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Effect of all the control systems on the Sample vibrations</a> <ul> <li><a href="#orgb7f818b">1.1. Experimental Setup</a></li> <li><a href="#org6339e93">1.2. Load data</a></li> <li><a href="#orgb2bbf2a">1.3. Analysis - Time Domain</a></li> <li><a href="#org939455f">1.4. Analysis - Frequency Domain</a> <ul> <li><a href="#org98343aa">1.4.1. Vibrations at the sample location</a></li> <li><a href="#org2406379">1.4.2. Vibrations on the marble</a></li> </ul> </li> <li><a href="#orgcd6174b">1.5. Effect of the control system on the transmissibility from ground to sample</a></li> <li><a href="#orgb74951a">1.6. Conclusion</a></li> </ul> </li> <li><a href="#orged1a63a">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a> <ul> <li><a href="#orgb02d791">2.1. Experimental Setup</a></li> <li><a href="#orgc25694f">2.2. Load data</a></li> <li><a href="#org91c4f39">2.3. Analysis - Time Domain</a></li> <li><a href="#org748e4fb">2.4. Analysis - Frequency Domain</a> <ul> <li><a href="#orgf475151">2.4.1. Vibrations at the sample location</a></li> <li><a href="#orgd931999">2.4.2. Vibrations on the marble</a></li> </ul> </li> <li><a href="#org02fa0f5">2.5. Conclusion</a></li> </ul> </li> <li><a href="#org419641c">3. Effect of the Symetrie Driver</a> <ul> <li><a href="#org0376ec1">3.1. Experimental Setup</a></li> <li><a href="#orgd322b02">3.2. Load data</a></li> <li><a href="#orgab00c14">3.3. Analysis - Time Domain</a></li> <li><a href="#orgb49b710">3.4. Analysis - Frequency Domain</a> <ul> <li><a href="#org29e0984">3.4.1. Vibrations at the sample location</a></li> </ul> </li> <li><a href="#org0edc5e7">3.5. Conclusion</a></li> </ul> </li> <li><a href="#orgf05c480">4. Transfer function from one stage to the other</a> <ul> <li><a href="#org314ff6f">4.1. Experimental Setup</a> <ul> <li><a href="#orgc56982c">4.1.1. From Marble to Ty - <code>mat/meas_010.mat</code></a></li> <li><a href="#org28719df">4.1.2. From Marble to Ry - <code>mat/meas_011.mat</code></a></li> <li><a href="#orgfd497bf">4.1.3. From Ty to Ry - <code>mat/meas_012.mat</code></a></li> </ul> </li> <li><a href="#orgeb58991">4.2. Load data</a></li> <li><a href="#org62dcb2b">4.3. Analysis - Time Domain</a></li> <li><a href="#org7d7634e">4.4. Analysis - Frequency Domain</a></li> <li><a href="#orgefefe3f">4.5. Conclusion</a></li> </ul> </li> </ul> </div> </div> <p> <a href="../index.html">Back to main page</a>. </p> <p> For all the measurements shown here: </p> <ul class="org-ul"> <li>geophones used are L22 with a resonance frequency of 1Hz</li> <li>the signals are amplified with voltage amplifiers with a gain of 60dB</li> <li>the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz</li> </ul> <div id="outline-container-orge3291f9" class="outline-2"> <h2 id="orge3291f9"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2> <div class="outline-text-2" id="text-1"> <p> <a id="orgce98253"></a> </p> <div class="note"> <p> All the files (data and Matlab scripts) are accessible <a href="data/effect_control_all.zip">here</a>. </p> </div> </div> <div id="outline-container-orgb7f818b" class="outline-3"> <h3 id="orgb7f818b"><span class="section-number-3">1.1</span> Experimental Setup</h3> <div class="outline-text-3" id="text-1-1"> <p> We here measure the signals of two geophones: </p> <ul class="org-ul"> <li>One is located on top of the Sample platform</li> <li>One is located on the marble</li> </ul> <p> The signal from the top geophone does not go trought the slip-ring. </p> <p> First, all the control systems are turned ON, then, they are turned one by one. Each measurement are done during 50s. </p> <table id="orge386ef2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption> <colgroup> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-left">Ty</th> <th scope="col" class="org-left">Ry</th> <th scope="col" class="org-left">Slip Ring</th> <th scope="col" class="org-left">Spindle</th> <th scope="col" class="org-left">Hexapod</th> <th scope="col" class="org-left">Meas. file</th> </tr> </thead> <tbody> <tr> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><code>meas_003.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><code>meas_004.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><code>meas_005.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left"><b>ON</b></td> <td class="org-left"><code>meas_006.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left"><code>meas_007.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><code>meas_008.mat</code></td> </tr> </tbody> </table> <p> Each of the <code>mat</code> file contains one array <code>data</code> with 3 columns: </p> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <colgroup> <col class="org-right" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-right">Column number</th> <th scope="col" class="org-left">Description</th> </tr> </thead> <tbody> <tr> <td class="org-right">1</td> <td class="org-left">Geophone - Marble</td> </tr> <tr> <td class="org-right">2</td> <td class="org-left">Geophone - Sample</td> </tr> <tr> <td class="org-right">3</td> <td class="org-left">Time</td> </tr> </tbody> </table> </div> </div> <div id="outline-container-org6339e93" class="outline-3"> <h3 id="org6339e93"><span class="section-number-3">1.2</span> Load data</h3> <div class="outline-text-3" id="text-1-2"> <p> We load the data of the z axis of two geophones. </p> <div class="org-src-container"> <pre class="src src-matlab">d3 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_003.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d3 = d3.data; d4 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_004.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d4 = d4.data; d5 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_005.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d5 = d5.data; d6 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_006.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d6 = d6.data; d7 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_007.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d7 = d7.data; d8 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_008.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d8 = d8.data; </pre> </div> </div> </div> <div id="outline-container-orgb2bbf2a" class="outline-3"> <h3 id="orgb2bbf2a"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3> <div class="outline-text-3" id="text-1-3"> <p> First, we can look at the time domain data and compare all the measurements: </p> <ul class="org-ul"> <li>comparison for the geophone at the sample location (figure <a href="#org1d9fd16">1</a>)</li> <li>comparison for the geophone on the granite (figure <a href="#org9c5a166">2</a>)</li> </ul> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org1d9fd16" class="figure"> <p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" /> </p> <p><span class="figure-number">Figure 1: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p> </div> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d3<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-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d4<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-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d5<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-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d6<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-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d7<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-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d8<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-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org9c5a166" class="figure"> <p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" /> </p> <p><span class="figure-number">Figure 2: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p> </div> </div> </div> <div id="outline-container-org939455f" class="outline-3"> <h3 id="org939455f"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3> <div class="outline-text-3" id="text-1-4"> <div class="org-src-container"> <pre class="src src-matlab">dt = d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> </div> <div id="outline-container-org98343aa" class="outline-4"> <h4 id="org98343aa"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4> <div class="outline-text-4" id="text-1-4-1"> <p> First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px3, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px4, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px5, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px6, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px7, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px8, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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> And we compare all the signals (figures <a href="#org19f9706">3</a> and <a href="#orgfb18b9c">4</a>). </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org19f9706" class="figure"> <p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" /> </p> <p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the signal coming from the top geophone</p> </div> <div id="orgfb18b9c" class="figure"> <p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" /> </p> <p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p> </div> </div> </div> <div id="outline-container-org2406379" class="outline-4"> <h4 id="org2406379"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4> <div class="outline-text-4" id="text-1-4-2"> <p> Now we plot the same curves for the geophone located on the marble. </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px3, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d3<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-2">)</span>, win, <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>px4, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d4<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-2">)</span>, win, <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>px5, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d5<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-2">)</span>, win, <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>px6, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d6<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-2">)</span>, win, <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>px7, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d7<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-2">)</span>, win, <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>px8, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d8<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-2">)</span>, win, <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> And we compare the Amplitude Spectral Densities (figures <a href="#org24e988b">5</a> and <a href="#org50ff18b">6</a>) </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org24e988b" class="figure"> <p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" /> </p> <p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the signal coming from the top geophone</p> </div> <div id="org50ff18b" class="figure"> <p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" /> </p> <p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p> </div> </div> </div> </div> <div id="outline-container-orgcd6174b" class="outline-3"> <h3 id="orgcd6174b"><span class="section-number-3">1.5</span> Effect of the control system on the transmissibility from ground to sample</h3> <div class="outline-text-3" id="text-1-5"> <p> As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure <a href="#org79e59b9">7</a>). </p> <div class="org-src-container"> <pre class="src src-matlab">dt = d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <p> First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T3, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d3<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-2">)</span>, d3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>T4, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d4<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-2">)</span>, d4<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>T5, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d5<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-2">)</span>, d5<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>T6, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d6<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-2">)</span>, d6<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>T7, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d7<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-2">)</span>, d7<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>T8, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>d8<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-2">)</span>, d8<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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 class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T3<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T4<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T5<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T6<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T7<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T8<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T3<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T4<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T5<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T6<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T7<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T8<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>; linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org79e59b9" class="figure"> <p><img src="figs/trans_comp.png" alt="trans_comp.png" /> </p> <p><span class="figure-number">Figure 7: </span>Comparison of the transfer function from the geophone on the marble to the geophone at the sample location</p> </div> </div> </div> <div id="outline-container-orgb74951a" class="outline-3"> <h3 id="orgb74951a"><span class="section-number-3">1.6</span> Conclusion</h3> <div class="outline-text-3" id="text-1-6"> <div class="important"> <ul class="org-ul"> <li>The control system of the Ty stage induces a lot of vibrations of the marble</li> </ul> </div> <div class="note"> <ul class="org-ul"> <li>Why it seems that the measurement noise at high frequency is the limiting factor when the slip ring is ON but not when it is OFF?</li> </ul> </div> </div> </div> </div> <div id="outline-container-orged1a63a" class="outline-2"> <h2 id="orged1a63a"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2> <div class="outline-text-2" id="text-2"> <p> <a id="orgb4369e7"></a> </p> <div class="note"> <p> All the files (data and Matlab scripts) are accessible <a href="data/effect_control_one.zip">here</a>. </p> </div> </div> <div id="outline-container-orgb02d791" class="outline-3"> <h3 id="orgb02d791"><span class="section-number-3">2.1</span> Experimental Setup</h3> <div class="outline-text-3" id="text-2-1"> <p> We here measure the signals of two geophones: </p> <ul class="org-ul"> <li>One is located on top of the Sample platform</li> <li>One is located on the marble</li> </ul> <p> The signal from the top geophone does go trought the slip-ring. </p> <p> All the control systems are turned OFF, then, they are turned on one at a time. </p> <p> Each measurement are done during 100s. </p> <p> The settings of the voltage amplifier are shown on figure <a href="#org3c63500">8</a>. A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier. </p> <table id="orgcd4ff5c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <caption class="t-above"><span class="table-number">Table 2:</span> Summary of the measurements and the states of the control systems</caption> <colgroup> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-left">Ty</th> <th scope="col" class="org-left">Ry</th> <th scope="col" class="org-left">Slip Ring</th> <th scope="col" class="org-left">Spindle</th> <th scope="col" class="org-left">Hexapod</th> <th scope="col" class="org-left">Meas. file</th> </tr> </thead> <tbody> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><code>meas_013.mat</code></td> </tr> <tr> <td class="org-left"><b>ON</b></td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><code>meas_014.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><code>meas_015.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><code>meas_016.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left">OFF</td> <td class="org-left"><code>meas_017.mat</code></td> </tr> <tr> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left">OFF</td> <td class="org-left"><b>ON</b></td> <td class="org-left"><code>meas_018.mat</code></td> </tr> </tbody> </table> <p> Each of the <code>mat</code> file contains one array <code>data</code> with 3 columns: </p> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <colgroup> <col class="org-right" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-right">Column number</th> <th scope="col" class="org-left">Description</th> </tr> </thead> <tbody> <tr> <td class="org-right">1</td> <td class="org-left">Geophone - Marble</td> </tr> <tr> <td class="org-right">2</td> <td class="org-left">Geophone - Sample</td> </tr> <tr> <td class="org-right">3</td> <td class="org-left">Time</td> </tr> </tbody> </table> <div id="org3c63500" class="figure"> <p><img src="./img/IMG_20190507_101459.jpg" alt="IMG_20190507_101459.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 8: </span>Voltage amplifier settings for the measurement</p> </div> </div> </div> <div id="outline-container-orgc25694f" class="outline-3"> <h3 id="orgc25694f"><span class="section-number-3">2.2</span> Load data</h3> <div class="outline-text-3" id="text-2-2"> <p> We load the data of the z axis of two geophones. </p> <div class="org-src-container"> <pre class="src src-matlab">d_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_013.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_of = d_of.data; d_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_014.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_ty = d_ty.data; d_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_015.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_ry = d_ry.data; d_sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_016.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_sr = d_sr.data; d_rz = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_017.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_rz = d_rz.data; d_he = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_018.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_he = d_he.data; </pre> </div> </div> </div> <div id="outline-container-org91c4f39" class="outline-3"> <h3 id="org91c4f39"><span class="section-number-3">2.3</span> Analysis - Time Domain</h3> <div class="outline-text-3" id="text-2-3"> <p> First, we can look at the time domain data and compare all the measurements: </p> <ul class="org-ul"> <li>comparison for the geophone at the sample location (figure <a href="#orgc6c9092">9</a>)</li> <li>comparison for the geophone on the granite (figure <a href="#org8c9eb5f">10</a>)</li> </ul> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span>; plot<span class="org-rainbow-delimiters-depth-2">(</span>d_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_ty<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-string">'DisplayName', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-2">)</span>; plot<span class="org-rainbow-delimiters-depth-2">(</span>d_ry<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_ry<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-string">'DisplayName', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-2">)</span>; plot<span class="org-rainbow-delimiters-depth-2">(</span>d_sr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_sr<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-2">)</span>; plot<span class="org-rainbow-delimiters-depth-2">(</span>d_rz<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_rz<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-string">'DisplayName', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-2">)</span>; plot<span class="org-rainbow-delimiters-depth-2">(</span>d_he<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span>, d_he<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-string">'DisplayName', 'Hexa ON'</span><span class="org-rainbow-delimiters-depth-2">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-2">)</span>; xlim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-3">]</span><span class="org-rainbow-delimiters-depth-2">)</span>; legend<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'Location', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-2">)</span>; </pre> </div> <div id="orgc6c9092" class="figure"> <p><img src="figs/time_domain_sample_lpf.png" alt="time_domain_sample_lpf.png" /> </p> <p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p> </div> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_of<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-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_ty<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-2">)</span>, <span class="org-string">'DisplayName', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_ry<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-2">)</span>, <span class="org-string">'DisplayName', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_sr<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-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_rz<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-2">)</span>, <span class="org-string">'DisplayName', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_he<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_he<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-2">)</span>, <span class="org-string">'DisplayName', 'Hexa ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org8c9eb5f" class="figure"> <p><img src="figs/time_domain_marble_lpf.png" alt="time_domain_marble_lpf.png" /> </p> <p><span class="figure-number">Figure 10: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p> </div> </div> </div> <div id="outline-container-org748e4fb" class="outline-3"> <h3 id="org748e4fb"><span class="section-number-3">2.4</span> Analysis - Frequency Domain</h3> <div class="outline-text-3" id="text-2-4"> <div class="org-src-container"> <pre class="src src-matlab">dt = d_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> </div> <div id="outline-container-orgf475151" class="outline-4"> <h4 id="orgf475151"><span class="section-number-4">2.4.1</span> Vibrations at the sample location</h4> <div class="outline-text-4" id="text-2-4-1"> <p> First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_of, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px_ty, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px_sr, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px_rz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>px_he, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_he<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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> And we compare all the signals (figures <a href="#orgfcdac5a">11</a> and <a href="#orgdc64e82">12</a>). </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_of<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ty<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_rz<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_he<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="orgfcdac5a" class="figure"> <p><img src="figs/psd_sample_comp_lpf.png" alt="psd_sample_comp_lpf.png" /> </p> <p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the signal coming from the top geophone</p> </div> <div id="orgdc64e82" class="figure"> <p><img src="figs/psd_sample_comp_high_freq_lpf.png" alt="psd_sample_comp_high_freq_lpf.png" /> </p> <p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p> </div> </div> </div> <div id="outline-container-orgd931999" class="outline-4"> <h4 id="orgd931999"><span class="section-number-4">2.4.2</span> Vibrations on the marble</h4> <div class="outline-text-4" id="text-2-4-2"> <p> Now we plot the same curves for the geophone located on the marble. </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_of, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_of<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-2">)</span>, win, <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>px_ty, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_ty<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-2">)</span>, win, <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>px_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_ry<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-2">)</span>, win, <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>px_sr, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_sr<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-2">)</span>, win, <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>px_rz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_rz<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-2">)</span>, win, <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>px_he, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_he<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-2">)</span>, win, <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> And we compare the Amplitude Spectral Densities (figures <a href="#org0aa0d45">13</a> and <a href="#orgf325170">14</a>) </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_of<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'All OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ty<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'S-R ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_rz<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Rz ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_he<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Hexa ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org0aa0d45" class="figure"> <p><img src="figs/psd_marble_comp_lpf.png" alt="psd_marble_comp_lpf.png" /> </p> <p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the signal coming from geophone located on the marble</p> </div> <div id="orgf325170" class="figure"> <p><img src="figs/psd_marble_comp_lpf_high_freq.png" alt="psd_marble_comp_lpf_high_freq.png" /> </p> <p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the signal coming from the geophone located on the marble (zoom at high frequencies)</p> </div> </div> </div> </div> <div id="outline-container-org02fa0f5" class="outline-3"> <h3 id="org02fa0f5"><span class="section-number-3">2.5</span> Conclusion</h3> <div class="outline-text-3" id="text-2-5"> <div class="important"> <ul class="org-ul"> <li>The Ty stage induces vibrations of the marble and at the sample location above 100Hz</li> <li>The hexapod stage induces vibrations at the sample position above 220Hz</li> </ul> </div> </div> </div> </div> <div id="outline-container-org419641c" class="outline-2"> <h2 id="org419641c"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2> <div class="outline-text-2" id="text-3"> <p> <a id="org16105f2"></a> </p> <div class="note"> <p> All the files (data and Matlab scripts) are accessible <a href="data/effect_symetrie_driver.zip">here</a>. </p> </div> </div> <div id="outline-container-org0376ec1" class="outline-3"> <h3 id="org0376ec1"><span class="section-number-3">3.1</span> Experimental Setup</h3> <div class="outline-text-3" id="text-3-1"> <p> We here measure the signals of two geophones: </p> <ul class="org-ul"> <li>One is located on top of the Sample platform</li> <li>One is located on the marble</li> </ul> <p> The signal from the top geophone does go trought the slip-ring. </p> <p> All the control systems are turned OFF except the Hexapod one. </p> <p> Each measurement are done during 100s. </p> <p> The settings of the voltage amplifier are: </p> <ul class="org-ul"> <li>DC</li> <li>60dB</li> <li>1kHz</li> </ul> <p> A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier. </p> <p> The measurements are: </p> <ul class="org-ul"> <li><code>meas_018.mat</code>: Hexapod's driver on the granite</li> <li><code>meas_019.mat</code>: Hexapod's driver on the ground</li> </ul> <p> Each of the <code>mat</code> file contains one array <code>data</code> with 3 columns: </p> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <colgroup> <col class="org-right" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-right">Column number</th> <th scope="col" class="org-left">Description</th> </tr> </thead> <tbody> <tr> <td class="org-right">1</td> <td class="org-left">Geophone - Marble</td> </tr> <tr> <td class="org-right">2</td> <td class="org-left">Geophone - Sample</td> </tr> <tr> <td class="org-right">3</td> <td class="org-left">Time</td> </tr> </tbody> </table> </div> </div> <div id="outline-container-orgd322b02" class="outline-3"> <h3 id="orgd322b02"><span class="section-number-3">3.2</span> Load data</h3> <div class="outline-text-3" id="text-3-2"> <p> We load the data of the z axis of two geophones. </p> <div class="org-src-container"> <pre class="src src-matlab">d_18 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_018.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_18 = d_18.data; d_19 = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_019.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; d_19 = d_19.data; </pre> </div> </div> </div> <div id="outline-container-orgab00c14" class="outline-3"> <h3 id="orgab00c14"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3> <div class="outline-text-3" id="text-3-3"> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_19<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_19<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-2">)</span>, <span class="org-string">'DisplayName', 'Driver - Ground'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>d_18<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, d_18<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-2">)</span>, <span class="org-string">'DisplayName', 'Driver - Granite'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">50</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'bestoutside'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="orge312f8b" class="figure"> <p><img src="figs/time_domain_hexa_driver.png" alt="time_domain_hexa_driver.png" /> </p> <p><span class="figure-number">Figure 15: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p> </div> </div> </div> <div id="outline-container-orgb49b710" class="outline-3"> <h3 id="orgb49b710"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3> <div class="outline-text-3" id="text-3-4"> <div class="org-src-container"> <pre class="src src-matlab">dt = d_18<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> d_18<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> </div> <div id="outline-container-org29e0984" class="outline-4"> <h4 id="org29e0984"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4> <div class="outline-text-4" id="text-3-4-1"> <p> First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_18, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_18<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-2">)</span>, win, <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>px_19, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>d_19<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-2">)</span>, win, <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 class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_19<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Driver - Ground'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_18<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Driver - Granite'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org5b1abf9" class="figure"> <p><img src="figs/psd_hexa_driver.png" alt="psd_hexa_driver.png" /> </p> <p><span class="figure-number">Figure 16: </span>Amplitude Spectral Density of the signal coming from the top geophone</p> </div> <div id="orge028598" class="figure"> <p><img src="figs/psd_hexa_driver_high_freq.png" alt="psd_hexa_driver_high_freq.png" /> </p> <p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p> </div> </div> </div> </div> <div id="outline-container-org0edc5e7" class="outline-3"> <h3 id="org0edc5e7"><span class="section-number-3">3.5</span> Conclusion</h3> <div class="outline-text-3" id="text-3-5"> <div class="important"> <p> Even tough the Hexapod's driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground. </p> </div> </div> </div> </div> <div id="outline-container-orgf05c480" class="outline-2"> <h2 id="orgf05c480"><span class="section-number-2">4</span> Transfer function from one stage to the other</h2> <div class="outline-text-2" id="text-4"> <p> <a id="org0be507d"></a> </p> <div class="note"> <p> All the files (data and Matlab scripts) are accessible <a href="data/tf_stages_geophone.zip">here</a>. </p> </div> </div> <div id="outline-container-org314ff6f" class="outline-3"> <h3 id="org314ff6f"><span class="section-number-3">4.1</span> Experimental Setup</h3> <div class="outline-text-3" id="text-4-1"> <p> For all the measurements in this section: </p> <ul class="org-ul"> <li>all the control stages are OFF.</li> <li>the measurements are on the \(z\) direction</li> </ul> </div> <div id="outline-container-orgc56982c" class="outline-4"> <h4 id="orgc56982c"><span class="section-number-4">4.1.1</span> From Marble to Ty - <code>mat/meas_010.mat</code></h4> <div class="outline-text-4" id="text-4-1-1"> <p> One geophone is on the marble, one is on the Ty stage (see figures <a href="#orged2b8d6">18</a>, <a href="#org4f68210">19</a> and <a href="#orga6a543e">20</a>). </p> <p> The <code>data</code> array contains the following columns: </p> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <colgroup> <col class="org-right" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-right">Column</th> <th scope="col" class="org-left">Description</th> </tr> </thead> <tbody> <tr> <td class="org-right">1</td> <td class="org-left">Ground</td> </tr> <tr> <td class="org-right">2</td> <td class="org-left">Ty</td> </tr> <tr> <td class="org-right">3</td> <td class="org-left">Time</td> </tr> </tbody> </table> <div id="orged2b8d6" class="figure"> <p><img src="./img/IMG_20190430_155330.jpg" alt="IMG_20190430_155330.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 18: </span>Setup with one geophone on the marble and one on top of the translation stage</p> </div> <div id="org4f68210" class="figure"> <p><img src="./img/IMG_20190430_155335.jpg" alt="IMG_20190430_155335.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 19: </span>Setup with one geophone on the marble and one on top of the translation stage - Close up view</p> </div> <div id="orga6a543e" class="figure"> <p><img src="./img/IMG_20190430_155342.jpg" alt="IMG_20190430_155342.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 20: </span>Setup with one geophone on the marble and one on top of the translation stage - Top view</p> </div> </div> </div> <div id="outline-container-org28719df" class="outline-4"> <h4 id="org28719df"><span class="section-number-4">4.1.2</span> From Marble to Ry - <code>mat/meas_011.mat</code></h4> <div class="outline-text-4" id="text-4-1-2"> <p> One geophone is on the marble, one is on the Ry stage (see figure <a href="#org3c59300">21</a>) </p> <p> The <code>data</code> array contains the following columns: </p> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <colgroup> <col class="org-right" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-right">Column</th> <th scope="col" class="org-left">Description</th> </tr> </thead> <tbody> <tr> <td class="org-right">1</td> <td class="org-left">Ground</td> </tr> <tr> <td class="org-right">2</td> <td class="org-left">Ry</td> </tr> <tr> <td class="org-right">3</td> <td class="org-left">Time</td> </tr> </tbody> </table> <div id="org3c59300" class="figure"> <p><img src="./img/IMG_20190430_163919.jpg" alt="IMG_20190430_163919.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 21: </span>Setup with one geophone on the marble and one on top of the Tilt Stage</p> </div> </div> </div> <div id="outline-container-orgfd497bf" class="outline-4"> <h4 id="orgfd497bf"><span class="section-number-4">4.1.3</span> From Ty to Ry - <code>mat/meas_012.mat</code></h4> <div class="outline-text-4" id="text-4-1-3"> <p> One geophone is on the Ty stage, one is on the Ry stage (see figures <a href="#org87ee9cc">22</a>, <a href="#orgd4fa83b">23</a> and <a href="#org49d1927">24</a>) One geophone on the Ty stage, one geophone on the Ry stage. </p> <p> The <code>data</code> array contains the following columns: </p> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <colgroup> <col class="org-right" /> <col class="org-left" /> </colgroup> <thead> <tr> <th scope="col" class="org-right">Column</th> <th scope="col" class="org-left">Description</th> </tr> </thead> <tbody> <tr> <td class="org-right">1</td> <td class="org-left">Ty</td> </tr> <tr> <td class="org-right">2</td> <td class="org-left">Ry</td> </tr> <tr> <td class="org-right">3</td> <td class="org-left">Time</td> </tr> </tbody> </table> <div id="org87ee9cc" class="figure"> <p><img src="./img/IMG_20190430_170405.jpg" alt="IMG_20190430_170405.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 22: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage</p> </div> <div id="orgd4fa83b" class="figure"> <p><img src="./img/IMG_20190430_170418.jpg" alt="IMG_20190430_170418.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 23: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view</p> </div> <div id="org49d1927" class="figure"> <p><img src="./img/IMG_20190430_170425.jpg" alt="IMG_20190430_170425.jpg" width="500px" /> </p> <p><span class="figure-number">Figure 24: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view</p> </div> </div> </div> </div> <div id="outline-container-orgeb58991" class="outline-3"> <h3 id="orgeb58991"><span class="section-number-3">4.2</span> Load data</h3> <div class="outline-text-3" id="text-4-2"> <p> We load the data of the z axis of two geophones. </p> <div class="org-src-container"> <pre class="src src-matlab">m_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_010.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ty = m_ty.data; m_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_011.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ry = m_ry.data; ty_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_012.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_ry = ty_ry.data; </pre> </div> </div> </div> <div id="outline-container-org62dcb2b" class="outline-3"> <h3 id="org62dcb2b"><span class="section-number-3">4.3</span> Analysis - Time Domain</h3> <div class="outline-text-3" id="text-4-3"> <p> First, we can look at the time domain data. </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<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-2">)</span>, <span class="org-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="orgf85137c" class="figure"> <p><img src="figs/time_domain_m_ty.png" alt="time_domain_m_ty.png" /> </p> <p><span class="figure-number">Figure 25: </span>Time domain - Marble and translation stage</p> </div> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<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-2">)</span>, <span class="org-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org097b9c9" class="figure"> <p><img src="figs/time_domain_m_ry.png" alt="time_domain_m_ry.png" /> </p> <p><span class="figure-number">Figure 26: </span>Time domain - Marble and tilt stage</p> </div> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<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-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="orgc6dfbdc" class="figure"> <p><img src="figs/time_domain_ty_ry.png" alt="time_domain_ty_ry.png" /> </p> <p><span class="figure-number">Figure 27: </span>Time domain - Translation stage and tilt stage</p> </div> </div> </div> <div id="outline-container-org7d7634e" class="outline-3"> <h3 id="org7d7634e"><span class="section-number-3">4.4</span> Analysis - Frequency Domain</h3> <div class="outline-text-3" id="text-4-4"> <div class="org-src-container"> <pre class="src src-matlab">dt = m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <p> First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure <a href="#org25d24fa">28</a>). We also plot their coherence (figure <a href="#org95ff63f">29</a>). </p> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<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-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>T_m_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<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-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>T_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<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-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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 class="org-src-container"> <pre class="src src-matlab"><span class="org-type">figure</span>; ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty - Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold on; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; hold off; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>; linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; </pre> </div> <div id="org25d24fa" class="figure"> <p><img src="figs/compare_tf_geophones.png" alt="compare_tf_geophones.png" /> </p> <p><span class="figure-number">Figure 28: </span>Transfer function from the first geophone to the second geophone for the three experiments</p> </div> <div class="org-src-container"> <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<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-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>coh_m_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<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-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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>coh_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<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-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <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="org95ff63f" class="figure"> <p><img src="figs/coherence_two_geophones.png" alt="coherence_two_geophones.png" /> </p> <p><span class="figure-number">Figure 29: </span>Coherence between the two geophones for the three experiments</p> </div> </div> </div> <div id="outline-container-orgefefe3f" class="outline-3"> <h3 id="orgefefe3f"><span class="section-number-3">4.5</span> Conclusion</h3> <div class="outline-text-3" id="text-4-5"> <div class="important"> <p> These measurements are not relevant. </p> </div> </div> </div> </div> </div> <div id="postamble" class="status"> <p class="author">Author: Dehaeze Thomas</p> <p class="date">Created: 2019-05-10 ven. 11:35</p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> </div> </body> </html>