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< body >
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< div id = "org-div-home-and-up" >
< a accesskey = "h" href = "../index.html" > UP < / a >
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< a accesskey = "H" href = "../index.html" > HOME < / a >
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< / div > < div id = "content" >
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< h1 class = "title" > Effect on the control system of each stages on the vibration of the station< / h1 >
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< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#orgbbaaa98" > 1. Effect of all the control systems on the Sample vibrations< / a >
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< ul >
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< li > < a href = "#org06b693f" > 1.1. Experimental Setup< / a > < / li >
< li > < a href = "#orgd47a227" > 1.2. Load data< / a > < / li >
< li > < a href = "#orgef1cef2" > 1.3. Analysis - Time Domain< / a > < / li >
< li > < a href = "#orgab71525" > 1.4. Analysis - Frequency Domain< / a >
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< ul >
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< li > < a href = "#org93314dd" > 1.4.1. Vibrations at the sample location< / a > < / li >
< li > < a href = "#org39db171" > 1.4.2. Vibrations on the marble< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org8f07d2e" > 1.5. Effect of the control system on the transmissibility from ground to sample< / a > < / li >
< li > < a href = "#org47a7f4c" > 1.6. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org96b6d66" > 2. Effect of all the control systems on the Sample vibrations - One stage at a time< / a >
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< ul >
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< li > < a href = "#org21aea52" > 2.1. Experimental Setup< / a > < / li >
< li > < a href = "#orgf9fa5d1" > 2.2. Load data< / a > < / li >
< li > < a href = "#orgb1aceca" > 2.3. Voltage to Velocity< / a > < / li >
< li > < a href = "#org9deea89" > 2.4. Analysis - Time Domain< / a > < / li >
< li > < a href = "#orga52ae70" > 2.5. Analysis - Frequency Domain< / a >
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< ul >
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< li > < a href = "#orgc044b46" > 2.5.1. Vibrations at the sample location< / a > < / li >
< li > < a href = "#orgff12b0a" > 2.5.2. Vibrations on the marble< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orgf832269" > 2.6. Conclusion< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org76bb785" > 3. Effect of the Symetrie Driver< / a >
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< ul >
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< li > < a href = "#org3e3d670" > 3.1. Experimental Setup< / a > < / li >
< li > < a href = "#org2c5eb48" > 3.2. Load data< / a > < / li >
< li > < a href = "#org7b92812" > 3.3. Analysis - Time Domain< / a > < / li >
< li > < a href = "#orgd042971" > 3.4. Analysis - Frequency Domain< / a >
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< ul >
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< li > < a href = "#orgdc25bb2" > 3.4.1. Vibrations at the sample location< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org2a573c2" > 3.5. Conclusion< / a > < / li >
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< / ul >
< / li >
< / ul >
< / div >
< / div >
< 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 >
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< div id = "outline-container-orgbbaaa98" class = "outline-2" >
< h2 id = "orgbbaaa98" > < span class = "section-number-2" > 1< / span > Effect of all the control systems on the Sample vibrations< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
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< a id = "orgdddc824" > < / a >
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< / p >
< div class = "note" >
< p >
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All the files (data and Matlab scripts) are accessible < a href = "data/effect_control_all.zip" > here< / a > .
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< / p >
< / div >
< / div >
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< div id = "outline-container-org06b693f" class = "outline-3" >
< h3 id = "org06b693f" > < span class = "section-number-3" > 1.1< / span > Experimental Setup< / h3 >
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< div class = "outline-text-3" id = "text-1-1" >
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< 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 >
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< table id = "org3dc1795" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > 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 >
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< div id = "outline-container-orgd47a227" class = "outline-3" >
< h3 id = "orgd47a227" > < span class = "section-number-3" > 1.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
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< 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 >
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< div id = "outline-container-orgef1cef2" class = "outline-3" >
< h3 id = "orgef1cef2" > < span class = "section-number-3" > 1.3< / span > Analysis - Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
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< p >
First, we can look at the time domain data and compare all the measurements:
< / p >
< ul class = "org-ul" >
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< li > comparison for the geophone at the sample location (figure < a href = "#orge122156" > 1< / a > )< / li >
< li > comparison for the geophone on the granite (figure < a href = "#org812d3e0" > 2< / a > )< / li >
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< / 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 >
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< div id = "orge122156" class = "figure" >
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< p > < img src = "figs/time_domain_sample.png" alt = "time_domain_sample.png" / >
< / p >
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< 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 >
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< / 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 >
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< div id = "org812d3e0" class = "figure" >
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< p > < img src = "figs/time_domain_marble.png" alt = "time_domain_marble.png" / >
< / p >
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< 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 >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgab71525" class = "outline-3" >
< h3 id = "orgab71525" > < span class = "section-number-3" > 1.4< / span > Analysis - Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-1-4" >
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< 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 >
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< div id = "outline-container-org93314dd" class = "outline-4" >
< h4 id = "org93314dd" > < span class = "section-number-4" > 1.4.1< / span > Vibrations at the sample location< / h4 >
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< div class = "outline-text-4" id = "text-1-4-1" >
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< 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 >
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And we compare all the signals (figures < a href = "#org7432b3d" > 3< / a > and < a href = "#orgefd2377" > 4< / a > ).
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< / 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 > ;
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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 >
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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 >
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< div id = "org7432b3d" class = "figure" >
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< p > < img src = "figs/psd_sample_comp.png" alt = "psd_sample_comp.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > Amplitude Spectral Density of the signal coming from the top geophone< / p >
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< / div >
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< div id = "orgefd2377" class = "figure" >
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< p > < img src = "figs/psd_sample_comp_high_freq.png" alt = "psd_sample_comp_high_freq.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 4: < / span > Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org39db171" class = "outline-4" >
< h4 id = "org39db171" > < span class = "section-number-4" > 1.4.2< / span > Vibrations on the marble< / h4 >
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< div class = "outline-text-4" id = "text-1-4-2" >
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< 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 >
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And we compare the Amplitude Spectral Densities (figures < a href = "#orga0ae73f" > 5< / a > and < a href = "#orgcfb23f8" > 6< / a > )
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< / 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 > ;
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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 >
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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 >
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< div id = "orga0ae73f" class = "figure" >
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< p > < img src = "figs/psd_marble_comp.png" alt = "psd_marble_comp.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 5: < / span > Amplitude Spectral Density of the signal coming from the top geophone< / p >
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< / div >
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< div id = "orgcfb23f8" class = "figure" >
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< p > < img src = "figs/psd_marble_comp_high_freq.png" alt = "psd_marble_comp_high_freq.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 6: < / span > Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org8f07d2e" class = "outline-3" >
< h3 id = "org8f07d2e" > < span class = "section-number-3" > 1.5< / span > Effect of the control system on the transmissibility from ground to sample< / h3 >
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< div class = "outline-text-3" id = "text-1-5" >
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< p >
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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 = "#orgd9f2aae" > 7< / a > ).
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< / 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 >
2019-05-15 17:24:56 +02:00
< div id = "orgd9f2aae" class = "figure" >
2019-05-02 14:06:23 +02:00
< p > < img src = "figs/trans_comp.png" alt = "trans_comp.png" / >
< / p >
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< 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 >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org47a7f4c" class = "outline-3" >
< h3 id = "org47a7f4c" > < span class = "section-number-3" > 1.6< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-1-6" >
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< 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 >
2019-05-15 17:24:56 +02:00
< div id = "outline-container-org96b6d66" class = "outline-2" >
< h2 id = "org96b6d66" > < span class = "section-number-2" > 2< / span > Effect of all the control systems on the Sample vibrations - One stage at a time< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
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< a id = "org0b65553" > < / a >
2019-05-10 16:06:43 +02:00
< / p >
< div class = "note" >
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/effect_control_one.zip" > here< / a > .
< / p >
2019-05-02 14:06:23 +02:00
< / div >
2019-05-10 16:06:43 +02:00
< / div >
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< div id = "outline-container-org21aea52" class = "outline-3" >
< h3 id = "org21aea52" > < span class = "section-number-3" > 2.1< / span > Experimental Setup< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
2019-05-02 14:06:23 +02:00
< p >
2019-05-09 09:13:10 +02:00
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 >
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The settings of the voltage amplifier are shown on figure < a href = "#orga2e0c1e" > 8< / a > :
< / p >
< ul class = "org-ul" >
< li > gain of 60dB< / li >
< li > AC/DC option set on DC< / li >
< li > Low pass filter set at 1kHz< / li >
< / ul >
< p >
2019-05-09 09:13:10 +02:00
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
< / p >
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< table id = "org879a5e4" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
2019-05-09 09:13:10 +02:00
< 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 >
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< div id = "orga2e0c1e" class = "figure" >
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< p > < img src = "./img/IMG_20190507_101459.jpg" alt = "IMG_20190507_101459.jpg" width = "500px" / >
< / p >
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< p > < span class = "figure-number" > Figure 8: < / span > Voltage amplifier settings for the measurement< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgf9fa5d1" class = "outline-3" >
< h3 id = "orgf9fa5d1" > < span class = "section-number-3" > 2.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
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< 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 >
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< div id = "outline-container-orgb1aceca" class = "outline-3" >
< h3 id = "orgb1aceca" > < span class = "section-number-3" > 2.3< / span > Voltage to Velocity< / h3 >
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< div class = "outline-text-3" id = "text-2-3" >
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< p >
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We convert the measured voltage to velocity using the function < code > voltageToVelocityL22< / code > (accessible < a href = "file:///home/thomas/MEGA/These/meas/src/index.html" > here< / a > ).
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > gain = < span class = "org-highlight-numbers-number" > 60< / span > ; < span class = "org-comment" > % [dB]< / span >
d_of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_ty< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_ry< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_sr< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_rz< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_he< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_of< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_ty< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_ry< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_sr< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_rz< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
d_he< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = voltageToVelocityL22< 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 > , 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 > , gain< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< / div >
< / div >
< div id = "outline-container-org9deea89" class = "outline-3" >
< h3 id = "org9deea89" > < span class = "section-number-3" > 2.4< / span > Analysis - Time Domain< / h3 >
< div class = "outline-text-3" id = "text-2-4" >
< p >
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First, we can look at the time domain data and compare all the measurements:
< / p >
< ul class = "org-ul" >
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< li > comparison for the geophone at the sample location (figure < a href = "#org0c06ee9" > 9< / a > )< / li >
< li > comparison for the geophone on the granite (figure < a href = "#org45a64e1" > 10< / a > )< / li >
< li > relative displacement of the sample with respect to the marble (figure < a href = "#org45a64e1" > 10< / a > )< / li >
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< / ul >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
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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 > < 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" > 2< / 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" > 2< / 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" > 2< / 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" > 2< / 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" > 2< / 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 > ;
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hold off;
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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" > 'Velocity < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > m/s< / 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 > ;
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< / pre >
< / div >
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< div id = "org0c06ee9" class = "figure" >
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< p > < img src = "figs/time_domain_sample_lpf.png" alt = "time_domain_sample_lpf.png" / >
< / p >
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< 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 >
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< / 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;
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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" > 'Velocity < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > m/s< / 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 > ;
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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 >
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< div id = "org45a64e1" class = "figure" >
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< p > < img src = "figs/time_domain_marble_lpf.png" alt = "time_domain_marble_lpf.png" / >
< / p >
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< 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 >
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< / div >
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< 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 > , < span class = "org-highlight-numbers-number" > 1e6< / span > < span class = "org-type" > *< / span > lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > , d_of< 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-type" > -< / span > d_of< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > , d_of< 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 > < 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 > , < span class = "org-highlight-numbers-number" > 1e6< / span > < span class = "org-type" > *< / span > lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / 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-type" > -< / span > d_ty< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / 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" > 3< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / 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 > , < span class = "org-highlight-numbers-number" > 1e6< / span > < span class = "org-type" > *< / span > lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / 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-type" > -< / span > d_ry< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / 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" > 3< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / 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 > , < span class = "org-highlight-numbers-number" > 1e6< / span > < span class = "org-type" > *< / span > lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / 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-type" > -< / span > d_sr< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / 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" > 3< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / 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 > , < span class = "org-highlight-numbers-number" > 1e6< / span > < span class = "org-type" > *< / span > lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / 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-type" > -< / span > d_rz< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / 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" > 3< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / 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 > , < span class = "org-highlight-numbers-number" > 1e6< / span > < span class = "org-type" > *< / span > lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / 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-type" > -< / span > d_he< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / 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" > 3< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / 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" > '< / span > Relative Displacement < span class = "org-rainbow-delimiters-depth-2" > [< / span > $< span class = "org-type" > \< / span > mu m$< 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" > 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 = "orgbad8646" class = "figure" >
< p > < img src = "figs/time_domain_relative_disp.png" alt = "time_domain_relative_disp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > Relative displacement of the sample with respect to the marble< / p >
< / div >
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< / div >
< / div >
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< div id = "outline-container-orga52ae70" class = "outline-3" >
< h3 id = "orga52ae70" > < span class = "section-number-3" > 2.5< / span > Analysis - Frequency Domain< / h3 >
< div class = "outline-text-3" id = "text-2-5" >
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< 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 >
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< div id = "outline-container-orgc044b46" class = "outline-4" >
< h4 id = "orgc044b46" > < span class = "section-number-4" > 2.5.1< / span > Vibrations at the sample location< / h4 >
< div class = "outline-text-4" id = "text-2-5-1" >
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< 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 >
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And we compare all the signals (figures < a href = "#org87295b7" > 12< / a > and < a href = "#orgd42d7db" > 13< / a > ).
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< / 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 > ;
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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 > m< span class = "org-type" > /< / span > s< 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 >
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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 >
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< div id = "org87295b7" class = "figure" >
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< p > < img src = "figs/psd_sample_comp_lpf.png" alt = "psd_sample_comp_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 12: < / span > Amplitude Spectral Density of the sample velocity< / p >
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< / div >
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< div id = "orgd42d7db" class = "figure" >
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< p > < img src = "figs/psd_sample_comp_high_freq_lpf.png" alt = "psd_sample_comp_high_freq_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 13: < / span > Amplitude Spectral Density of the sample velocity (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgff12b0a" class = "outline-4" >
< h4 id = "orgff12b0a" > < span class = "section-number-4" > 2.5.2< / span > Vibrations on the marble< / h4 >
< div class = "outline-text-4" id = "text-2-5-2" >
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< 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 >
2019-05-15 17:24:56 +02:00
And we compare the Amplitude Spectral Densities (figures < a href = "#org7f25560" > 14< / a > and < a href = "#orgc96b599" > 15< / a > )
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< / 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 > ;
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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 > m< span class = "org-type" > /< / span > s< 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 >
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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 >
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< div id = "org7f25560" class = "figure" >
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< p > < img src = "figs/psd_marble_comp_lpf.png" alt = "psd_marble_comp_lpf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 14: < / span > Amplitude Spectral Density of the marble velocity< / p >
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< / div >
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< div id = "orgc96b599" class = "figure" >
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< p > < img src = "figs/psd_marble_comp_lpf_high_freq.png" alt = "psd_marble_comp_lpf_high_freq.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 15: < / span > Amplitude Spectral Density of the marble velocity (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgf832269" class = "outline-3" >
< h3 id = "orgf832269" > < span class = "section-number-3" > 2.6< / span > Conclusion< / h3 >
< div class = "outline-text-3" id = "text-2-6" >
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< div class = "important" >
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< 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 >
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< / div >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org76bb785" class = "outline-2" >
< h2 id = "org76bb785" > < span class = "section-number-2" > 3< / span > Effect of the Symetrie Driver< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< p >
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< a id = "orga49b7fb" > < / a >
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< / p >
< div class = "note" >
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/effect_symetrie_driver.zip" > here< / a > .
< / p >
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< / div >
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< / div >
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< div id = "outline-container-org3e3d670" class = "outline-3" >
< h3 id = "org3e3d670" > < span class = "section-number-3" > 3.1< / span > Experimental Setup< / h3 >
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< div class = "outline-text-3" id = "text-3-1" >
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< 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 >
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< div id = "outline-container-org2c5eb48" class = "outline-3" >
< h3 id = "org2c5eb48" > < span class = "section-number-3" > 3.2< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-3-2" >
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< 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 >
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< div id = "outline-container-org7b92812" class = "outline-3" >
< h3 id = "org7b92812" > < span class = "section-number-3" > 3.3< / span > Analysis - Time Domain< / h3 >
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< div class = "outline-text-3" id = "text-3-3" >
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< 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 >
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< div id = "org6d6c3ee" class = "figure" >
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< p > < img src = "figs/time_domain_hexa_driver.png" alt = "time_domain_hexa_driver.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 16: < / span > Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-orgd042971" class = "outline-3" >
< h3 id = "orgd042971" > < span class = "section-number-3" > 3.4< / span > Analysis - Frequency Domain< / h3 >
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< div class = "outline-text-3" id = "text-3-4" >
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< 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 >
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< div id = "outline-container-orgdc25bb2" class = "outline-4" >
< h4 id = "orgdc25bb2" > < span class = "section-number-4" > 3.4.1< / span > Vibrations at the sample location< / h4 >
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< div class = "outline-text-4" id = "text-3-4-1" >
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< 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 >
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< div id = "orgb3d2af2" class = "figure" >
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< p > < img src = "figs/psd_hexa_driver.png" alt = "psd_hexa_driver.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 17: < / span > Amplitude Spectral Density of the signal coming from the top geophone< / p >
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< / div >
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< div id = "orgdf358e8" class = "figure" >
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< p > < img src = "figs/psd_hexa_driver_high_freq.png" alt = "psd_hexa_driver_high_freq.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 18: < / span > Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)< / p >
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< / div >
< / div >
< / div >
< / div >
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< div id = "outline-container-org2a573c2" class = "outline-3" >
< h3 id = "org2a573c2" > < span class = "section-number-3" > 3.5< / span > Conclusion< / h3 >
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< div class = "outline-text-3" id = "text-3-5" >
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< 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 >
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< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
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< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2019-05-15 mer. 17:24< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
