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< / div > < div id = "content" >
< h1 class = "title" > Vibrations induced by simultaneous scans of the translation stage and of the slip-ring< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#orge303e87" > 1. Measurement description< / a > < / li >
< li > < a href = "#orgc23d6dc" > 2. Data Analysis< / a >
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< ul >
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< li > < a href = "#org629d4b4" > 2.1. Load data< / a > < / li >
< li > < a href = "#org79a2c27" > 2.2. Voltage to Velocity< / a > < / li >
< li > < a href = "#org1bafa09" > 2.3. Time domain plots< / a > < / li >
< li > < a href = "#org05973bc" > 2.4. Frequency Domain< / a > < / li >
< li > < a href = "#org57188a5" > 2.5. Ty motion and current< / a >
< ul >
< li > < a href = "#org07bb77c" > 2.5.1. Data pre-processing< / a > < / li >
< li > < a href = "#org8bcb0f7" > 2.5.2. Time domain data< / a > < / li >
< / ul >
< / li >
< li > < a href = "#org005d22e" > 2.6. Conclusion< / a > < / li >
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< / ul >
< / li >
< / ul >
< / div >
< / div >
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< div id = "outline-container-orge303e87" class = "outline-2" >
< h2 id = "orge303e87" > < span class = "section-number-2" > 1< / span > Measurement description< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
< b > Setup< / b > :
All the stages are OFF except the translation stage and the Slip-Ring.
< / p >
< p >
Each of the signal is amplified by voltage amplifiers with the following settings:
< / p >
< ul class = "org-ul" >
< li > Gain: 40dB< / li >
< li > AC/DC option: AC< / li >
< li > Low pass filter: 1kHz< / li >
< / ul >
< p >
The slip-ring is rotating at 60rpm. At the same time, scans with the translation stage are done at 1Hz with an amplitude of 600000cnt (= 3mm).
< / p >
< p >
Two geophones are used to measure the motion in the vertical direction of the marble and of the sample.
< / p >
< p >
< b > Goal< / b > :
< / p >
< ul class = "org-ul" >
< li > The goal is to estimate the vibrations induced by the simultaneous scans of the spindle (here the slip-ring is used as the spindle is not fully functional yet) and of the translation stage< / li >
< / ul >
< p >
< b > Measurements< / b > :
< / p >
< p >
Three measurements are done:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Measurement File< / th >
< th scope = "col" class = "org-left" > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > < code > mat/data_050.mat< / code > < / td >
< td class = "org-left" > Slip-Ring at 1Hz, Ty OFF< / td >
< / tr >
< tr >
< td class = "org-left" > < code > mat/data_051.mat< / code > < / td >
< td class = "org-left" > Slip-Ring at 1Hz, Ty ON (The current and cnt error of Ty is also registered)< / td >
< / tr >
< tr >
< td class = "org-left" > < code > mat/data_052.mat< / code > < / td >
< td class = "org-left" > Slip-Ring at 1Hz, Ty 1Hz 600000cnt< / td >
< / tr >
< / tbody >
< / table >
< p >
Each of the measurement < code > mat< / code > file contains one < code > data< / code > array with 3 columns:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< th scope = "col" class = "org-right" > Column number< / th >
< th scope = "col" class = "org-left" > Description< / th >
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< / thead >
< tbody >
< tr >
< td class = "org-right" > 1< / td >
< td class = "org-left" > Geophone on the marble< / td >
< / tr >
< tr >
< td class = "org-right" > 2< / td >
< td class = "org-left" > Geophone at the sample location< / 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-orgc23d6dc" class = "outline-2" >
< h2 id = "orgc23d6dc" > < span class = "section-number-2" > 2< / span > Data Analysis< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< p >
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< a id = "org4563c51" > < / a >
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< / p >
< div class = "note" >
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/disturbance_ty_sr.zip" > here< / a > .
< / p >
< / div >
< / div >
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< div id = "outline-container-org629d4b4" class = "outline-3" >
< h3 id = "org629d4b4" > < span class = "section-number-3" > 2.1< / span > Load data< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > ty_of = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_050.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ty_of = ty_of.data;
ty_on = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_051.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ty_on = ty_on.data;
ty_1h = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'mat/data_052.mat', 'data'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; ty_1h = ty_1h.data;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org79a2c27" class = "outline-3" >
< h3 id = "org79a2c27" > < span class = "section-number-3" > 2.2< / span > Voltage to Velocity< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
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< p >
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" > 40< / span > ; < span class = "org-comment" > % [dB]< / span >
ty_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 > ty_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 > , ty_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 > ;
ty_on< 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 > ty_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_on< 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 > ;
ty_1h< 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 > ty_1h< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_1h< 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 > ;
ty_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 > ty_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 > , ty_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 > ;
ty_on< 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 > ty_on< 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 > , ty_on< 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 > ;
ty_1h< 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 > ty_1h< 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 > , ty_1h< 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-org1bafa09" class = "outline-3" >
< h3 id = "org1bafa09" > < span class = "section-number-3" > 2.3< / span > Time domain plots< / h3 >
< div class = "outline-text-3" id = "text-2-3" >
< p >
We plot the measured velocity of the marble (figure < a href = "#org53f1c30" > 1< / a > ), sample (figure < a href = "#org6938117" > 2< / a > ) and the relative velocity of the sample with respect to the marble (figure < a href = "#orgfd8af3e" > 3< / a > ).
< / p >
< p >
We also integrate the relative velocity to obtain the relative displacement (figure < a href = "#org425e005" > 4< / a > ).
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_1h< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_1h< 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 > , 'DisplayName', 'Marble < span class = "org-type" > -< / span > Ty < span class = "org-highlight-numbers-number" > 1Hz< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Marble - Ty ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_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 > , ty_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', 'Marble - Ty 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" > '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" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "org53f1c30" class = "figure" >
< p > < img src = "figs/ty_marble_time.png" alt = "ty_marble_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Velocity of the marble in the vertical direction< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_1h< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_1h< 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 > , 'DisplayName', 'Sample < span class = "org-type" > -< / span > Ty < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_on< 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', 'Sample - Ty - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_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 > , ty_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', 'Sample - Ty - 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" > '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" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "org6938117" class = "figure" >
< p > < img src = "figs/ty_sample_time.png" alt = "ty_sample_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Velocity of the sample in the vertical direction< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_1h< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_1h< 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-type" > -< / span > ty_1h< 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 > , 'DisplayName', 'Relative Velocity < span class = "org-type" > -< / span > Ty < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_on< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , ty_on< 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-type" > -< / span > ty_on< 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', 'Relative Velocity - Ty - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_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 > , ty_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-type" > -< / span > ty_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', 'Relative Velocity - Ty - 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" > '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" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "orgfd8af3e" class = "figure" >
< p > < img src = "figs/ty_relative_time.png" alt = "ty_relative_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Relative velocity of the sample with respect to the marble< / p >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_1h< 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 > , lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > s, ty_1h< 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 > ty_1h< 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 > , ty_1h< 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 > , 'DisplayName', 'Relative Displacement< span class = "org-type" > -< / span > Ty < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_on< 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 > , lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > s, ty_on< 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 > ty_on< 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 > , ty_on< 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', 'Relative Displacement- Ty - ON'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_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 > , lsim< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > s, ty_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 > ty_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 > , ty_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', 'Relative Displacement- Ty - 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" > 'Displacement < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > m< / 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" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "org425e005" class = "figure" >
< p > < img src = "figs/ty_relative_disp_time.png" alt = "ty_relative_disp_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Relative Displacement of the sample with respect to the marble< / p >
< / div >
< / div >
< / div >
< div id = "outline-container-org05973bc" class = "outline-3" >
< h3 id = "org05973bc" > < span class = "section-number-3" > 2.4< / span > Frequency Domain< / h3 >
< div class = "outline-text-3" id = "text-2-4" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > dt = ty_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 > ty_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; < span class = "org-comment" > % [Hz]< / span >
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 >
< p >
Then we compute the Power Spectral Density using < code > pwelch< / code > function.
< / p >
< p >
First 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 > pxof_m, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_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 > pxon_m, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_on< 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 > px1h_m, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_1h< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
And for the geophone located at the sample position.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxof_s, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_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 > pxon_s, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_on< 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 > px1h_s, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_1h< 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 >
Finally, for the relative velocity.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxof_r, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_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-type" > -< / span > ty_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 > pxon_r, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_on< 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-type" > -< / span > ty_on< 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 > px1h_r, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > ty_1h< 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-type" > -< / span > ty_1h< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< p >
And we plot the ASD of the measured velocities:
< / p >
< ul class = "org-ul" >
< li > figure < a href = "#org00eb9e9" > 5< / a > for the geophone located on the marble< / li >
< li > figure < a href = "#org192c441" > 6< / a > for the geophone at the sample position< / li >
< li > figure < a href = "#org1b88cd2" > 7< / a > for the relative velocity< / li >
< / ul >
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< 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 > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > px1h_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , 'DisplayName', 'Marble < span class = "org-type" > -< / span > Ty < span class = "org-highlight-numbers-number" > 1Hz< / 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 > pxon_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Marble - 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 > pxof_m< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Marble - Ty OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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hold off;
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< 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 > ASD of the measured velocity $< 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 >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / 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 > ;
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< / pre >
< / div >
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< div id = "org00eb9e9" class = "figure" >
< p > < img src = "figs/psd_marble_compare.png" alt = "psd_marble_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Comparison of the ASD of the measured velocities from the Geophone on the marble< / p >
< / div >
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< div class = "org-src-container" >
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< 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 > px1h_s< span class = "org-rainbow-delimiters-depth-2" > )< / span > , 'DisplayName', 'Sample < span class = "org-type" > -< / span > Ty < span class = "org-highlight-numbers-number" > 1Hz< / 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 > pxon_s< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Sample - 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 > pxof_s< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Sample - Ty OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
hold off;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'xscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'yscale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > '< / span > ASD of the measured velocity $< 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 >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / 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 > ;
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< / pre >
< / div >
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< div id = "org192c441" class = "figure" >
< p > < img src = "figs/psd_sample_compare.png" alt = "psd_sample_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Comparison of the ASD of the measured velocities from the Geophone at the sample location< / p >
< / div >
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< 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 > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > px1h_r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , 'DisplayName', 'Relative < span class = "org-type" > -< / span > Ty < span class = "org-highlight-numbers-number" > 1Hz< / 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 > pxon_r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Relative - 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 > pxof_r< span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'DisplayName', 'Relative - Ty OFF'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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hold off;
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< 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 > ASD of the measured velocity $< 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 >
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Location', 'southwest'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
xlim< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 500< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "org1b88cd2" class = "figure" >
< p > < img src = "figs/psd_relative_compare.png" alt = "psd_relative_compare.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > Comparison of the ASD of the relative velocity< / p >
< / div >
< / div >
< / div >
< div id = "outline-container-org57188a5" class = "outline-3" >
< h3 id = "org57188a5" > < span class = "section-number-3" > 2.5< / span > Ty motion and current< / h3 >
< div class = "outline-text-3" id = "text-2-5" >
< p >
The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
< / p >
< / div >
< div id = "outline-container-org07bb77c" class = "outline-4" >
< h4 id = "org07bb77c" > < span class = "section-number-4" > 2.5.1< / span > Data pre-processing< / h4 >
< div class = "outline-text-4" id = "text-2-5-1" >
< p >
Let's look at at the start of the csv file.
< / p >
< div class = "org-src-container" >
< pre class = "src src-bash" > sed -n < span class = "org-highlight-numbers-number" > 1,30p< / span > mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
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< / pre >
< / div >
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< p >
The real data starts at line 29.
We then load this < code > cvs< / code > file starting at line 29.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > tye_on = csvread< span class = "org-rainbow-delimiters-depth-1" > (< / span > "mat< span class = "org-type" > /< / span > Ty< span class = "org-type" > -< / span > when< span class = "org-type" > -< / span > Rz< span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > .csv", < span class = "org-highlight-numbers-number" > 29< / span > , < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
tye_1h = csvread< span class = "org-rainbow-delimiters-depth-1" > (< / span > "mat< span class = "org-type" > /< / span > Ty< span class = "org-type" > -< / span > when< span class = "org-type" > -< / span > Rz< span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > < span class = "org-type" > -< / span > and< span class = "org-type" > -< / span > Ty< span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > .csv", < span class = "org-highlight-numbers-number" > 29< / span > , < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
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< / div >
< / div >
< / div >
< div id = "outline-container-org8bcb0f7" class = "outline-4" >
< h4 id = "org8bcb0f7" > < span class = "section-number-4" > 2.5.2< / span > Time domain data< / h4 >
< div class = "outline-text-4" id = "text-2-5-2" >
< p >
We plot the position of the translation stage measured by the encoders.
< / p >
< p >
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
< / p >
< p >
The result is shown on figure < a href = "#orgfeb408e" > 8< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > tye_on< 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-rainbow-delimiters-depth-2" > (< / span > tye_on< 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 > mean< span class = "org-rainbow-delimiters-depth-3" > (< / span > tye_on< span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 200000< / 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" > 5< / 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" > '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" > 'Position < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > mm< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-string" > 'Ty - ON'< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > }< / span > < / span > < span class = "org-string" > , 'Location', 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > tye_1h< 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-rainbow-delimiters-depth-2" > (< / span > tye_1h< 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 > mean< span class = "org-rainbow-delimiters-depth-3" > (< / span > tye_1h< span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 200000< / 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" > 5< / 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" > '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" > 'Position < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > mm< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > {< / span > 'Ty < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > '< span class = "org-rainbow-delimiters-depth-2" > }< / span > , 'Location', 'northeast'< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "orgfeb408e" class = "figure" >
< p > < img src = "figs/ty_position_time.png" alt = "ty_position_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > Y position of the translation stage measured by the encoders< / p >
< / div >
< p >
We also plot the current as function of the time on figure < a href = "#orgbd294dc" > 9< / a > .
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > tye_on< 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 > , tye_on< 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-type" > -< / span > mean< span class = "org-rainbow-delimiters-depth-2" > (< / span > tye_on< 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-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" > 5< / 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" > '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" > 'Current < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > A< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-string" > 'Ty - ON'< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > }< / span > < / span > < span class = "org-string" > , 'Location', 'northeast'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
subplot< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 2< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > tye_1h< 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 > , tye_1h< 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-type" > -< / span > mean< span class = "org-rainbow-delimiters-depth-2" > (< / span > tye_1h< 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-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" > 5< / 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" > '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" > 'Current < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > A< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
legend< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > {< / span > 'Ty < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1Hz< / span > '< span class = "org-rainbow-delimiters-depth-2" > }< / span > , 'Location', 'northeast'< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div id = "orgbd294dc" class = "figure" >
< p > < img src = "figs/ty_current_time.png" alt = "ty_current_time.png" / >
< / p >
< p > < span class = "figure-number" > Figure 9: < / span > Current going through the actuator of the translation stage< / p >
< / div >
< / div >
< / div >
< / div >
< div id = "outline-container-org005d22e" class = "outline-3" >
< h3 id = "org005d22e" > < span class = "section-number-3" > 2.6< / span > Conclusion< / h3 >
< div class = "outline-text-3" id = "text-2-6" >
< div class = "important" >
< ul class = "org-ul" >
< li > < / li >
< / ul >
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< / div >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2019-05-15 15:49:48 +02:00
< p class = "date" > Created: 2019-05-15 mer. 15:49< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
< / div >
< / body >
< / html >
