> </div>
<div id="outline-container-orgac83bb1" class="outline-2"> <div id="outline-container-orga751c46" class="outline-2">
<h2 id="orgac83bb1"><span class="section-number-2">2</span> Importation of the data</h2> <h2 id="orga751c46"><span class="section-number-2">2</span> Importation of the data</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
First, load all the measurement files: First, load all the measurement files:
@ -322,10 +330,10 @@ meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highli
</div> </div>
<p> <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> </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> <caption class="t-above"><span class="table-number">Table 1:</span> Channels for measurements 1 to 4</caption>
<colgroup> <colgroup>
@ -378,9 +386,9 @@ For the measurements 1 to 4, the measurement channels are shown table <a href="#
<p> <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> </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> <caption class="t-above"><span class="table-number">Table 2:</span> Channels for measurement 5</caption>
<colgroup> <colgroup>
@ -416,8 +424,8 @@ For the measurement 5, the channels are shown table <a href="#org00892de">2</a>.
</div> </div>
</div> </div>
<div id="outline-container-orge44c773" class="outline-2"> <div id="outline-container-orgbb22f41" class="outline-2">
<h2 id="orge44c773"><span class="section-number-2">3</span> Variables for analysis</h2> <h2 id="orgbb22f41"><span class="section-number-2">3</span> Variables for analysis</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
We define the sampling frequency and the time vectors for the plots. 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"> <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> <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>; 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>; 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>; 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>; 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>; 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>; 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> </pre>
</div> </div>
@ -453,11 +461,11 @@ Then we define the windows that will be used to average the results.
</div> </div>
</div> </div>
<div id="outline-container-orgcb0a2db" class="outline-2"> <div id="outline-container-orgfad99e2" class="outline-2">
<h2 id="orgcb0a2db"><span class="section-number-2">4</span> Coherence between the two vertical geophones on the Tilt Stage</h2> <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"> <div class="outline-text-2" id="text-4">
<p> <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> </p>
<div class="org-src-container"> <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>; <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>
<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><img src="figs/coherence_vertical_tilt_sensors.png" alt="coherence_vertical_tilt_sensors.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Coherence between the two vertical sensors positionned on the Tilt Stage</p> <p><span class="figure-number">Figure 2: </span>Coherence between the two vertical sensors positionned on the Tilt Stage</p>
</div> </div>
<p> <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> </p>
<div class="org-src-container"> <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>; <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>
<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><img src="figs/tf_vertical_tilt_sensors.png" alt="tf_vertical_tilt_sensors.png" />
</p> </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> <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> </div>
<div id="outline-container-orgc619b39" class="outline-2"> <div id="outline-container-org95ba164" class="outline-2">
<h2 id="orgc619b39"><span class="section-number-2">5</span> Data Post Processing</h2> <h2 id="org95ba164"><span class="section-number-2">5</span> Data Post Processing</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
<p> <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: 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> </div>
<div id="outline-container-org03ef418" class="outline-2"> <div id="outline-container-org7ad093b" class="outline-2">
<h2 id="org03ef418"><span class="section-number-2">6</span> Normalization</h2> <h2 id="org7ad093b"><span class="section-number-2">6</span> Normalization</h2>
<div class="outline-text-2" id="text-6"> <div class="outline-text-2" id="text-6">
<p> <p>
Parameters of the geophone are defined below. 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>
<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> <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_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> 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> </pre>
</div> </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><img src="figs/L4C_bode_plot.png" alt="L4C_bode_plot.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Bode plot of the L4C Geophone</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> </div>
<div id="outline-container-org8583637" class="outline-2"> <div id="outline-container-org2a0c6af" class="outline-2">
<h2 id="org8583637"><span class="section-number-2">7</span> Measurement 1 - Effect of Ty stage</h2> <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"> <div class="outline-text-2" id="text-7">
<p> <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> </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> <caption class="t-above"><span class="table-number">Table 3:</span> Stages configuration - Measurement 1</caption>
<colgroup> <colgroup>
@ -658,7 +666,7 @@ The configuration for this measurement is shown table <a href="#orgc1f3234">3</a
</table> </table>
<p> <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> </p>
<div class="important"> <div class="important">
@ -670,7 +678,7 @@ How can we explain that?
</div> </div>
<div id="orgf931943" class="figure"> <div id="orge80ff30" class="figure">
<p><img src="figs/meas1.png" alt="meas1.png" /> <p><img src="figs/meas1.png" alt="meas1.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Time domain - measurement 1</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>
<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> </p>
<div id="orgb6bceab" class="figure"> <div id="orga73c9be" class="figure">
<p><img src="figs/meas1_disp.png" alt="meas1_disp.png" /> <p><img src="figs/meas1_disp.png" alt="meas1_disp.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Y displacement of the Ty stage</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> </div>
<p> <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> </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><img src="figs/meas1_ry_z_psd.png" alt="meas1_ry_z_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>PSD of the Z velocity of Ry stage - measurement 1</p> <p><span class="figure-number">Figure 7: </span>PSD of the Z velocity of Ry stage - measurement 1</p>
</div> </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><img src="figs/meas1_ry_tilt_psd.png" alt="meas1_ry_tilt_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>PSD of the Rotation of Ry Stage - measurement 1</p> <p><span class="figure-number">Figure 8: </span>PSD of the Rotation of Ry Stage - measurement 1</p>
</div> </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><img src="figs/meas1_ty_y_psd.png" alt="meas1_ty_y_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>PSD of the Ty velocity in the Y direction - measurement 1</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> </div>
<div id="outline-container-org47192a7" class="outline-2"> <div id="outline-container-orgc84b427" class="outline-2">
<h2 id="org47192a7"><span class="section-number-2">8</span> Measurement 2 - Effect of Ry stage</h2> <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"> <div class="outline-text-2" id="text-8">
<p> <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> </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> <caption class="t-above"><span class="table-number">Table 4:</span> Stages configuration - Measurement 2</caption>
<colgroup> <colgroup>
@ -806,25 +814,25 @@ The tilt stage is turned ON at around 326 seconds (table <a href="#orgba0882e">4
</table> </table>
<p> <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> </p>
<div id="org9bf6e90" class="figure"> <div id="orgd48d30c" class="figure">
<p><img src="figs/meas2.png" alt="meas2.png" /> <p><img src="figs/meas2.png" alt="meas2.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Time domain - measurement 2</p> <p><span class="figure-number">Figure 10: </span>Time domain - measurement 2</p>
</div> </div>
<div id="org767f834" class="figure"> <div id="org603b8af" class="figure">
<p><img src="figs/meas2_disp.png" alt="meas2_disp.png" /> <p><img src="figs/meas2_disp.png" alt="meas2_disp.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Time domain - measurement 2</p> <p><span class="figure-number">Figure 11: </span>Time domain - measurement 2</p>
</div> </div>
<p> <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> </p>
<div class="org-src-container"> <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>; <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>
<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><img src="figs/meas2_ry_z_psd.png" alt="meas2_ry_z_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>PSD of the Z velocity of Ry Stage - measurement 2</p> <p><span class="figure-number">Figure 12: </span>PSD of the Z velocity of Ry Stage - measurement 2</p>
</div> </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><img src="figs/meas2_ry_tilt_psd.png" alt="meas2_ry_tilt_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>PSD of the Rotation motion of Ry Stage - measurement 2</p> <p><span class="figure-number">Figure 13: </span>PSD of the Rotation motion of Ry Stage - measurement 2</p>
</div> </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><img src="figs/meas2_ty_y_psd.png" alt="meas2_ty_y_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>PSD of the Ty velocity in the Y direction - measurement 2</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> </div>
<div id="outline-container-org0c3a1d4" class="outline-2"> <div id="outline-container-org735052a" class="outline-2">
<h2 id="org0c3a1d4"><span class="section-number-2">9</span> Measurement 3 - Effect of the Hexapod</h2> <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"> <div class="outline-text-2" id="text-9">
<p> <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> </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> <caption class="t-above"><span class="table-number">Table 5:</span> Stages configuration - Measurement 3</caption>
<colgroup> <colgroup>
@ -926,25 +934,25 @@ The hexapod is turned off after 406 seconds (table <a href="#org8b4187d">5</a>).
</table> </table>
<p> <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> </p>
<div id="org08fc17d" class="figure"> <div id="orgf7e79c3" class="figure">
<p><img src="figs/meas3.png" alt="meas3.png" /> <p><img src="figs/meas3.png" alt="meas3.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Time domain - measurement 3</p> <p><span class="figure-number">Figure 15: </span>Time domain - measurement 3</p>
</div> </div>
<div id="org4ae7ca4" class="figure"> <div id="org5206570" class="figure">
<p><img src="figs/meas3_disp.png" alt="meas3_disp.png" /> <p><img src="figs/meas3_disp.png" alt="meas3_disp.png" />
</p> </p>
<p><span class="figure-number">Figure 16: </span>Time domain - measurement 3</p> <p><span class="figure-number">Figure 16: </span>Time domain - measurement 3</p>
</div> </div>
<p> <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> </p>
<div class="org-src-container"> <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>; <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>
<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><img src="figs/meas3_hexa_z_psd.png" alt="meas3_hexa_z_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 17: </span>PSD of the Z velocity of the Hexapod - measurement 3</p> <p><span class="figure-number">Figure 17: </span>PSD of the Z velocity of the Hexapod - measurement 3</p>
</div> </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><img src="figs/meas3_ry_z_psd.png" alt="meas3_ry_z_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 18: </span>PSD of the Z velocity of the Ry stage - measurement 3</p> <p><span class="figure-number">Figure 18: </span>PSD of the Z velocity of the Ry stage - measurement 3</p>
</div> </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><img src="figs/meas3_ty_y_psd.png" alt="meas3_ty_y_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 19: </span>PSD of the Ty velocity in the Y direction - measurement 3</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"> <div class="important">
<p> <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> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>at 17Hz</li> <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> </div>
<div id="outline-container-org1529580" class="outline-2"> <div id="outline-container-org567caf5" class="outline-2">
<h2 id="org1529580"><span class="section-number-2">10</span> Measurement 4 - Effect of the Splip-Ring and Spindle</h2> <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"> <div class="outline-text-2" id="text-10">
<p> <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> </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> <caption class="t-above"><span class="table-number">Table 6:</span> Stages configuration - Measurement 4</caption>
<colgroup> <colgroup>
@ -1058,18 +1066,18 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
</table> </table>
<div id="orgf0966f9" class="figure"> <div id="org2d96c98" class="figure">
<p><img src="figs/meas4.png" alt="meas4.png" /> <p><img src="figs/meas4.png" alt="meas4.png" />
</p> </p>
<p><span class="figure-number">Figure 20: </span>Time domain - measurement 4</p> <p><span class="figure-number">Figure 20: </span>Time domain - measurement 4</p>
</div> </div>
<p> <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> </p>
<div id="org62b5bdf" class="figure"> <div id="org3420b14" class="figure">
<p><img src="figs/meas4_int.png" alt="meas4_int.png" /> <p><img src="figs/meas4_int.png" alt="meas4_int.png" />
</p> </p>
<p><span class="figure-number">Figure 21: </span>Time domain - measurement 4</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. The PSD of each track are computed using the code below.
</p> </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><img src="figs/meas4_hexa_z_psd.png" alt="meas4_hexa_z_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 22: </span>PSD of the Z velocity of the Hexapod - measurement 4</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. We plot the PSD of the displacement.
</p> </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><img src="figs/meas4_hexa_z_psd_int.png" alt="meas4_hexa_z_psd_int.png" />
</p> </p>
<p><span class="figure-number">Figure 23: </span>PSD<sub>INT</sub> of the Z velocity of the Hexapod - measurement 4</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. And we compute the Cumulative amplitude spectrum.
</p> </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><img src="figs/meas4_ry_z_psd.png" alt="meas4_ry_z_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 24: </span>PSD of the Ry rotation in the Y direction - measurement 4</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><img src="figs/meas4_ty_y_psd.png" alt="meas4_ty_y_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 25: </span>PSD of the Ty velocity in the Y direction - measurement 4</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"> <div class="important">
<p> <p>
Turning ON the splipring seems to not add motions on the stages measured. 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>
<p> <p>
@ -1133,26 +1141,26 @@ Turning ON the spindle induces motions:
</div> </div>
</div> </div>
<div id="outline-container-orga767d61" class="outline-2"> <div id="outline-container-orgbd1a834" class="outline-2">
<h2 id="orga767d61"><span class="section-number-2">11</span> Measurement 5 - Transmission from ground to marble</h2> <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"> <div class="outline-text-2" id="text-11">
<p> <p>
This measurement just consists of measurement of Y-Z motion of the ground and the marble. This measurement just consists of measurement of Y-Z motion of the ground and the marble.
</p> </p>
<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> </p>
<div id="orgc513617" class="figure"> <div id="org3d00bca" class="figure">
<p><img src="figs/meas5.png" alt="meas5.png" /> <p><img src="figs/meas5.png" alt="meas5.png" />
</p> </p>
<p><span class="figure-number">Figure 26: </span>Time domain - measurement 5</p> <p><span class="figure-number">Figure 26: </span>Time domain - measurement 5</p>
</div> </div>
<p> <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> </p>
<div class="org-src-container"> <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>
<div id="org28b0b94" class="figure"> <div id="orgc4070a5" class="figure">
<p><img src="figs/meas5_z_psd.png" alt="meas5_z_psd.png" /> <p><img src="figs/meas5_z_psd.png" alt="meas5_z_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 27: </span>PSD of the ground and marble in the Z direction</p> <p><span class="figure-number">Figure 27: </span>PSD of the ground and marble in the Z direction</p>
</div> </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><img src="figs/meas5_y_psd.png" alt="meas5_y_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 28: </span>PSD of the ground and marble in the Y direction</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> <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. 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> </p>
<div class="org-src-container"> <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>
<div id="orgbb283a9" class="figure"> <div id="org30b772d" class="figure">
<p><img src="figs/meas5_tf.png" alt="meas5_tf.png" /> <p><img src="figs/meas5_tf.png" alt="meas5_tf.png" />
</p> </p>
<p><span class="figure-number">Figure 29: </span>Transfer function estimation - measurement 5</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>
<div id="orga357e58" class="figure"> <div id="orgd6d1e80" class="figure">
<p><img src="figs/meas5_coh.png" alt="meas5_coh.png" /> <p><img src="figs/meas5_coh.png" alt="meas5_coh.png" />
</p> </p>
<p><span class="figure-number">Figure 30: </span>Coherence - measurement 5</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> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-04-02 mar. 10:39</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> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>

49
2018-10-15 - Marc/index.org
View File

@ -25,10 +25,27 @@
#+PROPERTY: header-args:matlab+ :exports both #+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export #+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs #+PROPERTY: header-args:matlab+ :output-dir figs
#+PROPERTY: header-args:matlab+ :tangle matlab/meas_analysis_geophones.m
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export #+PROPERTY: header-args:shell :eval no-export
:END: :END:
* ZIP file containing the data and matlab files :ignore:
#+begin_src bash :exports none :results none
if [ matlab/meas_analysis_geophones.m -nt data/meas_analysis_geophones.zip ]; then
cp matlab/meas_analysis_geophones.m meas_analysis_geophones.m;
zip data/meas_analysis_geophones \
mat/Measurement*.mat \
meas_analysis_geophones.m
rm meas_analysis_geophones.m;
fi
#+end_src
#+begin_note
All the files (data and Matlab scripts) are accessible [[file:data/meas_analysis_geophones.zip][here]].
#+end_note
* Matlab Init :noexport:ignore: * Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) #+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>> <<matlab-dir>>
@ -69,7 +86,7 @@ Change the track name for measurements 3 and 4.
For the measurements 1 to 4, the measurement channels are shown table [[tab:meas_14]]. For the measurements 1 to 4, the measurement channels are shown table [[tab:meas_14]].
#+begin_src matlab :exports results :results table :post addhdr(*this*) #+begin_src matlab :exports results :results table :tangle no :post addhdr(*this*)
table_string = sprintf(' | Channel 1 | Channel 2 | Channel 3 \n'); table_string = sprintf(' | Channel 1 | Channel 2 | Channel 3 \n');
for i = 1:4 for i = 1:4
table_string = [table_string, sprintf('Meas. %i | %s | %s | %s \n', i, meas{i}.Track1_Name, meas{i}.Track2_Name, meas{i}.Track3_Name)]; table_string = [table_string, sprintf('Meas. %i | %s | %s | %s \n', i, meas{i}.Track1_Name, meas{i}.Track2_Name, meas{i}.Track3_Name)];
@ -89,9 +106,9 @@ For the measurements 1 to 4, the measurement channels are shown table [[tab:meas
For the measurement 5, the channels are shown table [[tab:meas_5]]. For the measurement 5, the channels are shown table [[tab:meas_5]].
#+begin_src matlab :exports results :results table :post addhdr(*this*) #+begin_src matlab :exports results :results table :tangle no :post addhdr(*this*)
table_string = sprintf(' | Channel 1 | Channel 2 | Channel 3 | Channel 4 \n'); table_string = sprintf(' | Channel 1 | Channel 2 | Channel 3 | Channel 4 \n');
i = 5 i = 5;
table_string = [table_string, sprintf('Meas. %i | %s | %s | %s | %s \n', i, meas{i}.Track1_Name, meas{i}.Track2_Name, meas{i}.Track3_Name, meas{i}.Track4_Name)]; table_string = [table_string, sprintf('Meas. %i | %s | %s | %s | %s \n', i, meas{i}.Track1_Name, meas{i}.Track2_Name, meas{i}.Track3_Name, meas{i}.Track4_Name)];
ans = table_string ans = table_string
#+end_src #+end_src
@ -109,11 +126,11 @@ We define the sampling frequency and the time vectors for the plots.
#+begin_src matlab :exports code :results silent #+begin_src matlab :exports code :results silent
Fs = 256; % [Hz] Fs = 256; % [Hz]
dt = 1/(Fs); dt = 1/(Fs);
t1 = dt*[0:length(meas{1}.Track1)-1]; t1 = dt*(0:length(meas{1}.Track1)-1);
t2 = dt*[0:length(meas{2}.Track1)-1]; t2 = dt*(0:length(meas{2}.Track1)-1);
t3 = dt*[0:length(meas{3}.Track1)-1]; t3 = dt*(0:length(meas{3}.Track1)-1);
t4 = dt*[0:length(meas{4}.Track1)-1]; t4 = dt*(0:length(meas{4}.Track1)-1);
t5 = dt*[0:length(meas{5}.Track1)-1]; t5 = dt*(0:length(meas{5}.Track1)-1);
#+end_src #+end_src
For the frequency analysis, we define the frequency limits for the plot. For the frequency analysis, we define the frequency limits for the plot.
@ -159,13 +176,13 @@ We then compute the transfer function from one sensor to the other (figure [[fig
#+begin_src matlab :results none :exports none #+begin_src matlab :results none :exports none
figure; figure;
ax1 = subaxis(2,1,1); ax1 = subplot(2,1,1);
plot(f, abs(tf23)); plot(f, abs(tf23));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'XTickLabel',[]);
ylabel('Magnitude [V/(m/s)]'); ylabel('Magnitude [V/(m/s)]');
ax2 = subaxis(2,1,2); ax2 = subplot(2,1,2);
plot(f, 180/pi*angle(tf23)); plot(f, 180/pi*angle(tf23));
set(gca,'xscale','log'); set(gca,'xscale','log');
yticks(-180:90:180); yticks(-180:90:180);
@ -228,13 +245,13 @@ Measurements will be normalized by the inverse of this transfer function in orde
freqs = logspace(-2, 2, 1000); freqs = logspace(-2, 2, 1000);
figure; figure;
ax1 = subaxis(2,1,1); ax1 = subplot(2,1,1);
plot(freqs, abs(squeeze(freqresp(L4C_G, freqs, 'Hz')))); plot(freqs, abs(squeeze(freqresp(L4C_G, freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]); set(gca, 'XTickLabel',[]);
ylabel('Magnitude [V/(m/s)]'); ylabel('Magnitude [V/(m/s)]');
ax2 = subaxis(2,1,2); ax2 = subplot(2,1,2);
plot(freqs, 180/pi*angle(squeeze(freqresp(L4C_G, freqs, 'Hz')))); plot(freqs, 180/pi*angle(squeeze(freqresp(L4C_G, freqs, 'Hz'))));
set(gca,'xscale','log'); set(gca,'xscale','log');
yticks(-180:90:180); yticks(-180:90:180);
@ -806,7 +823,7 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
#+begin_src matlab :exports none :results silent #+begin_src matlab :exports none :results silent
figure; figure;
subaxis(1, 2, 1); subplot(1, 2, 1);
hold on; hold on;
plot(t4, cumtrapz(t4, meas{4}.Track1)); plot(t4, cumtrapz(t4, meas{4}.Track1));
plot(t4, cumtrapz(t4, meas{4}.Track2)); plot(t4, cumtrapz(t4, meas{4}.Track2));
@ -816,7 +833,7 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
xlabel('Time [s]'); ylabel('Displacement [m]'); xlabel('Time [s]'); ylabel('Displacement [m]');
legend({meas{4}.Track1_Name, meas{4}.Track2_Name, meas{4}.Track3_Name}, 'Location', 'northwest') legend({meas{4}.Track1_Name, meas{4}.Track2_Name, meas{4}.Track3_Name}, 'Location', 'northwest')
subaxis(1, 2, 2); subplot(1, 2, 2);
hold on; hold on;
plot(t4, cumtrapz(t4, meas{4}.Track1)); plot(t4, cumtrapz(t4, meas{4}.Track1));
plot(t4, cumtrapz(t4, meas{4}.Track2)); plot(t4, cumtrapz(t4, meas{4}.Track2));
@ -1101,7 +1118,7 @@ The transfer functions are shown on figure [[fig:meas5_tf]] and the coherence on
#+begin_src matlab :exports none :results silent #+begin_src matlab :exports none :results silent
figure; figure;
ax1 = subaxis(2,1,1); ax1 = subplot(2,1,1);
hold on; hold on;
plot(fz, abs(tfz)); plot(fz, abs(tfz));
plot(fy, abs(tfy)); plot(fy, abs(tfy));
@ -1109,7 +1126,7 @@ The transfer functions are shown on figure [[fig:meas5_tf]] and the coherence on
set(gca, 'XTickLabel',[]); set(gca, 'XTickLabel',[]);
ylabel('Magnitude'); ylabel('Magnitude');
hold off; hold off;
ax2 = subaxis(2,1,2); ax2 = subplot(2,1,2);
hold on; hold on;
plot(fz, 180/pi*angle(tfz)); plot(fz, 180/pi*angle(tfz));
plot(fy, 180/pi*angle(tfy)); plot(fy, 180/pi*angle(tfy));

837
2018-10-15 - Marc/matlab/meas_analysis_geophones.m Normal file
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@ -0,0 +1,837 @@
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
% Importation of the data
% First, load all the measurement files:
meas = {};
meas{1} = load('./mat/Measurement1.mat');
meas{2} = load('./mat/Measurement2.mat');
meas{3} = load('./mat/Measurement3.mat');
meas{4} = load('./mat/Measurement4.mat');
meas{5} = load('./mat/Measurement5.mat');
% Change the track name for measurements 3 and 4.
meas{3}.Track1_Name = 'Input 1: Hexa Z';
meas{4}.Track1_Name = 'Input 1: Hexa Z';
% Variables for analysis
% We define the sampling frequency and the time vectors for the plots.
Fs = 256; % [Hz]
dt = 1/(Fs);
t1 = dt*(0:length(meas{1}.Track1)-1);
t2 = dt*(0:length(meas{2}.Track1)-1);
t3 = dt*(0:length(meas{3}.Track1)-1);
t4 = dt*(0:length(meas{4}.Track1)-1);
t5 = dt*(0:length(meas{5}.Track1)-1);
% For the frequency analysis, we define the frequency limits for the plot.
fmin = 1; % [Hz]
fmax = 100; % [Hz]
% Then we define the windows that will be used to average the results.
psd_window = hanning(2*fmin/dt);
% Coherence between the two vertical geophones on the Tilt Stage
% We first compute the coherence between the two geophones located on the tilt stage. The result is shown on figure [[fig:coherence_vertical_tilt_sensors]].
[coh, f] = mscohere(meas{1}.Track1(:), meas{1}.Track2(:), psd_window, [], [], Fs);
figure;
plot(f, coh);
set(gca, 'xscale', 'log');
ylim([0, 1]);
xlabel('Frequency [Hz]'); ylabel('Coherence');
% #+NAME: fig:coherence_vertical_tilt_sensors
% #+CAPTION: Coherence between the two vertical sensors positionned on the Tilt Stage
% #+RESULTS: fig:coherence_vertical_tilt_sensors
% [[file:figs/coherence_vertical_tilt_sensors.png]]
% We then compute the transfer function from one sensor to the other (figure [[fig:tf_vertical_tilt_sensors]]).
[tf23, f] = tfestimate(meas{1}.Track1(:), meas{1}.Track2(:), psd_window, [], [], Fs);
figure;
ax1 = subplot(2,1,1);
plot(f, abs(tf23));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude [V/(m/s)]');
ax2 = subplot(2,1,2);
plot(f, 180/pi*angle(tf23));
set(gca,'xscale','log');
yticks(-180:90:180);
ylim([-180 180]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
linkaxes([ax1,ax2],'x');
% Data Post Processing
% 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:
meas1_z = (meas{1}.Track1+meas{1}.Track2)/2;
meas1_tilt = (meas{1}.Track1-meas{1}.Track2)/2;
meas{1}.Track1 = meas1_z;
meas{1}.Track1_Y_Magnitude = 'Meter / second';
meas{1}.Track1_Name = 'Ry Z';
meas{1}.Track2 = meas1_tilt;
meas{1}.Track2_Y_Magnitude = 'Rad / second';
meas{1}.Track2_Name = 'Ry Tilt';
meas2_z = (meas{2}.Track1+meas{2}.Track2)/2;
meas2_tilt = (meas{2}.Track1-meas{2}.Track2)/2;
meas{2}.Track1 = meas2_z;
meas{2}.Track1_Y_Magnitude = 'Meter / second';
meas{2}.Track1_Name = 'Ry Z';
meas{2}.Track2 = meas2_tilt;
meas{2}.Track2_Y_Magnitude = 'Rad / second';
meas{2}.Track2_Name = 'Ry Tilt';
% Normalization
% Parameters of the geophone are defined below.
% The transfer function from geophone velocity to measured voltage is shown on figure [[fig:L4C_bode_plot]].
% Measurements will be normalized by the inverse of this transfer function in order to go from voltage measurement to velocity measurement.
L4C_w0 = 2*pi; % [rad/s]
L4C_ksi = 0.28;
L4C_G0 = 276.8; % [V/(m/s)]
L4C_G = L4C_G0*(s/L4C_w0)^2/((s/L4C_w0)^2 + 2*L4C_ksi*(s/L4C_w0) + 1);
freqs = logspace(-2, 2, 1000);
figure;
ax1 = subplot(2,1,1);
plot(freqs, abs(squeeze(freqresp(L4C_G, freqs, 'Hz'))));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude [V/(m/s)]');
ax2 = subplot(2,1,2);
plot(freqs, 180/pi*angle(squeeze(freqresp(L4C_G, freqs, 'Hz'))));
set(gca,'xscale','log');
yticks(-180:90:180);
ylim([-180 180]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
linkaxes([ax1,ax2],'x');
% #+NAME: fig:L4C_bode_plot
% #+CAPTION: Bode plot of the L4C Geophone
% #+RESULTS: fig:L4C_bode_plot
% [[file:figs/L4C_bode_plot.png]]
meas{1}.Track1 = (meas{1}.Track1)./276.8;
meas{1}.Track2 = (meas{1}.Track2)./276.8;
meas{1}.Track3 = (meas{1}.Track3)./276.8;
meas{2}.Track1 = (meas{2}.Track1)./276.8;
meas{2}.Track2 = (meas{2}.Track2)./276.8;
meas{2}.Track3 = (meas{2}.Track3)./276.8;
meas{3}.Track1 = (meas{3}.Track1)./276.8;
meas{3}.Track2 = (meas{3}.Track2)./276.8;
meas{3}.Track3 = (meas{3}.Track3)./276.8;
meas{4}.Track1 = (meas{4}.Track1)./276.8;
meas{4}.Track2 = (meas{4}.Track2)./276.8;
meas{4}.Track3 = (meas{4}.Track3)./276.8;
meas{5}.Track1 = (meas{5}.Track1)./276.8;
meas{5}.Track2 = (meas{5}.Track2)./276.8;
meas{5}.Track3 = (meas{5}.Track3)./276.8;
meas{5}.Track4 = (meas{5}.Track4)./276.8;
meas{1}.Track1_norm = lsim(inv(L4C_G), meas{1}.Track1, t1);
meas{1}.Track2_norm = lsim(inv(L4C_G), meas{1}.Track2, t1);
meas{1}.Track3_norm = lsim(inv(L4C_G), meas{1}.Track3, t1);
meas{2}.Track1_norm = lsim(inv(L4C_G), meas{2}.Track1, t2);
meas{2}.Track2_norm = lsim(inv(L4C_G), meas{2}.Track2, t2);
meas{2}.Track3_norm = lsim(inv(L4C_G), meas{2}.Track3, t2);
meas{3}.Track1_norm = lsim(inv(L4C_G), meas{3}.Track1, t3);
meas{3}.Track2_norm = lsim(inv(L4C_G), meas{3}.Track2, t3);
meas{3}.Track3_norm = lsim(inv(L4C_G), meas{3}.Track3, t3);
meas{4}.Track1_norm = lsim(inv(L4C_G), meas{4}.Track1, t4);
meas{4}.Track2_norm = lsim(inv(L4C_G), meas{4}.Track2, t4);
meas{4}.Track3_norm = lsim(inv(L4C_G), meas{4}.Track3, t4);
meas{5}.Track1_norm = lsim(inv(L4C_G), meas{5}.Track1, t5);
meas{5}.Track2_norm = lsim(inv(L4C_G), meas{5}.Track2, t5);
meas{5}.Track3_norm = lsim(inv(L4C_G), meas{5}.Track3, t5);
meas{5}.Track4_norm = lsim(inv(L4C_G), meas{5}.Track4, t5);
% Measurement 1 - Effect of Ty stage
% The configuration for this measurement is shown table [[tab:conf_meas1]].
% #+CAPTION: Stages configuration - Measurement 1
% #+NAME: tab:conf_meas1
% | Time | 0-309 | 309-end |
% |----------+-------+---------|
% | Ty | OFF | *ON* |
% | Ry | OFF | OFF |
% | SlipRing | OFF | OFF |
% | Spindle | OFF | OFF |
% | Hexa | OFF | OFF |
% We then plot the measurements in time domain (figure [[fig:meas1]]).
% #+begin_important
% We observe strange behavior when the Ty stage is turned on.
% How can we explain that?
% #+end_important
figure;
hold on;
plot(t1(ceil(300/dt):ceil(340/dt)), meas{1}.Track1(ceil(300/dt):ceil(340/dt)));
plot(t1(ceil(300/dt):ceil(340/dt)), meas{1}.Track2(ceil(300/dt):ceil(340/dt)));
plot(t1(ceil(300/dt):ceil(340/dt)), meas{1}.Track3(ceil(300/dt):ceil(340/dt)));
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{1}.Track1_Name, meas{1}.Track2_Name, meas{1}.Track3_Name}, 'Location', 'northeast')
% #+LABEL: fig:meas1
% #+CAPTION: Time domain - measurement 1
% #+RESULTS: fig:meas1
% [[file:figs/meas1.png]]
% To understand what is going on, instead of looking at the velocity, we can look at the displacement by integrating the data. The displacement is computed by integrating the velocity using =cumtrapz= function.
% Then we plot the position with respect to time (figure [[fig:meas1_disp]]).
figure;
hold on;
plot(t1, cumtrapz(t1, meas{1}.Track3));
hold off;
xlim([300, 340]);
xlabel('Time [s]'); ylabel('Displacement [m]');
% #+LABEL: fig:meas1_disp
% #+CAPTION: Y displacement of the Ty stage
% #+RESULTS: fig:meas1_disp
% [[file:figs/meas1_disp.png]]
% We when compute the power spectral density of each measurement before and after turning on the stage.
[pxx111, f11] = pwelch(meas{1}.Track1(1:ceil(300/dt)), psd_window, [], [], Fs);
[pxx112, f12] = pwelch(meas{1}.Track1(ceil(350/dt):end), psd_window, [], [], Fs);
[pxx121, ~] = pwelch(meas{1}.Track2(1:ceil(300/dt)), psd_window, [], [], Fs);
[pxx122, ~] = pwelch(meas{1}.Track2(ceil(350/dt):end), psd_window, [], [], Fs);
[pxx131, ~] = pwelch(meas{1}.Track3(1:ceil(300/dt)), psd_window, [], [], Fs);
[pxx132, ~] = pwelch(meas{1}.Track3(ceil(350/dt):end), psd_window, [], [], Fs);
% We finally plot the power spectral density of each track (figures [[fig:meas1_ry_z_psd]], [[fig:meas1_ry_tilt_psd]], [[fig:meas1_ty_y_psd]]).
figure;
hold on;
plot(f11, sqrt(pxx111)./abs(squeeze(freqresp(L4C_G, f11, 'Hz'))));
plot(f12, sqrt(pxx112)./abs(squeeze(freqresp(L4C_G, f12, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{1}.Track1_Name));
legend({'0-300', '350-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas1_ry_z_psd
% #+CAPTION: PSD of the Z velocity of Ry stage - measurement 1
% #+RESULTS: fig:meas1_ry_z_psd
% [[file:figs/meas1_ry_z_psd.png]]
figure;
hold on;
plot(f11, sqrt(pxx121)./abs(squeeze(freqresp(L4C_G, f11, 'Hz'))));
plot(f12, sqrt(pxx122)./abs(squeeze(freqresp(L4C_G, f12, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$rad/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{1}.Track2_Name));
legend({'0-300', '350-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas1_ry_tilt_psd
% #+CAPTION: PSD of the Rotation of Ry Stage - measurement 1
% #+RESULTS: fig:meas1_ry_tilt_psd
% [[file:figs/meas1_ry_tilt_psd.png]]
figure;
hold on;
plot(f11, sqrt(pxx131)./abs(squeeze(freqresp(L4C_G, f11, 'Hz'))));
plot(f12, sqrt(pxx132)./abs(squeeze(freqresp(L4C_G, f12, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{1}.Track3_Name));
legend({'0-300', '350-end'}, 'Location', 'southwest');
hold off;
% Measurement 2 - Effect of Ry stage
% The tilt stage is turned ON at around 326 seconds (table [[tab:conf_meas2]]).
% #+CAPTION: Stages configuration - Measurement 2
% #+NAME: tab:conf_meas2
% | Time | 0-326 | 326-end |
% |----------+-------+---------|
% | Ty | OFF | OFF |
% | Ry | OFF | *ON* |
% | SlipRing | OFF | OFF |
% | Spindle | OFF | OFF |
% | Hexa | OFF | OFF |
% We plot the time domain (figure [[fig:meas2]]) and we don't observe anything special in the time domain.
figure;
hold on;
plot(t2(ceil(300/dt):ceil(350/dt)), meas{2}.Track1(ceil(300/dt):ceil(350/dt)));
plot(t2(ceil(300/dt):ceil(350/dt)), meas{2}.Track3(ceil(300/dt):ceil(350/dt)));
plot(t2(ceil(300/dt):ceil(350/dt)), meas{2}.Track2(ceil(300/dt):ceil(350/dt)));
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{2}.Track1_Name, meas{2}.Track2_Name, meas{2}.Track3_Name}, 'Location', 'northeast')
xlim([300, 350]);
% #+LABEL: fig:meas2
% #+CAPTION: Time domain - measurement 2
% #+RESULTS: fig:meas2
% [[file:figs/meas2.png]]
figure;
hold on;
plot(t2, cumtrapz(t2, meas{2}.Track1));
plot(t2, cumtrapz(t2, meas{2}.Track2));
plot(t2, cumtrapz(t2, meas{2}.Track3));
hold off;
xlim([300, 350]);
xlabel('Time [s]'); ylabel('Displacement [m]');
legend({meas{2}.Track1_Name, meas{2}.Track2_Name, meas{2}.Track3_Name}, 'Location', 'northeast')
% #+LABEL: fig:meas2_disp
% #+CAPTION: Time domain - measurement 2
% #+RESULTS: fig:meas2_disp
% [[file:figs/meas2_disp.png]]
% We compute the PSD of each track and we plot them (figures [[fig:meas2_ry_z_psd]], [[fig:meas2_ry_tilt_psd]] and [[fig:meas2_ty_y_psd]] ).
[pxx211, f21] = pwelch(meas{2}.Track1(1:ceil(326/dt)), psd_window, [], [], Fs);
[pxx212, f22] = pwelch(meas{2}.Track1(ceil(326/dt):end), psd_window, [], [], Fs);
[pxx221, ~] = pwelch(meas{2}.Track2(1:ceil(326/dt)), psd_window, [], [], Fs);
[pxx222, ~] = pwelch(meas{2}.Track2(ceil(326/dt):end), psd_window, [], [], Fs);
[pxx231, ~] = pwelch(meas{2}.Track3(1:ceil(326/dt)), psd_window, [], [], Fs);
[pxx232, ~] = pwelch(meas{2}.Track3(ceil(326/dt):end), psd_window, [], [], Fs);
figure;
hold on;
plot(f21, sqrt(pxx211)./abs(squeeze(freqresp(L4C_G, f21, 'Hz'))));
plot(f22, sqrt(pxx212)./abs(squeeze(freqresp(L4C_G, f22, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{2}.Track1_Name));
legend({'0-326', '326-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas2_ry_z_psd
% #+CAPTION: PSD of the Z velocity of Ry Stage - measurement 2
% #+RESULTS: fig:meas2_ry_z_psd
% [[file:figs/meas2_ry_z_psd.png]]
figure;
hold on;
plot(f21, sqrt(pxx221)./abs(squeeze(freqresp(L4C_G, f21, 'Hz'))));
plot(f22, sqrt(pxx222)./abs(squeeze(freqresp(L4C_G, f22, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$rad/s/\sqrt(Hz)$]');
title(sprintf('%s', meas{2}.Track2_Name));
legend({'0-326', '326-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas2_ry_tilt_psd
% #+CAPTION: PSD of the Rotation motion of Ry Stage - measurement 2
% #+RESULTS: fig:meas2_ry_tilt_psd
% [[file:figs/meas2_ry_tilt_psd.png]]
figure;
hold on;
plot(f21, sqrt(pxx231)./abs(squeeze(freqresp(L4C_G, f21, 'Hz'))));
plot(f22, sqrt(pxx232)./abs(squeeze(freqresp(L4C_G, f22, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{2}.Track3_Name));
legend({'0-326', '326-end'}, 'Location', 'southwest');
hold off;
% Measurement 3 - Effect of the Hexapod
% The hexapod is turned off after 406 seconds (table [[tab:conf_meas3]]).
% #+CAPTION: Stages configuration - Measurement 3
% #+NAME: tab:conf_meas3
% | Time | 0-406 | 406-end |
% |----------+-------+---------|
% | Ty | OFF | OFF |
% | Ry | *ON* | *ON* |
% | SlipRing | OFF | OFF |
% | Spindle | OFF | OFF |
% | Hexa | *ON* | OFF |
% The time domain result is shown figure [[fig:meas3]].
figure;
hold on;
plot(t3(ceil(380/dt):ceil(420/dt)), meas{3}.Track1(ceil(380/dt):ceil(420/dt)));
plot(t3(ceil(380/dt):ceil(420/dt)), meas{3}.Track2(ceil(380/dt):ceil(420/dt)));
plot(t3(ceil(380/dt):ceil(420/dt)), meas{3}.Track3(ceil(380/dt):ceil(420/dt)));
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{3}.Track1_Name, meas{3}.Track2_Name, meas{3}.Track3_Name}, 'Location', 'northeast')
% #+LABEL: fig:meas3
% #+CAPTION: Time domain - measurement 3
% #+RESULTS: fig:meas3
% [[file:figs/meas3.png]]
figure;
hold on;
plot(t3, cumtrapz(t3, meas{3}.Track1));
plot(t3, cumtrapz(t3, meas{3}.Track2));
plot(t3, cumtrapz(t3, meas{3}.Track3));
hold off;
xlim([350, 450]);
xlabel('Time [s]'); ylabel('Displacement [m]');
legend({meas{3}.Track1_Name, meas{3}.Track2_Name, meas{3}.Track3_Name}, 'Location', 'northeast')
% #+LABEL: fig:meas3_disp
% #+CAPTION: Time domain - measurement 3
% #+RESULTS: fig:meas3_disp
% [[file:figs/meas3_disp.png]]
% We then compute the PSD of each track before and after turning off the hexapod and plot the results in the figures [[fig:meas3_hexa_z_psd]], [[fig:meas3_ry_z_psd]] and [[fig:meas3_ty_y_psd]].
[pxx311, f31] = pwelch(meas{3}.Track1(1:ceil(400/dt)), psd_window, [], [], Fs);
[pxx312, f32] = pwelch(meas{3}.Track1(ceil(420/dt):end), psd_window, [], [], Fs);
[pxx321, ~] = pwelch(meas{3}.Track2(1:ceil(400/dt)), psd_window, [], [], Fs);
[pxx322, ~] = pwelch(meas{3}.Track2(ceil(420/dt):end), psd_window, [], [], Fs);
[pxx331, ~] = pwelch(meas{3}.Track3(1:ceil(400/dt)), psd_window, [], [], Fs);
[pxx332, ~] = pwelch(meas{3}.Track3(ceil(420/dt):end), psd_window, [], [], Fs);
figure;
hold on;
plot(f31, sqrt(pxx311)./abs(squeeze(freqresp(L4C_G, f31, 'Hz'))));
plot(f32, sqrt(pxx312)./abs(squeeze(freqresp(L4C_G, f32, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{3}.Track1_Name));
legend({'0-400', '420-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas3_hexa_z_psd
% #+CAPTION: PSD of the Z velocity of the Hexapod - measurement 3
% #+RESULTS: fig:meas3_hexa_z_psd
% [[file:figs/meas3_hexa_z_psd.png]]
figure;
hold on;
plot(f31, sqrt(pxx321)./abs(squeeze(freqresp(L4C_G, f31, 'Hz'))));
plot(f32, sqrt(pxx322)./abs(squeeze(freqresp(L4C_G, f32, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{3}.Track2_Name));
legend({'0-400', '420-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas3_ry_z_psd
% #+CAPTION: PSD of the Z velocity of the Ry stage - measurement 3
% #+RESULTS: fig:meas3_ry_z_psd
% [[file:figs/meas3_ry_z_psd.png]]
figure;
hold on;
plot(f31, sqrt(pxx331)./abs(squeeze(freqresp(L4C_G, f31, 'Hz'))));
plot(f32, sqrt(pxx332)./abs(squeeze(freqresp(L4C_G, f32, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{3}.Track3_Name));
legend({'0-400', '420-end'}, 'Location', 'southwest');
hold off;
% Measurement 4 - Effect of the Splip-Ring and Spindle
% The slip ring is turned on at 300s, then the spindle is turned on at 620s (table [[tab:conf_meas4]]). The time domain signals are shown figure [[fig:meas4]].
% #+CAPTION: Stages configuration - Measurement 4
% #+NAME: tab:conf_meas4
% | Time | 0-300 | 300-620 | 620-end |
% |----------+-------+---------+---------|
% | Ty | OFF | OFF | OFF |
% | Ry | OFF | OFF | OFF |
% | SlipRing | OFF | *ON* | *ON* |
% | Spindle | OFF | OFF | *ON* |
% | Hexa | OFF | OFF | OFF |
figure;
hold on;
plot(t4, meas{4}.Track1);
plot(t4, meas{4}.Track2);
plot(t4, meas{4}.Track3);
hold off;
xlim([t4(1), t4(end)]);
xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{4}.Track1_Name, meas{4}.Track2_Name, meas{4}.Track3_Name}, 'Location', 'southwest')
% #+LABEL: fig:meas4
% #+CAPTION: Time domain - measurement 4
% #+RESULTS: fig:meas4
% [[file:figs/meas4.png]]
figure;
subplot(1, 2, 1);
hold on;
plot(t4, cumtrapz(t4, meas{4}.Track1));
plot(t4, cumtrapz(t4, meas{4}.Track2));
plot(t4, cumtrapz(t4, meas{4}.Track3));
hold off;
xlim([250, 350]);
xlabel('Time [s]'); ylabel('Displacement [m]');
legend({meas{4}.Track1_Name, meas{4}.Track2_Name, meas{4}.Track3_Name}, 'Location', 'northwest')
subplot(1, 2, 2);
hold on;
plot(t4, cumtrapz(t4, meas{4}.Track1));
plot(t4, cumtrapz(t4, meas{4}.Track2));
plot(t4, cumtrapz(t4, meas{4}.Track3));
hold off;
xlim([600, 650]);
xlabel('Time [s]'); ylabel('Displacement [m]');
% #+LABEL: fig:meas4_int
% #+CAPTION: Time domain - measurement 4
% #+RESULTS: fig:meas4_int
% [[file:figs/meas4_int.png]]
% The PSD of each track are computed using the code below.
[pxx411, f41] = pwelch(meas{4}.Track1(1:ceil(280/dt)), psd_window, [], [], Fs);
[pxx412, f42] = pwelch(meas{4}.Track1(ceil(280/dt):ceil(600/dt)), psd_window, [], [], Fs);
[pxx413, f43] = pwelch(meas{4}.Track1(ceil(640/dt):end), psd_window, [], [], Fs);
[pxx421, ~] = pwelch(meas{4}.Track2(1:ceil(280/dt)), psd_window, [], [], Fs);
[pxx422, ~] = pwelch(meas{4}.Track2(ceil(280/dt):ceil(600/dt)), psd_window, [], [], Fs);
[pxx423, ~] = pwelch(meas{4}.Track2(ceil(640/dt):end), psd_window, [], [], Fs);
[pxx431, ~] = pwelch(meas{4}.Track3(1:ceil(280/dt)), psd_window, [], [], Fs);
[pxx432, ~] = pwelch(meas{4}.Track3(ceil(280/dt):ceil(600/dt)), psd_window, [], [], Fs);
[pxx433, ~] = pwelch(meas{4}.Track3(ceil(640/dt):end), psd_window, [], [], Fs);
f41 = f41(2:end);
f42 = f42(2:end);
f43 = f43(2:end);
pxx411 = pxx411(2:end);
pxx412 = pxx412(2:end);
pxx413 = pxx413(2:end);
pxx421 = pxx421(2:end);
pxx422 = pxx422(2:end);
pxx423 = pxx423(2:end);
pxx431 = pxx431(2:end);
pxx432 = pxx432(2:end);
pxx433 = pxx433(2:end);
figure;
hold on;
plot(f41, sqrt(pxx411)./abs(squeeze(freqresp(L4C_G, f41, 'Hz'))));
plot(f42, sqrt(pxx412)./abs(squeeze(freqresp(L4C_G, f42, 'Hz'))));
plot(f43, sqrt(pxx413)./abs(squeeze(freqresp(L4C_G, f43, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{4}.Track1_Name));
legend({'0-280', '320-600', '640-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas4_hexa_z_psd
% #+CAPTION: PSD of the Z velocity of the Hexapod - measurement 4
% #+RESULTS: fig:meas4_hexa_z_psd
% [[file:figs/meas4_hexa_z_psd.png]]
% We plot the PSD of the displacement.
figure;
hold on;
plot(f41, sqrt(pxx411)./abs(squeeze(freqresp(L4C_G, f41, 'Hz')))./(2*pi*f41));
plot(f42, sqrt(pxx412)./abs(squeeze(freqresp(L4C_G, f42, 'Hz')))./(2*pi*f42));
plot(f43, sqrt(pxx413)./abs(squeeze(freqresp(L4C_G, f43, 'Hz')))./(2*pi*f43));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/\sqrt{Hz}$]');
title(sprintf('%s', meas{4}.Track1_Name));
legend({'0-280', '320-600', '640-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas4_hexa_z_psd_int
% #+CAPTION: PSD_INT of the Z velocity of the Hexapod - measurement 4
% #+RESULTS: fig:meas4_hexa_z_psd_int
% [[file:figs/meas4_hexa_z_psd_int.png]]
% And we compute the Cumulative amplitude spectrum.
figure;
hold on;
plot(f41, sqrt(cumsum(pxx431./abs(squeeze(freqresp(L4C_G, f41, 'Hz'))).^2./(2*pi*f41).*(f41 - [0; f41(1:end-1)]))));
plot(f42, sqrt(cumsum(pxx432./abs(squeeze(freqresp(L4C_G, f42, 'Hz'))).^2./(2*pi*f42).*(f42 - [0; f42(1:end-1)]))));
plot(f43, sqrt(cumsum(pxx433./abs(squeeze(freqresp(L4C_G, f43, 'Hz'))).^2./(2*pi*f43).*(f43 - [0; f43(1:end-1)]))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CAS [$m$ rms]');
title(sprintf('%s', meas{4}.Track1_Name));
legend({'0-280', '320-600', '640-end'}, 'Location', 'southwest');
hold off;
figure;
hold on;
plot(f41, sqrt(pxx421)./abs(squeeze(freqresp(L4C_G, f41, 'Hz'))));
plot(f42, sqrt(pxx422)./abs(squeeze(freqresp(L4C_G, f42, 'Hz'))));
plot(f43, sqrt(pxx423)./abs(squeeze(freqresp(L4C_G, f43, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{4}.Track2_Name));
legend({'0-280', '320-600', '640-end'}, 'Location', 'southwest');
hold off;
% #+LABEL: fig:meas4_ry_z_psd
% #+CAPTION: PSD of the Ry rotation in the Y direction - measurement 4
% #+RESULTS: fig:meas4_ry_z_psd
% [[file:figs/meas4_ry_z_psd.png]]
figure;
hold on;
plot(f41, sqrt(pxx431)./abs(squeeze(freqresp(L4C_G, f41, 'Hz'))));
plot(f42, sqrt(pxx432)./abs(squeeze(freqresp(L4C_G, f42, 'Hz'))));
plot(f43, sqrt(pxx433)./abs(squeeze(freqresp(L4C_G, f43, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
title(sprintf('%s', meas{4}.Track3_Name));
legend({'0-280', '320-600', '640-end'}, 'Location', 'southwest');
hold off;
% Measurement 5 - Transmission from ground to marble
% This measurement just consists of measurement of Y-Z motion of the ground and the marble.
% The time domain signals are shown on figure [[fig:meas5]].
figure;
hold on;
plot(t5, meas{5}.Track1);
plot(t5, meas{5}.Track2);
plot(t5, meas{5}.Track3);
plot(t5, meas{5}.Track4);
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{5}.Track1_Name, meas{5}.Track2_Name, meas{5}.Track3_Name, meas{5}.Track4_Name}, 'Location', 'northeast')
% #+LABEL: fig:meas5
% #+CAPTION: Time domain - measurement 5
% #+RESULTS: fig:meas5
% [[file:figs/meas5.png]]
% We compute the PSD of each track and we plot the PSD of the Z motion for the ground and marble on figure [[fig:meas5_z_psd]] and for the Y motion on figure [[fig:meas5_y_psd]].
[pxx51, f51] = pwelch(meas{5}.Track1(:), psd_window, [], [], Fs);
[pxx52, f52] = pwelch(meas{5}.Track2(:), psd_window, [], [], Fs);
[pxx53, f53] = pwelch(meas{5}.Track3(:), psd_window, [], [], Fs);
[pxx54, f54] = pwelch(meas{5}.Track4(:), psd_window, [], [], Fs);
figure;
hold on;
plot(f51, sqrt(pxx51)./abs(squeeze(freqresp(L4C_G, f51, 'Hz'))));
plot(f52, sqrt(pxx52)./abs(squeeze(freqresp(L4C_G, f52, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
legend({meas{5}.Track1_Name, meas{5}.Track2_Name}, 'Location', 'northwest');
hold off;
% #+LABEL: fig:meas5_z_psd
% #+CAPTION: PSD of the ground and marble in the Z direction
% #+RESULTS: fig:meas5_z_psd
% [[file:figs/meas5_z_psd.png]]
figure;
hold on;
plot(f53, sqrt(pxx53)./abs(squeeze(freqresp(L4C_G, f53, 'Hz'))));
plot(f54, sqrt(pxx54)./abs(squeeze(freqresp(L4C_G, f54, 'Hz'))));
xlim([fmin, fmax]);
xticks([1, 10, 100]);
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
legend({meas{5}.Track3_Name, meas{5}.Track4_Name}, 'Location', 'northwest');
hold off;
% #+LABEL: fig:meas5_y_psd
% #+CAPTION: PSD of the ground and marble in the Y direction
% #+RESULTS: fig:meas5_y_psd
% [[file:figs/meas5_y_psd.png]]
% 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 [[fig:meas5_tf]] and the coherence on figure [[fig:meas5_coh]].
[tfz, fz] = tfestimate(meas{5}.Track1(:), meas{5}.Track2(:), psd_window, [], [], Fs);
[tfy, fy] = tfestimate(meas{5}.Track3(:), meas{5}.Track4(:), psd_window, [], [], Fs);
figure;
ax1 = subplot(2,1,1);
hold on;
plot(fz, abs(tfz));
plot(fy, abs(tfy));
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');
hold off;
ax2 = subplot(2,1,2);
hold on;
plot(fz, 180/pi*angle(tfz));
plot(fy, 180/pi*angle(tfy));
set(gca,'xscale','log');
yticks(-180:90:180);
ylim([-180 180]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
linkaxes([ax1,ax2],'x');
xlim([fmin, fmax]);
legend({'Z direction', 'Y direction'}, 'Location', 'southwest')
% #+LABEL: fig:meas5_tf
% #+CAPTION: Transfer function estimation - measurement 5
% #+RESULTS: fig:meas5_tf
% [[file:figs/meas5_tf.png]]
[cohz, fz] = mscohere(meas{5}.Track1(:), meas{5}.Track2(:), psd_window, [], [], Fs);
[cohy, fy] = mscohere(meas{5}.Track3(:), meas{5}.Track4(:), psd_window, [], [], Fs);
figure;
hold on;
plot(fz, cohz);
plot(fy, cohy);
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
ylabel('Coherence');
xlabel('Frequency [Hz]');
xlim([fmin, fmax]);
legend({'Z direction', 'Y direction'}, 'Location', 'southwest')