Integration of geophone to have the displacement
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@ -3,7 +3,7 @@
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2019-03-19 mar. 16:42 -->
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<!-- 2019-04-02 mar. 10:39 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Measurement Analysis</title>
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@ -245,28 +245,6 @@ for the JavaScript code in this tag.
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<body>
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<div id="content">
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@ -275,17 +253,17 @@ for the JavaScript code in this tag.
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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="#orgc1db046">1. Measurement Description</a></li>
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<li><a href="#org9b5288f">2. Importation of the data</a></li>
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<li><a href="#org0c9206e">3. Variables for analysis</a></li>
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<li><a href="#org876fa12">4. Coherence between the two vertical geophones on the Tilt Stage</a></li>
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<li><a href="#org0e81d2f">5. Data Post Processing</a></li>
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<li><a href="#org07adbbe">6. Normalization</a></li>
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<li><a href="#org854c7bf">7. Measurement 1 - Effect of Ty stage</a></li>
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<li><a href="#orga8c4982">8. Measurement 2 - Effect of Ry stage</a></li>
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<li><a href="#orga79f5f4">9. Measurement 3 - Effect of the Hexapod</a></li>
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<li><a href="#org8731abc">10. Measurement 4 - Effect of the Splip-Ring and Spindle</a></li>
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<li><a href="#org33dc0ed">11. Measurement 5 - Transmission from ground to marble</a></li>
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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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@ -294,11 +272,11 @@ for the JavaScript code in this tag.
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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-orgc1db046" class="outline-2">
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<h2 id="orgc1db046"><span class="section-number-2">1</span> Measurement Description</h2>
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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="org25ddba6" class="figure">
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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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@ -318,19 +296,19 @@ The goal is to see what noise is injected in the system due to the regulation lo
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</div>
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</div>
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<div id="outline-container-org9b5288f" class="outline-2">
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<h2 id="org9b5288f"><span class="section-number-2">2</span> Importation of the data</h2>
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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 style="color: #DCDCCC;">{}</span>;
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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>;
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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>;
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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>;
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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>;
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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>;
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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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@ -338,16 +316,16 @@ meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">5</span>
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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 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';
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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';
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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="#orgde7c9fb">1</a>.
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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="orgde7c9fb" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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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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@ -400,9 +378,9 @@ For the measurements 1 to 4, the measurement channels are shown table <a href="#
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<p>
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For the measurement 5, the channels are shown table <a href="#orgb2a1d3a">2</a>.
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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="orgb2a1d3a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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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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@ -438,21 +416,21 @@ For the measurement 5, the channels are shown table <a href="#orgb2a1d3a">2</a>.
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</div>
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</div>
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<div id="outline-container-org0c9206e" class="outline-2">
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<h2 id="org0c9206e"><span class="section-number-2">3</span> Variables for analysis</h2>
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<div id="outline-container-orge44c773" class="outline-2">
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<h2 id="orge44c773"><span class="section-number-2">3</span> Variables for analysis</h2>
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<div class="outline-text-2" id="text-3">
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<p>
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We define the sampling frequency and the time vectors for the plots.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">Fs = <span style="color: #BFEBBF;">256</span>; <span style="color: #7F9F7F;">% [Hz]</span>
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dt = <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">/</span><span style="color: #DCDCCC;">(</span>Fs<span style="color: #DCDCCC;">)</span>;
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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>;
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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>;
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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>;
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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>;
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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>;
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<pre class="src src-matlab">Fs = <span class="org-highlight-numbers-number">256</span>; <span class="org-comment">% [Hz]</span>
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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>;
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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>;
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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>;
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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>;
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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>;
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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>;
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</pre>
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</div>
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@ -460,8 +438,8 @@ t5 = dt<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">[</s
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For the frequency analysis, we define the frequency limits for the plot.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">fmin = <span style="color: #BFEBBF;">1</span>; <span style="color: #7F9F7F;">% [Hz]</span>
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fmax = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">% [Hz]</span>
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<pre class="src src-matlab">fmin = <span class="org-highlight-numbers-number">1</span>; <span class="org-comment">% [Hz]</span>
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fmax = <span class="org-highlight-numbers-number">100</span>; <span class="org-comment">% [Hz]</span>
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</pre>
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</div>
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@ -469,40 +447,40 @@ fmax = <span style="color: #BFEBBF;">100</span>; <span style="color: #7F9F7F;">%
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Then we define the windows that will be used to average the results.
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</p>
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<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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org876fa12" class="outline-2">
|
||||
<h2 id="org876fa12"><span class="section-number-2">4</span> Coherence between the two vertical geophones on the Tilt Stage</h2>
|
||||
<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="#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>
|
||||
<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>
|
||||
</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>
|
||||
<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="#org0f2e1db">3</a>).
|
||||
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 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>
|
||||
</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>
|
||||
<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 id="outline-container-org0e81d2f" class="outline-2">
|
||||
<h2 id="org0e81d2f"><span class="section-number-2">5</span> Data Post Processing</h2>
|
||||
<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 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 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 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 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 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 style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">}</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 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>.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 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 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>;
|
||||
meas<span style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</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 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 style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</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 style="color: #DCDCCC;">{</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">}</span>.Track2_Name = <span style="color: #CC9393;">'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-org07adbbe" class="outline-2">
|
||||
<h2 id="org07adbbe"><span class="section-number-2">6</span> Normalization</h2>
|
||||
<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="#org56c2445">4</a>.
|
||||
The transfer function from geophone velocity to measured voltage is shown on figure <a href="#org47ba141">4</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -558,34 +536,78 @@ Measurements will be normalized by the inverse of this transfer function in orde
|
||||
</p>
|
||||
|
||||
<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>
|
||||
L4C_ksi = <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">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_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>;
|
||||
<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>
|
||||
L4C_G = L4C_G0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span>L4C_w0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>L4C_w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>L4C_ksi<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>L4C_w0<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org56c2445" class="figure">
|
||||
<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>
|
||||
|
||||
<p>
|
||||
Time domain data are just normalized using the sensibility of the sensor (\(276.8 V/m/s\)).
|
||||
</p>
|
||||
<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-org854c7bf" class="outline-2">
|
||||
<h2 id="org854c7bf"><span class="section-number-2">7</span> Measurement 1 - Effect of Ty stage</h2>
|
||||
<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="#org7881134">3</a>.
|
||||
The configuration for this measurement is shown table <a href="#orgc1f3234">3</a>.
|
||||
</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>
|
||||
|
||||
<colgroup>
|
||||
@ -636,7 +658,7 @@ The configuration for this measurement is shown table <a href="#org7881134">3</a
|
||||
</table>
|
||||
|
||||
<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>
|
||||
|
||||
<div class="important">
|
||||
@ -648,7 +670,7 @@ How can we explain that?
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7592c33" class="figure">
|
||||
<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>
|
||||
@ -657,17 +679,12 @@ How can we explain that?
|
||||
<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>
|
||||
<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>
|
||||
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>
|
||||
|
||||
<div id="orgf6e2558" class="figure">
|
||||
<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>
|
||||
@ -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.
|
||||
</p>
|
||||
<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>;
|
||||
<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>;
|
||||
<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 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 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>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 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 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>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="#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>
|
||||
|
||||
|
||||
<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>
|
||||
<p><span class="figure-number">Figure 7: </span>PSD of the Z velocity of Ry stage - measurement 1</p>
|
||||
</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>
|
||||
<p><span class="figure-number">Figure 8: </span>PSD of the Rotation of Ry Stage - measurement 1</p>
|
||||
</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>
|
||||
<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 id="outline-container-orga8c4982" class="outline-2">
|
||||
<h2 id="orga8c4982"><span class="section-number-2">8</span> Measurement 2 - Effect of Ry stage</h2>
|
||||
<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="#org6ee7543">4</a>).
|
||||
The tilt stage is turned ON at around 326 seconds (table <a href="#orgba0882e">4</a>).
|
||||
</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>
|
||||
|
||||
<colgroup>
|
||||
@ -789,50 +806,57 @@ The tilt stage is turned ON at around 326 seconds (table <a href="#org6ee7543">4
|
||||
</table>
|
||||
|
||||
<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>
|
||||
|
||||
|
||||
<div id="org17e1967" class="figure">
|
||||
<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="#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>
|
||||
<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>;
|
||||
<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>;
|
||||
<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 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 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>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 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 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>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="org5ee261f" class="figure">
|
||||
<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 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 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>
|
||||
<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 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>
|
||||
<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 class="important">
|
||||
@ -844,14 +868,14 @@ We observe no noticeable difference when the Tilt-stage is turned ON expect a sm
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga79f5f4" class="outline-2">
|
||||
<h2 id="orga79f5f4"><span class="section-number-2">9</span> Measurement 3 - Effect of the Hexapod</h2>
|
||||
<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="#org3542637">5</a>).
|
||||
The hexapod is turned off after 406 seconds (table <a href="#org8b4187d">5</a>).
|
||||
</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>
|
||||
|
||||
<colgroup>
|
||||
@ -902,55 +926,62 @@ The hexapod is turned off after 406 seconds (table <a href="#org3542637">5</a>).
|
||||
</table>
|
||||
|
||||
<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>
|
||||
|
||||
|
||||
<div id="orgcdae346" class="figure">
|
||||
<div id="org08fc17d" class="figure">
|
||||
<p><img src="figs/meas3.png" alt="meas3.png" />
|
||||
</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>
|
||||
|
||||
<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>
|
||||
<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>;
|
||||
<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>;
|
||||
<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 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 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>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 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 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>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="org862aff7" class="figure">
|
||||
<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 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 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>
|
||||
<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 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>
|
||||
<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 class="important">
|
||||
<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>
|
||||
<ul class="org-ul">
|
||||
<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 id="outline-container-org8731abc" class="outline-2">
|
||||
<h2 id="org8731abc"><span class="section-number-2">10</span> Measurement 4 - Effect of the Splip-Ring and Spindle</h2>
|
||||
<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="#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>
|
||||
|
||||
<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>
|
||||
|
||||
<colgroup>
|
||||
@ -1027,42 +1058,66 @@ The slip ring is turned on at 300s, then the spindle is turned on at 620s (table
|
||||
</table>
|
||||
|
||||
|
||||
<div id="orgcdcd20d" class="figure">
|
||||
<div id="orgf0966f9" class="figure">
|
||||
<p><img src="figs/meas4.png" alt="meas4.png" />
|
||||
</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>
|
||||
|
||||
<p>
|
||||
The PSD of each track are computed using the code below.
|
||||
</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>
|
||||
<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>
|
||||
|
||||
<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>
|
||||
<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 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>
|
||||
<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 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="#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>
|
||||
@ -1078,79 +1133,79 @@ Turning ON the spindle induces motions:
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org33dc0ed" class="outline-2">
|
||||
<h2 id="org33dc0ed"><span class="section-number-2">11</span> Measurement 5 - Transmission from ground to marble</h2>
|
||||
<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="#orgc71b335">22</a>.
|
||||
The time domain signals are shown on figure <a href="#orgc513617">26</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgc71b335" class="figure">
|
||||
<div id="orgc513617" class="figure">
|
||||
<p><img src="figs/meas5.png" alt="meas5.png" />
|
||||
</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>
|
||||
|
||||
<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>
|
||||
|
||||
<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>;
|
||||
<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 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 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>;
|
||||
<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="org69a4967" class="figure">
|
||||
<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 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 id="orgf96e7c0" class="figure">
|
||||
<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 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>
|
||||
|
||||
<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="#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>
|
||||
|
||||
<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>;
|
||||
<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>;
|
||||
<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="orgd1bec89" class="figure">
|
||||
<div id="orgbb283a9" class="figure">
|
||||
<p><img src="figs/meas5_tf.png" alt="meas5_tf.png" />
|
||||
</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 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>;
|
||||
<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>;
|
||||
<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="org4f5ea21" class="figure">
|
||||
<div id="orga357e58" class="figure">
|
||||
<p><img src="figs/meas5_coh.png" alt="meas5_coh.png" />
|
||||
</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 class="important">
|
||||
@ -1165,7 +1220,7 @@ But the coherence is not good above 20Hz, so it is difficult to estimate resonan
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<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>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
@ -242,7 +242,51 @@ Measurements will be normalized by the inverse of this transfer function in orde
|
||||
#+RESULTS: fig:L4C_bode_plot
|
||||
[[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
|
||||
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
|
||||
figure;
|
||||
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)), (1/276.8).*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}.Track1(ceil(300/dt):ceil(340/dt)));
|
||||
plot(t1(ceil(300/dt):ceil(340/dt)), meas{1}.Track2(ceil(300/dt):ceil(340/dt)));
|
||||
plot(t1(ceil(300/dt):ceil(340/dt)), meas{1}.Track3(ceil(300/dt):ceil(340/dt)));
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Velocity [m/s]');
|
||||
legend({meas{1}.Track1_Name, meas{1}.Track2_Name, meas{1}.Track3_Name}, 'Location', 'northeast')
|
||||
@ -287,17 +331,14 @@ We then plot the measurements in time domain (figure [[fig:meas1]]).
|
||||
[[file:figs/meas1.png]]
|
||||
|
||||
To understand what is going on, instead of looking at the velocity, we can look at the displacement by integrating the data. The displacement is computed by integrating the velocity using =cumtrapz= function.
|
||||
#+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]]).
|
||||
#+begin_src matlab :exports none :results silent
|
||||
figure;
|
||||
hold on;
|
||||
plot(tdisp, xdisp);
|
||||
plot(t1, cumtrapz(t1, meas{1}.Track3));
|
||||
hold off;
|
||||
xlim([300, 340]);
|
||||
xlabel('Time [s]'); ylabel('Displacement [m]');
|
||||
#+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
|
||||
figure;
|
||||
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)), (1/276.8).*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}.Track1(ceil(300/dt):ceil(350/dt)));
|
||||
plot(t2(ceil(300/dt):ceil(350/dt)), meas{2}.Track3(ceil(300/dt):ceil(350/dt)));
|
||||
plot(t2(ceil(300/dt):ceil(350/dt)), meas{2}.Track2(ceil(300/dt):ceil(350/dt)));
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Velocity [m/s]');
|
||||
legend({meas{2}.Track1_Name, meas{2}.Track2_Name, meas{2}.Track3_Name}, 'Location', 'northeast')
|
||||
@ -448,6 +489,29 @@ We plot the time domain (figure [[fig:meas2]]) and we don't observe anything spe
|
||||
#+RESULTS: fig:meas2
|
||||
[[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]] ).
|
||||
#+begin_src matlab :exports code :results silent
|
||||
[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
|
||||
figure;
|
||||
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)), (1/276.8).*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}.Track1(ceil(380/dt):ceil(420/dt)));
|
||||
plot(t3(ceil(380/dt):ceil(420/dt)), meas{3}.Track2(ceil(380/dt):ceil(420/dt)));
|
||||
plot(t3(ceil(380/dt):ceil(420/dt)), meas{3}.Track3(ceil(380/dt):ceil(420/dt)));
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Velocity [m/s]');
|
||||
legend({meas{3}.Track1_Name, meas{3}.Track2_Name, meas{3}.Track3_Name}, 'Location', 'northeast')
|
||||
@ -576,6 +640,29 @@ The time domain result is shown figure [[fig:meas3]].
|
||||
#+RESULTS: fig:meas3
|
||||
[[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]].
|
||||
#+begin_src matlab :exports code :results silent
|
||||
[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
|
||||
figure;
|
||||
hold on;
|
||||
plot(t4, (1/276.8).*meas{4}.Track1);
|
||||
plot(t4, (1/276.8).*meas{4}.Track2);
|
||||
plot(t4, (1/276.8).*meas{4}.Track3);
|
||||
plot(t4, meas{4}.Track1);
|
||||
plot(t4, meas{4}.Track2);
|
||||
plot(t4, meas{4}.Track3);
|
||||
hold off;
|
||||
xlim([t4(1), t4(end)]);
|
||||
xlabel('Time [s]'); ylabel('Velocity [m/s]');
|
||||
legend({meas{4}.Track1_Name, meas{4}.Track2_Name, meas{4}.Track3_Name}, 'Location', 'southwest')
|
||||
#+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
|
||||
[[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.
|
||||
#+begin_src matlab :exports none :results silent
|
||||
[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);
|
||||
[pxx432, ~] = pwelch(meas{4}.Track3(ceil(280/dt):ceil(600/dt)), psd_window, [], [], Fs);
|
||||
[pxx433, ~] = pwelch(meas{4}.Track3(ceil(640/dt):end), psd_window, [], [], Fs);
|
||||
|
||||
f41 = f41(2:end);
|
||||
f42 = f42(2:end);
|
||||
f43 = f43(2:end);
|
||||
|
||||
pxx411 = pxx411(2:end);
|
||||
pxx412 = pxx412(2:end);
|
||||
pxx413 = pxx413(2:end);
|
||||
|
||||
pxx421 = pxx421(2:end);
|
||||
pxx422 = pxx422(2:end);
|
||||
pxx423 = pxx423(2:end);
|
||||
|
||||
pxx431 = pxx431(2:end);
|
||||
pxx432 = pxx432(2:end);
|
||||
pxx433 = pxx433(2:end);
|
||||
#+end_src
|
||||
|
||||
#+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
|
||||
[[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
|
||||
figure;
|
||||
hold on;
|
||||
@ -818,10 +1002,10 @@ The time domain signals are shown on figure [[fig:meas5]].
|
||||
#+begin_src matlab :exports results :results silent
|
||||
figure;
|
||||
hold on;
|
||||
plot(t5, (1/276.8).*meas{5}.Track1);
|
||||
plot(t5, (1/276.8).*meas{5}.Track2);
|
||||
plot(t5, (1/276.8).*meas{5}.Track3);
|
||||
plot(t5, (1/276.8).*meas{5}.Track4);
|
||||
plot(t5, meas{5}.Track1);
|
||||
plot(t5, meas{5}.Track2);
|
||||
plot(t5, meas{5}.Track3);
|
||||
plot(t5, meas{5}.Track4);
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Velocity [m/s]');
|
||||
legend({meas{5}.Track1_Name, meas{5}.Track2_Name, meas{5}.Track3_Name, meas{5}.Track4_Name}, 'Location', 'northeast')
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user