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Integration of geophone to have the displacement

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Thomas Dehaeze 2019-04-02 10:39:37 +02:00
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<title>Measurement Analysis</title> <title>Measurement Analysis</title>
@ -245,28 +245,6 @@ for the JavaScript code in this tag.
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@ -275,17 +253,17 @@ for the JavaScript code in this tag.
<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="#orgc1db046">1. Measurement Description</a></li> <li><a href="#orga57c824">1. Measurement Description</a></li>
<li><a href="#org9b5288f">2. Importation of the data</a></li> <li><a href="#orgac83bb1">2. Importation of the data</a></li>
<li><a href="#org0c9206e">3. Variables for analysis</a></li> <li><a href="#orge44c773">3. Variables for analysis</a></li>
<li><a href="#org876fa12">4. Coherence between the two vertical geophones on the Tilt Stage</a></li> <li><a href="#orgcb0a2db">4. Coherence between the two vertical geophones on the Tilt Stage</a></li>
<li><a href="#org0e81d2f">5. Data Post Processing</a></li> <li><a href="#orgc619b39">5. Data Post Processing</a></li>
<li><a href="#org07adbbe">6. Normalization</a></li> <li><a href="#org03ef418">6. Normalization</a></li>
<li><a href="#org854c7bf">7. Measurement 1 - Effect of Ty stage</a></li> <li><a href="#org8583637">7. Measurement 1 - Effect of Ty stage</a></li>
<li><a href="#orga8c4982">8. Measurement 2 - Effect of Ry stage</a></li> <li><a href="#org47192a7">8. Measurement 2 - Effect of Ry stage</a></li>
<li><a href="#orga79f5f4">9. Measurement 3 - Effect of the Hexapod</a></li> <li><a href="#org0c3a1d4">9. Measurement 3 - Effect of the Hexapod</a></li>
<li><a href="#org8731abc">10. Measurement 4 - Effect of the Splip-Ring and Spindle</a></li> <li><a href="#org1529580">10. Measurement 4 - Effect of the Splip-Ring and Spindle</a></li>
<li><a href="#org33dc0ed">11. Measurement 5 - Transmission from ground to marble</a></li> <li><a href="#orga767d61">11. Measurement 5 - Transmission from ground to marble</a></li>
</ul> </ul>
</div> </div>
</div> </div>
@ -294,11 +272,11 @@ for the JavaScript code in this tag.
<a href="../index.html">Back to main page</a>. <a href="../index.html">Back to main page</a>.
</p> </p>
<div id="outline-container-orgc1db046" class="outline-2"> <div id="outline-container-orga57c824" class="outline-2">
<h2 id="orgc1db046"><span class="section-number-2">1</span> Measurement Description</h2> <h2 id="orga57c824"><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="org25ddba6" class="figure"> <div id="orgc56bc67" class="figure">
<p><img src="./figs/setup_picture.png" alt="setup_picture.png" /> <p><img src="./figs/setup_picture.png" alt="setup_picture.png" />
</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>
@ -318,19 +296,19 @@ 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-org9b5288f" class="outline-2"> <div id="outline-container-orgac83bb1" class="outline-2">
<h2 id="org9b5288f"><span class="section-number-2">2</span> Importation of the data</h2> <h2 id="orgac83bb1"><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:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">meas = <span style="color: #DCDCCC;">{}</span>; <pre class="src src-matlab">meas = <span class="org-rainbow-delimiters-depth-1">{}</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</span> = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/Measurement1.mat'</span><span style="color: #DCDCCC;">)</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span> = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/Measurement1.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span> = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/Measurement2.mat'</span><span style="color: #DCDCCC;">)</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span> = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/Measurement2.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">}</span> = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/Measurement3.mat'</span><span style="color: #DCDCCC;">)</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span> = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/Measurement3.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">}</span> = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/Measurement4.mat'</span><span style="color: #DCDCCC;">)</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span> = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/Measurement4.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #DCDCCC;">}</span> = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./mat/Measurement5.mat'</span><span style="color: #DCDCCC;">)</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span> = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/Measurement5.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
@ -338,16 +316,16 @@ meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">5</span>
Change the track name for measurements 3 and 4. Change the track name for measurements 3 and 4.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">}</span>.Track1_Name = 'Input <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span> Hexa Z'; <pre class="src src-matlab">meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_Name = 'Input <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span> Hexa Z';
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">}</span>.Track1_Name = 'Input <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span> Hexa Z'; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_Name = 'Input <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span> Hexa Z';
</pre> </pre>
</div> </div>
<p> <p>
For the measurements 1 to 4, the measurement channels are shown table <a href="#orgde7c9fb">1</a>. For the measurements 1 to 4, the measurement channels are shown table <a href="#org7e4418b">1</a>.
</p> </p>
<table id="orgde7c9fb" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org7e4418b" 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>
@ -400,9 +378,9 @@ 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="#orgb2a1d3a">2</a>. For the measurement 5, the channels are shown table <a href="#org00892de">2</a>.
</p> </p>
<table id="orgb2a1d3a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org00892de" 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>
@ -438,21 +416,21 @@ For the measurement 5, the channels are shown table <a href="#orgb2a1d3a">2</a>.
</div> </div>
</div> </div>
<div id="outline-container-org0c9206e" class="outline-2"> <div id="outline-container-orge44c773" class="outline-2">
<h2 id="org0c9206e"><span class="section-number-2">3</span> Variables for analysis</h2> <h2 id="orge44c773"><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.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Fs = <span style="color: #BFEBBF;">256</span>; <span style="color: #7F9F7F;">% [Hz]</span> <pre class="src src-matlab">Fs = <span class="org-highlight-numbers-number">256</span>; <span class="org-comment">% [Hz]</span>
dt = <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">/</span><span style="color: #DCDCCC;">(</span>Fs<span style="color: #DCDCCC;">)</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 style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span><span style="color: #7CB8BB;">:</span>length<span style="color: #BFEBBF;">(</span>meas<span style="color: #D0BF8F;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">}</span>.Track1<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">]</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 style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span><span style="color: #7CB8BB;">:</span>length<span style="color: #BFEBBF;">(</span>meas<span style="color: #D0BF8F;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #D0BF8F;">}</span>.Track1<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">]</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 style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span><span style="color: #7CB8BB;">:</span>length<span style="color: #BFEBBF;">(</span>meas<span style="color: #D0BF8F;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #D0BF8F;">}</span>.Track1<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">]</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 style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span><span style="color: #7CB8BB;">:</span>length<span style="color: #BFEBBF;">(</span>meas<span style="color: #D0BF8F;">{</span><span style="color: #BFEBBF;">4</span><span style="color: #D0BF8F;">}</span>.Track1<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">]</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 style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</span><span style="color: #BFEBBF;">0</span><span style="color: #7CB8BB;">:</span>length<span style="color: #BFEBBF;">(</span>meas<span style="color: #D0BF8F;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #D0BF8F;">}</span>.Track1<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">]</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>
@ -460,8 +438,8 @@ t5 = dt<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</s
For the frequency analysis, we define the frequency limits for the plot. For the frequency analysis, we define the frequency limits for the plot.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">fmin = <span style="color: #BFEBBF;">1</span>; <span style="color: #7F9F7F;">% [Hz]</span> <pre class="src src-matlab">fmin = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% [Hz]</span>
fmax = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">% [Hz]</span> fmax = <span class="org-highlight-numbers-number">100</span>; <span class="org-comment">% [Hz]</span>
</pre> </pre>
</div> </div>
@ -469,40 +447,40 @@ fmax = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">%
Then we define the windows that will be used to average the results. Then we define the windows that will be used to average the results.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">psd_window = hanning<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>fmin<span style="color: #7CB8BB;">/</span>dt<span style="color: #DCDCCC;">)</span>; <pre class="src src-matlab">psd_window = hanning<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>fmin<span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org876fa12" class="outline-2"> <div id="outline-container-orgcb0a2db" class="outline-2">
<h2 id="org876fa12"><span class="section-number-2">4</span> Coherence between the two vertical geophones on the Tilt Stage</h2> <h2 id="orgcb0a2db"><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="#org6414ae2">2</a>. 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>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>coh, f<span style="color: #DCDCCC;">]</span> = mscohere<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</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>;
</pre> </pre>
</div> </div>
<div id="org6414ae2" class="figure"> <div id="org3d4d6fd" 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="#org0f2e1db">3</a>). We then compute the transfer function from one sensor to the other (figure <a href="#org62100a4">3</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>tf23, f<span style="color: #DCDCCC;">]</span> = tfestimate<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</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>;
</pre> </pre>
</div> </div>
<div id="org0f2e1db" class="figure"> <div id="org62100a4" 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>
@ -514,43 +492,43 @@ Even though the coherence is not very good, we observe no resonance between the
</div> </div>
</div> </div>
<div id="outline-container-org0e81d2f" class="outline-2"> <div id="outline-container-orgc619b39" class="outline-2">
<h2 id="org0e81d2f"><span class="section-number-2">5</span> Data Post Processing</h2> <h2 id="orgc619b39"><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:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">meas1_z = <span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #7CB8BB;">+</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span>; <pre class="src src-matlab">meas1_z = <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-type">+</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-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
meas1_tilt = <span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #7CB8BB;">-</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span>; meas1_tilt = <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-type">-</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-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</span>.Track1 = meas1_z; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1 = meas1_z;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</span>.Track1_Y_Magnitude = <span style="color: #CC9393;">'Meter / second'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_Y_Magnitude = <span class="org-string">'Meter / second'</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</span>.Track1_Name = <span style="color: #CC9393;">'Ry Z'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_Name = <span class="org-string">'Ry Z'</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</span>.Track2 = meas1_tilt; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2 = meas1_tilt;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</span>.Track2_Y_Magnitude = <span style="color: #CC9393;">'Rad / second'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_Y_Magnitude = <span class="org-string">'Rad / second'</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</span>.Track2_Name = <span style="color: #CC9393;">'Ry Tilt'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_Name = <span class="org-string">'Ry Tilt'</span>;
meas2_z = <span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #7CB8BB;">+</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span>; meas2_z = <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-type">+</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>.Track2<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
meas2_tilt = <span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #7CB8BB;">-</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">2</span>; meas2_tilt = <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-type">-</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>.Track2<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span>.Track1 = meas2_z; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1 = meas2_z;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span>.Track1_Y_Magnitude = <span style="color: #CC9393;">'Meter / second'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_Y_Magnitude = <span class="org-string">'Meter / second'</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span>.Track1_Name = <span style="color: #CC9393;">'Ry Z'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_Name = <span class="org-string">'Ry Z'</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span>.Track2 = meas2_tilt; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2 = meas2_tilt;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span>.Track2_Y_Magnitude = <span style="color: #CC9393;">'Rad / second'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_Y_Magnitude = <span class="org-string">'Rad / second'</span>;
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span>.Track2_Name = <span style="color: #CC9393;">'Ry Tilt'</span>; meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_Name = <span class="org-string">'Ry Tilt'</span>;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org07adbbe" class="outline-2"> <div id="outline-container-org03ef418" class="outline-2">
<h2 id="org07adbbe"><span class="section-number-2">6</span> Normalization</h2> <h2 id="org03ef418"><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="#org56c2445">4</a>. The transfer function from geophone velocity to measured voltage is shown on figure <a href="#org47ba141">4</a>.
</p> </p>
<p> <p>
@ -558,34 +536,78 @@ Measurements will be normalized by the inverse of this transfer function in orde
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">L4C_w0 = <span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span>; <span style="color: #7F9F7F;">% [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 style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">28</span>; L4C_ksi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">28</span>;
L4C_G0 = <span style="color: #BFEBBF;">276</span>.<span style="color: #BFEBBF;">8</span>; <span style="color: #7F9F7F;">% [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>
L4C_G = L4C_G0<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">(</span>s<span style="color: #7CB8BB;">/</span>L4C_w0<span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">/</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">(</span>s<span style="color: #7CB8BB;">/</span>L4C_w0<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span> <span style="color: #7CB8BB;">+</span> <span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>L4C_ksi<span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">(</span>s<span style="color: #7CB8BB;">/</span>L4C_w0<span style="color: #BFEBBF;">)</span> <span style="color: #7CB8BB;">+</span> <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>; 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="org56c2445" class="figure"> <div id="org47ba141" 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>
</div> </div>
<p> <div class="org-src-container">
Time domain data are just normalized using the sensibility of the sensor (\(276.8 V/m/s\)). <pre class="src src-matlab">meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1 = <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-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
</p> meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2 = <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>.Track2<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3 = <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>.Track3<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1 = <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-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2 = <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>.Track2<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3 = <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>.Track3<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1 = <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-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2 = <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>.Track2<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3 = <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>.Track3<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1 = <span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2 = <span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3 = <span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1 = <span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2 = <span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3 = <span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track4 = <span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track4<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span><span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab">meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<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>.Track1, t1<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<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, t1<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<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>.Track3, t1<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</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, t2<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</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>.Track2, t2<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</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>.Track3, t2<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</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, t3<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</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>.Track2, t3<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</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>.Track3, t3<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1, t4<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2, t4<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3, t4<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track1_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1, t5<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track2_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2, t5<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track3_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3, t5<span class="org-rainbow-delimiters-depth-1">)</span>;
meas<span class="org-rainbow-delimiters-depth-1">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-1">}</span>.Track4_norm = lsim<span class="org-rainbow-delimiters-depth-1">(</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>L4C_G<span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track4, t5<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div> </div>
</div> </div>
<div id="outline-container-org854c7bf" class="outline-2"> <div id="outline-container-org8583637" class="outline-2">
<h2 id="org854c7bf"><span class="section-number-2">7</span> Measurement 1 - Effect of Ty stage</h2> <h2 id="org8583637"><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="#org7881134">3</a>. The configuration for this measurement is shown table <a href="#orgc1f3234">3</a>.
</p> </p>
<table id="org7881134" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgc1f3234" 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>
@ -636,7 +658,7 @@ The configuration for this measurement is shown table <a href="#org7881134">3</a
</table> </table>
<p> <p>
We then plot the measurements in time domain (figure <a href="#org7592c33">5</a>). We then plot the measurements in time domain (figure <a href="#orgf931943">5</a>).
</p> </p>
<div class="important"> <div class="important">
@ -648,7 +670,7 @@ How can we explain that?
</div> </div>
<div id="org7592c33" class="figure"> <div id="orgf931943" 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>
@ -657,17 +679,12 @@ How can we explain that?
<p> <p>
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 <code>cumtrapz</code> function. 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 <code>cumtrapz</code> function.
</p> </p>
<div class="org-src-container">
<pre class="src src-matlab">tdisp = t1<span style="color: #DCDCCC;">(</span>ceil<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">300</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">340</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
xdisp = cumtrapz<span style="color: #DCDCCC;">(</span>tdisp, <span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">276</span>.<span style="color: #BFEBBF;">8</span><span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">.*</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">300</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">340</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p> <p>
Then we plot the position with respect to time (figure <a href="#orgf6e2558">6</a>). Then we plot the position with respect to time (figure <a href="#orgb6bceab">6</a>).
</p> </p>
<div id="orgf6e2558" class="figure"> <div id="orgb6bceab" 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>
@ -677,37 +694,37 @@ Then we plot the position with respect to time (figure <a href="#orgf6e2558">6</
We when compute the power spectral density of each measurement before and after turning on the stage. We when compute the power spectral density of each measurement before and after turning on the stage.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>pxx111, f11<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">300</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx111, f11<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">1</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">300</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>;
<span style="color: #DCDCCC;">[</span>pxx112, f12<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">350</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx112, f12<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">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">350</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">:</span>end<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>;
<span style="color: #DCDCCC;">[</span>pxx121, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">300</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx121, <span class="org-type">~</span><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">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<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">300</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>;
<span style="color: #DCDCCC;">[</span>pxx122, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">350</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx122, <span class="org-type">~</span><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">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">350</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">:</span>end<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>;
<span style="color: #DCDCCC;">[</span>pxx131, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">300</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx131, <span class="org-type">~</span><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">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3<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">300</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>;
<span style="color: #DCDCCC;">[</span>pxx132, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">350</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx132, <span class="org-type">~</span><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">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">350</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">:</span>end<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> </pre>
</div> </div>
<p> <p>
We finally plot the power spectral density of each track (figures <a href="#org2b52faf">7</a>, <a href="#org3106809">8</a>, <a href="#org28f9d2d">9</a>). 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>).
</p> </p>
<div id="org2b52faf" class="figure"> <div id="org767e453" 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="org3106809" class="figure"> <div id="org8cd1899" 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="org28f9d2d" class="figure"> <div id="org3030170" 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>
@ -731,14 +748,14 @@ It does not seems to have any effect on the Z motion of the tilt stage.
</div> </div>
</div> </div>
<div id="outline-container-orga8c4982" class="outline-2"> <div id="outline-container-org47192a7" class="outline-2">
<h2 id="orga8c4982"><span class="section-number-2">8</span> Measurement 2 - Effect of Ry stage</h2> <h2 id="org47192a7"><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="#org6ee7543">4</a>). The tilt stage is turned ON at around 326 seconds (table <a href="#orgba0882e">4</a>).
</p> </p>
<table id="org6ee7543" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgba0882e" 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>
@ -789,50 +806,57 @@ The tilt stage is turned ON at around 326 seconds (table <a href="#org6ee7543">4
</table> </table>
<p> <p>
We plot the time domain (figure <a href="#org17e1967">10</a>) and we don't observe anything special in the time domain. We plot the time domain (figure <a href="#org9bf6e90">10</a>) and we don't observe anything special in the time domain.
</p> </p>
<div id="org17e1967" class="figure"> <div id="org9bf6e90" 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">
<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> <p>
We compute the PSD of each track and we plot them (figures <a href="#org5ee261f">11</a>, <a href="#org7cc110d">12</a> and <a href="#org04b24ea">13</a> ). 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> ).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>pxx211, f21<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">326</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</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>;
<span style="color: #DCDCCC;">[</span>pxx212, f22<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">326</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx212, f22<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>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-type">:</span>end<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>;
<span style="color: #DCDCCC;">[</span>pxx221, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">326</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx221, <span class="org-type">~</span><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>.Track2<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>;
<span style="color: #DCDCCC;">[</span>pxx222, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">326</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx222, <span class="org-type">~</span><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>.Track2<span class="org-rainbow-delimiters-depth-2">(</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-type">:</span>end<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>;
<span style="color: #DCDCCC;">[</span>pxx231, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">326</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx231, <span class="org-type">~</span><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>.Track3<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>;
<span style="color: #DCDCCC;">[</span>pxx232, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">326</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx232, <span class="org-type">~</span><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>.Track3<span class="org-rainbow-delimiters-depth-2">(</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-type">:</span>end<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> </pre>
</div> </div>
<div id="org5ee261f" class="figure"> <div id="org23fbfb4" 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 11: </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="org7cc110d" class="figure"> <div id="org7a18c86" 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 12: </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="org04b24ea" class="figure"> <div id="orgdcf33e8" 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 13: </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>
</div> </div>
<div class="important"> <div class="important">
@ -844,14 +868,14 @@ We observe no noticeable difference when the Tilt-stage is turned ON expect a sm
</div> </div>
</div> </div>
<div id="outline-container-orga79f5f4" class="outline-2"> <div id="outline-container-org0c3a1d4" class="outline-2">
<h2 id="orga79f5f4"><span class="section-number-2">9</span> Measurement 3 - Effect of the Hexapod</h2> <h2 id="org0c3a1d4"><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="#org3542637">5</a>). The hexapod is turned off after 406 seconds (table <a href="#org8b4187d">5</a>).
</p> </p>
<table id="org3542637" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org8b4187d" 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>
@ -902,55 +926,62 @@ The hexapod is turned off after 406 seconds (table <a href="#org3542637">5</a>).
</table> </table>
<p> <p>
The time domain result is shown figure <a href="#orgcdae346">14</a>. The time domain result is shown figure <a href="#org08fc17d">15</a>.
</p> </p>
<div id="orgcdae346" class="figure"> <div id="org08fc17d" 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 14: </span>Time domain - measurement 3</p> <p><span class="figure-number">Figure 15: </span>Time domain - measurement 3</p>
</div>
<div id="org4ae7ca4" 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> </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="#org862aff7">15</a>, <a href="#org62414c0">16</a> and <a href="#orgc015c93">17</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="#org0c4287e">17</a>, <a href="#org899151a">18</a> and <a href="#org0fc8e31">19</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>pxx311, f31<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">400</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</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>;
<span style="color: #DCDCCC;">[</span>pxx312, f32<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">420</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx312, f32<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>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">420</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">:</span>end<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>;
<span style="color: #DCDCCC;">[</span>pxx321, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">400</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx321, <span class="org-type">~</span><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>.Track2<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>;
<span style="color: #DCDCCC;">[</span>pxx322, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">420</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx322, <span class="org-type">~</span><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>.Track2<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">420</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">:</span>end<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>;
<span style="color: #DCDCCC;">[</span>pxx331, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">:</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">400</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx331, <span class="org-type">~</span><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>.Track3<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>;
<span style="color: #DCDCCC;">[</span>pxx332, <span style="color: #7CB8BB;">~</span><span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span><span style="color: #BFEBBF;">420</span><span style="color: #7CB8BB;">/</span>dt<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">:</span>end<span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx332, <span class="org-type">~</span><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>.Track3<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">420</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">:</span>end<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> </pre>
</div> </div>
<div id="org862aff7" class="figure"> <div id="org0c4287e" 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 15: </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="org62414c0" class="figure"> <div id="org899151a" 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 16: </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="orgc015c93" class="figure"> <div id="org0fc8e31" 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 17: </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>
</div> </div>
<div class="important"> <div class="important">
<p> <p>
Turning ON induces some motion on the hexapod in the z direction (figure <a href="#org862aff7">15</a>), on the tilt stage in the z direction (figure <a href="#org62414c0">16</a>) and on the y motion of the Ty stage (figure <a href="#orgc015c93">17</a>): 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>):
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>at 17Hz</li> <li>at 17Hz</li>
@ -961,14 +992,14 @@ Turning ON induces some motion on the hexapod in the z direction (figure <a href
</div> </div>
</div> </div>
<div id="outline-container-org8731abc" class="outline-2"> <div id="outline-container-org1529580" class="outline-2">
<h2 id="org8731abc"><span class="section-number-2">10</span> Measurement 4 - Effect of the Splip-Ring and Spindle</h2> <h2 id="org1529580"><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="#orgb7f824f">6</a>). The time domain signals are shown figure <a href="#orgcdcd20d">18</a>. 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>.
</p> </p>
<table id="orgb7f824f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org274f078" 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>
@ -1027,42 +1058,66 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
</table> </table>
<div id="orgcdcd20d" class="figure"> <div id="orgf0966f9" 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 18: </span>Time domain - measurement 4</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>.
</p>
<div id="org62b5bdf" 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>
</div> </div>
<p> <p>
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="orgf66254d" class="figure"> <div id="orgfd7f8ce" 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 19: </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>
</div> </div>
<p>
We plot the PSD of the displacement.
</p>
<div id="org5ec6b1b" class="figure"> <div id="org917dbdc" 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>
</div>
<p>
And we compute the Cumulative amplitude spectrum.
</p>
<div id="orge4b6d59" 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 20: </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>
</div> </div>
<div id="orgd33d363" class="figure"> <div id="org08ad3dc" 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 21: </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>
</div> </div>
<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="#orgd33d363">21</a>): does that make any sense? It even seems to lower the motion of the Ty stage (figure <a href="#org08ad3dc">25</a>): does that make any sense?
</p> </p>
<p> <p>
@ -1078,79 +1133,79 @@ Turning ON the spindle induces motions:
</div> </div>
</div> </div>
<div id="outline-container-org33dc0ed" class="outline-2"> <div id="outline-container-orga767d61" class="outline-2">
<h2 id="org33dc0ed"><span class="section-number-2">11</span> Measurement 5 - Transmission from ground to marble</h2> <h2 id="orga767d61"><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="#orgc71b335">22</a>. The time domain signals are shown on figure <a href="#orgc513617">26</a>.
</p> </p>
<div id="orgc71b335" class="figure"> <div id="orgc513617" 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 22: </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="#org69a4967">23</a> and for the Y motion on figure <a href="#orgf96e7c0">24</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="#org28b0b94">27</a> and for the Y motion on figure <a href="#orgf797eae">28</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>pxx51, f51<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx51, f51<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">5</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>, 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>;
<span style="color: #DCDCCC;">[</span>pxx52, f52<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx52, f52<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">5</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>;
<span style="color: #DCDCCC;">[</span>pxx53, f53<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx53, f53<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">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3<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>;
<span style="color: #DCDCCC;">[</span>pxx54, f54<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track4<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>pxx54, f54<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">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track4<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> </pre>
</div> </div>
<div id="org69a4967" class="figure"> <div id="org28b0b94" 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 23: </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="orgf96e7c0" class="figure"> <div id="orgf797eae" 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 24: </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>
</div> </div>
<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="#orgd1bec89">25</a> and the coherence on figure <a href="#org4f5ea21">26</a>. The transfer functions are shown on figure <a href="#orgbb283a9">29</a> and the coherence on figure <a href="#orga357e58">30</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>tfz, fz<span style="color: #DCDCCC;">]</span> = tfestimate<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>tfz, fz<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">5</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">5</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>;
<span style="color: #DCDCCC;">[</span>tfy, fy<span style="color: #DCDCCC;">]</span> = tfestimate<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track4<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>tfy, fy<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">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3<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">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track4<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> </pre>
</div> </div>
<div id="orgd1bec89" class="figure"> <div id="orgbb283a9" 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 25: </span>Transfer function estimation - measurement 5</p> <p><span class="figure-number">Figure 29: </span>Transfer function estimation - measurement 5</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>cohz, fz<span style="color: #DCDCCC;">]</span> = mscohere<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track1<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track2<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>cohz, fz<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">5</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">5</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>;
<span style="color: #DCDCCC;">[</span>cohy, fy<span style="color: #DCDCCC;">]</span> = mscohere<span style="color: #DCDCCC;">(</span>meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track3<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, meas<span style="color: #BFEBBF;">{</span><span style="color: #BFEBBF;">5</span><span style="color: #BFEBBF;">}</span>.Track4<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span><span style="color: #BFEBBF;">)</span>, psd_window, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>; <span class="org-rainbow-delimiters-depth-1">[</span>cohy, fy<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">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track3<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">5</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track4<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> </pre>
</div> </div>
<div id="org4f5ea21" class="figure"> <div id="orga357e58" 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 26: </span>Coherence - measurement 5</p> <p><span class="figure-number">Figure 30: </span>Coherence - measurement 5</p>
</div> </div>
<div class="important"> <div class="important">
@ -1165,7 +1220,7 @@ But the coherence is not good above 20Hz, so it is difficult to estimate resonan
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-03-19 mar. 16:42</p> <p class="date">Created: 2019-04-02 mar. 10:39</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>

228
2018-10-15 - Marc/index.org
View File

@ -242,7 +242,51 @@ Measurements will be normalized by the inverse of this transfer function in orde
#+RESULTS: fig:L4C_bode_plot #+RESULTS: fig:L4C_bode_plot
[[file:figs/L4C_bode_plot.png]] [[file:figs/L4C_bode_plot.png]]
Time domain data are just normalized using the sensibility of the sensor ($276.8 V/m/s$). #+begin_src matlab :results none :exports code
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;
#+end_src
#+begin_src matlab :results none
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);
#+end_src
* Measurement 1 - Effect of Ty stage * Measurement 1 - Effect of Ty stage
The configuration for this measurement is shown table [[tab:conf_meas1]]. The configuration for this measurement is shown table [[tab:conf_meas1]].
@ -267,9 +311,9 @@ We then plot the measurements in time domain (figure [[fig:meas1]]).
#+begin_src matlab :exports none :results silent #+begin_src matlab :exports none :results silent
figure; figure;
hold on; hold on;
plot(t1(ceil(300/dt):ceil(340/dt)), (1/276.8).*meas{1}.Track1(ceil(300/dt):ceil(340/dt))); 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)), (1/276.8).*meas{1}.Track2(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)), (1/276.8).*meas{1}.Track3(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; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{1}.Track1_Name, meas{1}.Track2_Name, meas{1}.Track3_Name}, 'Location', 'northeast') legend({meas{1}.Track1_Name, meas{1}.Track2_Name, meas{1}.Track3_Name}, 'Location', 'northeast')
@ -287,17 +331,14 @@ We then plot the measurements in time domain (figure [[fig:meas1]]).
[[file:figs/meas1.png]] [[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. 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.
#+begin_src matlab :exports code :results silent
tdisp = t1(ceil(300/dt):ceil(340/dt));
xdisp = cumtrapz(tdisp, (1/276.8).*meas{1}.Track3(ceil(300/dt):ceil(340/dt)));
#+end_src
Then we plot the position with respect to time (figure [[fig:meas1_disp]]). Then we plot the position with respect to time (figure [[fig:meas1_disp]]).
#+begin_src matlab :exports none :results silent #+begin_src matlab :exports none :results silent
figure; figure;
hold on; hold on;
plot(tdisp, xdisp); plot(t1, cumtrapz(t1, meas{1}.Track3));
hold off; hold off;
xlim([300, 340]);
xlabel('Time [s]'); ylabel('Displacement [m]'); xlabel('Time [s]'); ylabel('Displacement [m]');
#+end_src #+end_src
@ -428,9 +469,9 @@ We plot the time domain (figure [[fig:meas2]]) and we don't observe anything spe
#+begin_src matlab :exports results :results silent #+begin_src matlab :exports results :results silent
figure; figure;
hold on; hold on;
plot(t2(ceil(300/dt):ceil(350/dt)), (1/276.8).*meas{2}.Track1(ceil(300/dt):ceil(350/dt))); 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)), (1/276.8).*meas{2}.Track3(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)), (1/276.8).*meas{2}.Track2(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; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{2}.Track1_Name, meas{2}.Track2_Name, meas{2}.Track3_Name}, 'Location', 'northeast') legend({meas{2}.Track1_Name, meas{2}.Track2_Name, meas{2}.Track3_Name}, 'Location', 'northeast')
@ -448,6 +489,29 @@ We plot the time domain (figure [[fig:meas2]]) and we don't observe anything spe
#+RESULTS: fig:meas2 #+RESULTS: fig:meas2
[[file:figs/meas2.png]] [[file:figs/meas2.png]]
#+begin_src matlab :exports none :results silent
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')
#+end_src
#+NAME: fig:meas2_disp
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/meas2_disp.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+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]] ). 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]] ).
#+begin_src matlab :exports code :results silent #+begin_src matlab :exports code :results silent
[pxx211, f21] = pwelch(meas{2}.Track1(1:ceil(326/dt)), psd_window, [], [], Fs); [pxx211, f21] = pwelch(meas{2}.Track1(1:ceil(326/dt)), psd_window, [], [], Fs);
@ -557,9 +621,9 @@ The time domain result is shown figure [[fig:meas3]].
#+begin_src matlab :exports results :results silent #+begin_src matlab :exports results :results silent
figure; figure;
hold on; hold on;
plot(t3(ceil(380/dt):ceil(420/dt)), (1/276.8).*meas{3}.Track1(ceil(380/dt):ceil(420/dt))); 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)), (1/276.8).*meas{3}.Track2(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)), (1/276.8).*meas{3}.Track3(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; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{3}.Track1_Name, meas{3}.Track2_Name, meas{3}.Track3_Name}, 'Location', 'northeast') legend({meas{3}.Track1_Name, meas{3}.Track2_Name, meas{3}.Track3_Name}, 'Location', 'northeast')
@ -576,6 +640,29 @@ The time domain result is shown figure [[fig:meas3]].
#+RESULTS: fig:meas3 #+RESULTS: fig:meas3
[[file:figs/meas3.png]] [[file:figs/meas3.png]]
#+begin_src matlab :exports none :results silent
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')
#+end_src
#+NAME: fig:meas3_disp
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/meas3_disp.pdf" :var figsize="wide-noral" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+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]]. 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]].
#+begin_src matlab :exports code :results silent #+begin_src matlab :exports code :results silent
[pxx311, f31] = pwelch(meas{3}.Track1(1:ceil(400/dt)), psd_window, [], [], Fs); [pxx311, f31] = pwelch(meas{3}.Track1(1:ceil(400/dt)), psd_window, [], [], Fs);
@ -685,10 +772,11 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
#+begin_src matlab :exports results :results silent #+begin_src matlab :exports results :results silent
figure; figure;
hold on; hold on;
plot(t4, (1/276.8).*meas{4}.Track1); plot(t4, meas{4}.Track1);
plot(t4, (1/276.8).*meas{4}.Track2); plot(t4, meas{4}.Track2);
plot(t4, (1/276.8).*meas{4}.Track3); plot(t4, meas{4}.Track3);
hold off; hold off;
xlim([t4(1), t4(end)]);
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
legend({meas{4}.Track1_Name, meas{4}.Track2_Name, meas{4}.Track3_Name}, 'Location', 'southwest') legend({meas{4}.Track1_Name, meas{4}.Track2_Name, meas{4}.Track3_Name}, 'Location', 'southwest')
#+end_src #+end_src
@ -704,6 +792,41 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
#+RESULTS: fig:meas4 #+RESULTS: fig:meas4
[[file:figs/meas4.png]] [[file:figs/meas4.png]]
#+begin_src matlab :exports none :results silent
figure;
subaxis(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')
subaxis(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]');
#+end_src
If we integrate this signal, we obtain Figure [[fig:meas4_int]].
#+NAME: fig:meas4_int
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/meas4_int.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+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. The PSD of each track are computed using the code below.
#+begin_src matlab :exports none :results silent #+begin_src matlab :exports none :results silent
[pxx411, f41] = pwelch(meas{4}.Track1(1:ceil(280/dt)), psd_window, [], [], Fs); [pxx411, f41] = pwelch(meas{4}.Track1(1:ceil(280/dt)), psd_window, [], [], Fs);
@ -717,6 +840,22 @@ The PSD of each track are computed using the code below.
[pxx431, ~] = pwelch(meas{4}.Track3(1:ceil(280/dt)), 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); [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); [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);
#+end_src #+end_src
#+begin_src matlab :exports none :results silent #+begin_src matlab :exports none :results silent
@ -745,6 +884,51 @@ The PSD of each track are computed using the code below.
#+RESULTS: fig:meas4_hexa_z_psd #+RESULTS: fig:meas4_hexa_z_psd
[[file:figs/meas4_hexa_z_psd.png]] [[file:figs/meas4_hexa_z_psd.png]]
We plot the PSD of the displacement.
#+begin_src matlab :exports none :results silent
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;
#+end_src
#+NAME: fig:meas4_hexa_z_psd_int
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/meas4_hexa_z_psd_int.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+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.
#+begin_src matlab :exports none :results silent
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;
#+end_src
#+begin_src matlab :exports none :results silent #+begin_src matlab :exports none :results silent
figure; figure;
hold on; hold on;
@ -818,10 +1002,10 @@ The time domain signals are shown on figure [[fig:meas5]].
#+begin_src matlab :exports results :results silent #+begin_src matlab :exports results :results silent
figure; figure;
hold on; hold on;
plot(t5, (1/276.8).*meas{5}.Track1); plot(t5, meas{5}.Track1);
plot(t5, (1/276.8).*meas{5}.Track2); plot(t5, meas{5}.Track2);
plot(t5, (1/276.8).*meas{5}.Track3); plot(t5, meas{5}.Track3);
plot(t5, (1/276.8).*meas{5}.Track4); plot(t5, meas{5}.Track4);
hold off; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); 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') legend({meas{5}.Track1_Name, meas{5}.Track2_Name, meas{5}.Track3_Name, meas{5}.Track4_Name}, 'Location', 'northeast')