1228 lines
86 KiB
HTML
1228 lines
86 KiB
HTML
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</head>
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<body>
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<div id="content">
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<h1 class="title">Measurement Analysis</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orga57c824">1. Measurement Description</a></li>
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<li><a href="#orgac83bb1">2. Importation of the data</a></li>
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<li><a href="#orge44c773">3. Variables for analysis</a></li>
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<li><a href="#orgcb0a2db">4. Coherence between the two vertical geophones on the Tilt Stage</a></li>
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<li><a href="#orgc619b39">5. Data Post Processing</a></li>
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<li><a href="#org03ef418">6. Normalization</a></li>
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<li><a href="#org8583637">7. Measurement 1 - Effect of Ty stage</a></li>
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<li><a href="#org47192a7">8. Measurement 2 - Effect of Ry stage</a></li>
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<li><a href="#org0c3a1d4">9. Measurement 3 - Effect of the Hexapod</a></li>
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<li><a href="#org1529580">10. Measurement 4 - Effect of the Splip-Ring and Spindle</a></li>
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<li><a href="#orga767d61">11. Measurement 5 - Transmission from ground to marble</a></li>
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</ul>
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</div>
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</div>
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<p>
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<a href="../index.html">Back to main page</a>.
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</p>
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<div id="outline-container-orga57c824" class="outline-2">
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<h2 id="orga57c824"><span class="section-number-2">1</span> Measurement Description</h2>
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<div class="outline-text-2" id="text-1">
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<div id="orgc56bc67" class="figure">
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<p><img src="./figs/setup_picture.png" alt="setup_picture.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the setup for the measurement</p>
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</div>
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<p>
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The sensor used are 3 L-4C geophones (<a href="../actuators-sensors/index.html#MissingReference">Documentation</a>).
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</p>
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<p>
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Each motor are turn off and then on.
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</p>
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<p>
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The goal is to see what noise is injected in the system due to the regulation loop of each stage.
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</p>
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</div>
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</div>
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<div id="outline-container-orgac83bb1" class="outline-2">
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<h2 id="orgac83bb1"><span class="section-number-2">2</span> Importation of the data</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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First, load all the measurement files:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">meas = <span class="org-rainbow-delimiters-depth-1">{}</span>;
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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>;
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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>;
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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>;
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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>;
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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>;
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</pre>
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</div>
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<p>
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Change the track name for measurements 3 and 4.
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</p>
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<div class="org-src-container">
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<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';
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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';
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</pre>
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</div>
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<p>
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For the measurements 1 to 4, the measurement channels are shown table <a href="#org7e4418b">1</a>.
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</p>
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<table id="org7e4418b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Channels for measurements 1 to 4</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"> </th>
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<th scope="col" class="org-left">Channel 1</th>
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<th scope="col" class="org-left">Channel 2</th>
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<th scope="col" class="org-left">Channel 3</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Meas. 1</td>
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<td class="org-left">Input 1: tilt1 Z</td>
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<td class="org-left">Input 2: tilt2 Z</td>
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<td class="org-left">Input 3: Ty Y</td>
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</tr>
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<tr>
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<td class="org-left">Meas. 2</td>
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<td class="org-left">Input 1: tilt1 Z</td>
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<td class="org-left">Input 2: tilt2 Z</td>
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<td class="org-left">Input 3: Ty Y</td>
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</tr>
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<tr>
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<td class="org-left">Meas. 3</td>
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<td class="org-left">Input 1: Hexa Z</td>
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<td class="org-left">Input 2: tilt2 Z</td>
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<td class="org-left">Input 3: Ty Y</td>
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</tr>
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<tr>
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<td class="org-left">Meas. 4</td>
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<td class="org-left">Input 1: Hexa Z</td>
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<td class="org-left">Input 2: tilt2 Z</td>
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<td class="org-left">Input 3: Ty Y</td>
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</tr>
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</tbody>
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</table>
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<p>
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For the measurement 5, the channels are shown table <a href="#org00892de">2</a>.
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</p>
|
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<table id="org00892de" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 2:</span> Channels for measurement 5</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left"> </th>
|
|
<th scope="col" class="org-left">Channel 1</th>
|
|
<th scope="col" class="org-left">Channel 2</th>
|
|
<th scope="col" class="org-left">Channel 3</th>
|
|
<th scope="col" class="org-left">Channel 4</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Meas. 5</td>
|
|
<td class="org-left">Input 1: Floor Z</td>
|
|
<td class="org-left">Input 2: Marble Z</td>
|
|
<td class="org-left">Input 3: Floor Y</td>
|
|
<td class="org-left">Input 4: Marble Y</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge44c773" class="outline-2">
|
|
<h2 id="orge44c773"><span class="section-number-2">3</span> Variables for analysis</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
We define the sampling frequency and the time vectors for the plots.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">Fs = <span class="org-highlight-numbers-number">256</span>; <span class="org-comment">% [Hz]</span>
|
|
dt = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
t1 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
t2 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
t3 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
t4 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
t5 = dt<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span><span class="org-type">:</span>length<span class="org-rainbow-delimiters-depth-2">(</span>meas<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-3">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">]</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
For the frequency analysis, we define the frequency limits for the plot.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">fmin = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% [Hz]</span>
|
|
fmax = <span class="org-highlight-numbers-number">100</span>; <span class="org-comment">% [Hz]</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then we define the windows that will be used to average the results.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgcb0a2db" class="outline-2">
|
|
<h2 id="orgcb0a2db"><span class="section-number-2">4</span> Coherence between the two vertical geophones on the Tilt Stage</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
We first compute the coherence between the two geophones located on the tilt stage. The result is shown on figure <a href="#org3d4d6fd">2</a>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh, f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org3d4d6fd" class="figure">
|
|
<p><img src="figs/coherence_vertical_tilt_sensors.png" alt="coherence_vertical_tilt_sensors.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Coherence between the two vertical sensors positionned on the Tilt Stage</p>
|
|
</div>
|
|
|
|
<p>
|
|
We then compute the transfer function from one sensor to the other (figure <a href="#org62100a4">3</a>).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>tf23, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track2<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org62100a4" class="figure">
|
|
<p><img src="figs/tf_vertical_tilt_sensors.png" alt="tf_vertical_tilt_sensors.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Transfer function from one vertical geophone on the tilt stage to the other vertical geophone on the tilt stage</p>
|
|
</div>
|
|
|
|
<p>
|
|
Even though the coherence is not very good, we observe no resonance between the two sensors.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc619b39" class="outline-2">
|
|
<h2 id="orgc619b39"><span class="section-number-2">5</span> Data Post Processing</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<p>
|
|
When using two geophone sensors on the same tilt stage (measurements 1 and 2), we post-process the data to obtain the z displacement and the rotation of the tilt stage:
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org03ef418" class="outline-2">
|
|
<h2 id="org03ef418"><span class="section-number-2">6</span> Normalization</h2>
|
|
<div class="outline-text-2" id="text-6">
|
|
<p>
|
|
Parameters of the geophone are defined below.
|
|
The transfer function from geophone velocity to measured voltage is shown on figure <a href="#org47ba141">4</a>.
|
|
</p>
|
|
|
|
<p>
|
|
Measurements will be normalized by the inverse of this transfer function in order to go from voltage measurement to velocity measurement.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">L4C_w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
|
|
L4C_ksi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">28</span>;
|
|
L4C_G0 = <span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>; <span class="org-comment">% [V/(m/s)]</span>
|
|
[Omitted long matching line]
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org47ba141" class="figure">
|
|
<p><img src="figs/L4C_bode_plot.png" alt="L4C_bode_plot.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Bode plot of the L4C Geophone</p>
|
|
</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 = <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>;
|
|
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 id="outline-container-org8583637" class="outline-2">
|
|
<h2 id="org8583637"><span class="section-number-2">7</span> Measurement 1 - Effect of Ty stage</h2>
|
|
<div class="outline-text-2" id="text-7">
|
|
<p>
|
|
The configuration for this measurement is shown table <a href="#orgc1f3234">3</a>.
|
|
</p>
|
|
|
|
<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>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Time</th>
|
|
<th scope="col" class="org-left">0-309</th>
|
|
<th scope="col" class="org-left">309-end</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Ty</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Ry</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">SlipRing</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Spindle</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Hexa</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
We then plot the measurements in time domain (figure <a href="#orgf931943">5</a>).
|
|
</p>
|
|
|
|
<div class="important">
|
|
<p>
|
|
We observe strange behavior when the Ty stage is turned on.
|
|
How can we explain that?
|
|
</p>
|
|
|
|
</div>
|
|
|
|
|
|
<div id="orgf931943" class="figure">
|
|
<p><img src="figs/meas1.png" alt="meas1.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Time domain - measurement 1</p>
|
|
</div>
|
|
|
|
<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.
|
|
</p>
|
|
|
|
<p>
|
|
Then we plot the position with respect to time (figure <a href="#orgb6bceab">6</a>).
|
|
</p>
|
|
|
|
<div id="orgb6bceab" class="figure">
|
|
<p><img src="figs/meas1_disp.png" alt="meas1_disp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Y displacement of the Ty stage</p>
|
|
</div>
|
|
|
|
<p>
|
|
We when compute the power spectral density of each measurement before and after turning on the stage.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<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 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 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 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 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 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>
|
|
</div>
|
|
|
|
<p>
|
|
We finally plot the power spectral density of each track (figures <a href="#org767e453">7</a>, <a href="#org8cd1899">8</a>, <a href="#org3030170">9</a>).
|
|
</p>
|
|
|
|
|
|
<div id="org767e453" class="figure">
|
|
<p><img src="figs/meas1_ry_z_psd.png" alt="meas1_ry_z_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>PSD of the Z velocity of Ry stage - measurement 1</p>
|
|
</div>
|
|
|
|
|
|
<div id="org8cd1899" class="figure">
|
|
<p><img src="figs/meas1_ry_tilt_psd.png" alt="meas1_ry_tilt_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>PSD of the Rotation of Ry Stage - measurement 1</p>
|
|
</div>
|
|
|
|
|
|
<div id="org3030170" class="figure">
|
|
<p><img src="figs/meas1_ty_y_psd.png" alt="meas1_ty_y_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>PSD of the Ty velocity in the Y direction - measurement 1</p>
|
|
</div>
|
|
|
|
<div class="important">
|
|
<p>
|
|
Turning on the Y-translation stage increases the velocity of the Ty stage in the Y direction and the rotation motion of the tilt stage:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>at 20Hz</li>
|
|
<li>at 40Hz</li>
|
|
<li>between 80Hz and 90Hz</li>
|
|
</ul>
|
|
|
|
<p>
|
|
It does not seems to have any effect on the Z motion of the tilt stage.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org47192a7" class="outline-2">
|
|
<h2 id="org47192a7"><span class="section-number-2">8</span> Measurement 2 - Effect of Ry stage</h2>
|
|
<div class="outline-text-2" id="text-8">
|
|
<p>
|
|
The tilt stage is turned ON at around 326 seconds (table <a href="#orgba0882e">4</a>).
|
|
</p>
|
|
|
|
<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>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Time</th>
|
|
<th scope="col" class="org-left">0-326</th>
|
|
<th scope="col" class="org-left">326-end</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Ty</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Ry</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">SlipRing</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Spindle</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Hexa</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
We plot the time domain (figure <a href="#org9bf6e90">10</a>) and we don't observe anything special in the time domain.
|
|
</p>
|
|
|
|
|
|
<div id="org9bf6e90" class="figure">
|
|
<p><img src="figs/meas2.png" alt="meas2.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Time domain - measurement 2</p>
|
|
</div>
|
|
|
|
|
|
<div id="org767f834" class="figure">
|
|
<p><img src="figs/meas2_disp.png" alt="meas2_disp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 11: </span>Time domain - measurement 2</p>
|
|
</div>
|
|
|
|
<p>
|
|
We compute the PSD of each track and we plot them (figures <a href="#org23fbfb4">12</a>, <a href="#org7a18c86">13</a> and <a href="#orgdcf33e8">14</a> ).
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx211, f21<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">326</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<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 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 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 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 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>
|
|
</div>
|
|
|
|
|
|
<div id="org23fbfb4" class="figure">
|
|
<p><img src="figs/meas2_ry_z_psd.png" alt="meas2_ry_z_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 12: </span>PSD of the Z velocity of Ry Stage - measurement 2</p>
|
|
</div>
|
|
|
|
|
|
<div id="org7a18c86" class="figure">
|
|
<p><img src="figs/meas2_ry_tilt_psd.png" alt="meas2_ry_tilt_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>PSD of the Rotation motion of Ry Stage - measurement 2</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgdcf33e8" class="figure">
|
|
<p><img src="figs/meas2_ty_y_psd.png" alt="meas2_ty_y_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>PSD of the Ty velocity in the Y direction - measurement 2</p>
|
|
</div>
|
|
|
|
<div class="important">
|
|
<p>
|
|
We observe no noticeable difference when the Tilt-stage is turned ON expect a small decrease of the Z motion of the tilt stage around 10Hz.
|
|
</p>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org0c3a1d4" class="outline-2">
|
|
<h2 id="org0c3a1d4"><span class="section-number-2">9</span> Measurement 3 - Effect of the Hexapod</h2>
|
|
<div class="outline-text-2" id="text-9">
|
|
<p>
|
|
The hexapod is turned off after 406 seconds (table <a href="#org8b4187d">5</a>).
|
|
</p>
|
|
|
|
<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>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Time</th>
|
|
<th scope="col" class="org-left">0-406</th>
|
|
<th scope="col" class="org-left">406-end</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Ty</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Ry</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">SlipRing</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Spindle</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Hexa</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
The time domain result is shown figure <a href="#org08fc17d">15</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org08fc17d" class="figure">
|
|
<p><img src="figs/meas3.png" alt="meas3.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 15: </span>Time domain - measurement 3</p>
|
|
</div>
|
|
|
|
|
|
<div id="org4ae7ca4" class="figure">
|
|
<p><img src="figs/meas3_disp.png" alt="meas3_disp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 16: </span>Time domain - measurement 3</p>
|
|
</div>
|
|
|
|
<p>
|
|
We then compute the PSD of each track before and after turning off the hexapod and plot the results in the figures <a href="#org0c4287e">17</a>, <a href="#org899151a">18</a> and <a href="#org0fc8e31">19</a>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx311, f31<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas<span class="org-rainbow-delimiters-depth-2">{</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">}</span>.Track1<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">400</span><span class="org-type">/</span>dt<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, psd_window, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<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 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 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 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 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>
|
|
</div>
|
|
|
|
|
|
<div id="org0c4287e" class="figure">
|
|
<p><img src="figs/meas3_hexa_z_psd.png" alt="meas3_hexa_z_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 17: </span>PSD of the Z velocity of the Hexapod - measurement 3</p>
|
|
</div>
|
|
|
|
|
|
<div id="org899151a" class="figure">
|
|
<p><img src="figs/meas3_ry_z_psd.png" alt="meas3_ry_z_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 18: </span>PSD of the Z velocity of the Ry stage - measurement 3</p>
|
|
</div>
|
|
|
|
|
|
<div id="org0fc8e31" class="figure">
|
|
<p><img src="figs/meas3_ty_y_psd.png" alt="meas3_ty_y_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 19: </span>PSD of the Ty velocity in the Y direction - measurement 3</p>
|
|
</div>
|
|
|
|
<div class="important">
|
|
<p>
|
|
Turning ON induces some motion on the hexapod in the z direction (figure <a href="#org0c4287e">17</a>), on the tilt stage in the z direction (figure <a href="#org899151a">18</a>) and on the y motion of the Ty stage (figure <a href="#org0fc8e31">19</a>):
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>at 17Hz</li>
|
|
<li>at 34Hz</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1529580" class="outline-2">
|
|
<h2 id="org1529580"><span class="section-number-2">10</span> Measurement 4 - Effect of the Splip-Ring and Spindle</h2>
|
|
<div class="outline-text-2" id="text-10">
|
|
<p>
|
|
The slip ring is turned on at 300s, then the spindle is turned on at 620s (table <a href="#org274f078">6</a>). The time domain signals are shown figure <a href="#orgf0966f9">20</a>.
|
|
</p>
|
|
|
|
<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>
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left">Time</th>
|
|
<th scope="col" class="org-left">0-300</th>
|
|
<th scope="col" class="org-left">300-620</th>
|
|
<th scope="col" class="org-left">620-end</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">Ty</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Ry</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">SlipRing</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Spindle</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left"><b>ON</b></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">Hexa</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
<td class="org-left">OFF</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
|
|
<div id="orgf0966f9" class="figure">
|
|
<p><img src="figs/meas4.png" alt="meas4.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 20: </span>Time domain - measurement 4</p>
|
|
</div>
|
|
|
|
<p>
|
|
If we integrate this signal, we obtain Figure <a href="#org62b5bdf">21</a>.
|
|
</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>
|
|
|
|
<p>
|
|
The PSD of each track are computed using the code below.
|
|
</p>
|
|
|
|
<div id="orgfd7f8ce" class="figure">
|
|
<p><img src="figs/meas4_hexa_z_psd.png" alt="meas4_hexa_z_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 22: </span>PSD of the Z velocity of the Hexapod - measurement 4</p>
|
|
</div>
|
|
|
|
<p>
|
|
We plot the PSD of the displacement.
|
|
</p>
|
|
|
|
<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>
|
|
<p><span class="figure-number">Figure 24: </span>PSD of the Ry rotation in the Y direction - measurement 4</p>
|
|
</div>
|
|
|
|
|
|
|
|
<div id="org08ad3dc" class="figure">
|
|
<p><img src="figs/meas4_ty_y_psd.png" alt="meas4_ty_y_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 25: </span>PSD of the Ty velocity in the Y direction - measurement 4</p>
|
|
</div>
|
|
|
|
|
|
<div class="important">
|
|
<p>
|
|
Turning ON the splipring seems to not add motions on the stages measured.
|
|
It even seems to lower the motion of the Ty stage (figure <a href="#org08ad3dc">25</a>): does that make any sense?
|
|
</p>
|
|
|
|
<p>
|
|
Turning ON the spindle induces motions:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>at 5Hz on each motion measured</li>
|
|
<li>at 22.5Hz on the Z motion of the Hexapod. Can this is due to some 50Hz?</li>
|
|
<li>at 62Hz on each motion measured</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga767d61" class="outline-2">
|
|
<h2 id="orga767d61"><span class="section-number-2">11</span> Measurement 5 - Transmission from ground to marble</h2>
|
|
<div class="outline-text-2" id="text-11">
|
|
<p>
|
|
This measurement just consists of measurement of Y-Z motion of the ground and the marble.
|
|
</p>
|
|
|
|
<p>
|
|
The time domain signals are shown on figure <a href="#orgc513617">26</a>.
|
|
</p>
|
|
|
|
|
|
<div id="orgc513617" class="figure">
|
|
<p><img src="figs/meas5.png" alt="meas5.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 26: </span>Time domain - measurement 5</p>
|
|
</div>
|
|
|
|
<p>
|
|
We compute the PSD of each track and we plot the PSD of the Z motion for the ground and marble on figure <a href="#org28b0b94">27</a> and for the Y motion on figure <a href="#orgf797eae">28</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<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 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 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 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>
|
|
</div>
|
|
|
|
|
|
<div id="org28b0b94" class="figure">
|
|
<p><img src="figs/meas5_z_psd.png" alt="meas5_z_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 27: </span>PSD of the ground and marble in the Z direction</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgf797eae" class="figure">
|
|
<p><img src="figs/meas5_y_psd.png" alt="meas5_y_psd.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 28: </span>PSD of the ground and marble in the Y direction</p>
|
|
</div>
|
|
|
|
<p>
|
|
Then, instead of looking at the Power Spectral Density, we can try to estimate the transfer function from a ground motion to the motion of the marble.
|
|
The transfer functions are shown on figure <a href="#orgbb283a9">29</a> and the coherence on figure <a href="#orga357e58">30</a>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<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 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>
|
|
</div>
|
|
|
|
|
|
<div id="orgbb283a9" class="figure">
|
|
<p><img src="figs/meas5_tf.png" alt="meas5_tf.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 29: </span>Transfer function estimation - measurement 5</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<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 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>
|
|
</div>
|
|
|
|
|
|
<div id="orga357e58" class="figure">
|
|
<p><img src="figs/meas5_coh.png" alt="meas5_coh.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 30: </span>Coherence - measurement 5</p>
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</div>
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<div class="important">
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<p>
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The marble seems to have a resonance at around 20Hz on the Y direction.
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But the coherence is not good above 20Hz, so it is difficult to estimate resonances.
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</p>
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</div>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Thomas Dehaeze</p>
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<p class="date">Created: 2019-04-02 mar. 10:39</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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