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< / script >
< / head >
< body >
< div id = "content" >
< h1 class = "title" > Measurement Analysis< / 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 = "#orga57c824" > 1. Measurement Description< / a > < / li >
< li > < a href = "#orgac83bb1" > 2. Importation of the data< / a > < / li >
< li > < a href = "#orge44c773" > 3. Variables for analysis< / a > < / li >
< li > < a href = "#orgcb0a2db" > 4. Coherence between the two vertical geophones on the Tilt Stage< / a > < / li >
< li > < a href = "#orgc619b39" > 5. Data Post Processing< / a > < / li >
< li > < a href = "#org03ef418" > 6. Normalization< / a > < / li >
< li > < a href = "#org8583637" > 7. Measurement 1 - Effect of Ty stage< / a > < / li >
< li > < a href = "#org47192a7" > 8. Measurement 2 - Effect of Ry stage< / a > < / li >
< li > < a href = "#org0c3a1d4" > 9. Measurement 3 - Effect of the Hexapod< / a > < / li >
< li > < a href = "#org1529580" > 10. Measurement 4 - Effect of the Splip-Ring and Spindle< / a > < / li >
< li > < a href = "#orga767d61" > 11. Measurement 5 - Transmission from ground to marble< / a > < / li >
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< / ul >
< / div >
< / div >
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< p >
< a href = "../index.html" > Back to main page< / a > .
< / p >
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< div id = "outline-container-orga57c824" class = "outline-2" >
< h2 id = "orga57c824" > < span class = "section-number-2" > 1< / span > Measurement Description< / h2 >
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< div class = "outline-text-2" id = "text-1" >
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< div id = "orgc56bc67" class = "figure" >
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< p > < img src = "./figs/setup_picture.png" alt = "setup_picture.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Picture of the setup for the measurement< / p >
< / div >
< p >
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The sensor used are 3 L-4C geophones (< a href = "../actuators-sensors/index.html#MissingReference" > Documentation< / a > ).
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< / p >
< p >
Each motor are turn off and then on.
< / p >
< p >
The goal is to see what noise is injected in the system due to the regulation loop of each stage.
< / p >
< / div >
< / div >
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< div id = "outline-container-orgac83bb1" class = "outline-2" >
< h2 id = "orgac83bb1" > < span class = "section-number-2" > 2< / span > Importation of the data< / h2 >
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< div class = "outline-text-2" id = "text-2" >
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< p >
First, load all the measurement files:
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > meas = < span class = "org-rainbow-delimiters-depth-1" > {}< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > './mat/Measurement1.mat'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > './mat/Measurement2.mat'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > './mat/Measurement3.mat'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > './mat/Measurement4.mat'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > = load< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > './mat/Measurement5.mat'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
< p >
Change the track name for measurements 3 and 4.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_Name = 'Input < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > Hexa Z';
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_Name = 'Input < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > Hexa Z';
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< / pre >
< / div >
< p >
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For the measurements 1 to 4, the measurement channels are shown table < a href = "#org7e4418b" > 1< / a > .
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< / p >
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< table id = "org7e4418b" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Channels for measurements 1 to 4< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" >   < / th >
< th scope = "col" class = "org-left" > Channel 1< / th >
< th scope = "col" class = "org-left" > Channel 2< / th >
< th scope = "col" class = "org-left" > Channel 3< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Meas. 1< / td >
< td class = "org-left" > Input 1: tilt1 Z< / td >
< td class = "org-left" > Input 2: tilt2 Z< / td >
< td class = "org-left" > Input 3: Ty Y< / td >
< / tr >
< tr >
< td class = "org-left" > Meas. 2< / td >
< td class = "org-left" > Input 1: tilt1 Z< / td >
< td class = "org-left" > Input 2: tilt2 Z< / td >
< td class = "org-left" > Input 3: Ty Y< / td >
< / tr >
< tr >
< td class = "org-left" > Meas. 3< / td >
< td class = "org-left" > Input 1: Hexa Z< / td >
< td class = "org-left" > Input 2: tilt2 Z< / td >
< td class = "org-left" > Input 3: Ty Y< / td >
< / tr >
< tr >
< td class = "org-left" > Meas. 4< / td >
< td class = "org-left" > Input 1: Hexa Z< / td >
< td class = "org-left" > Input 2: tilt2 Z< / td >
< td class = "org-left" > Input 3: Ty Y< / td >
< / tr >
< / tbody >
< / table >
< p >
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For the measurement 5, the channels are shown table < a href = "#org00892de" > 2< / a > .
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< / p >
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< table id = "org00892de" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > Channels for measurement 5< / caption >
< colgroup >
< 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" >   < / th >
< th scope = "col" class = "org-left" > Channel 1< / th >
< th scope = "col" class = "org-left" > Channel 2< / th >
< th scope = "col" class = "org-left" > Channel 3< / th >
< th scope = "col" class = "org-left" > Channel 4< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Meas. 5< / td >
< td class = "org-left" > Input 1: Floor Z< / td >
< td class = "org-left" > Input 2: Marble Z< / td >
< td class = "org-left" > Input 3: Floor Y< / td >
< td class = "org-left" > Input 4: Marble Y< / td >
< / tr >
< / tbody >
< / table >
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< / div >
< / div >
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< div id = "outline-container-orge44c773" class = "outline-2" >
< h2 id = "orge44c773" > < span class = "section-number-2" > 3< / span > Variables for analysis< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< p >
We define the sampling frequency and the time vectors for the plots.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > Fs = < span class = "org-highlight-numbers-number" > 256< / span > ; < span class = "org-comment" > % [Hz]< / span >
dt = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
t1 = dt< span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-type" > :< / span > length< span class = "org-rainbow-delimiters-depth-2" > (< / span > meas< span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
t2 = dt< span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-type" > :< / span > length< span class = "org-rainbow-delimiters-depth-2" > (< / span > meas< span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
t3 = dt< span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-type" > :< / span > length< span class = "org-rainbow-delimiters-depth-2" > (< / span > meas< span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
t4 = dt< span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-type" > :< / span > length< span class = "org-rainbow-delimiters-depth-2" > (< / span > meas< span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
t5 = dt< span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > [< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-type" > :< / span > length< span class = "org-rainbow-delimiters-depth-2" > (< / span > meas< span class = "org-rainbow-delimiters-depth-3" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > ;
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< / pre >
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< p >
For the frequency analysis, we define the frequency limits for the plot.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > fmin = < span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-comment" > % [Hz]< / span >
fmax = < span class = "org-highlight-numbers-number" > 100< / span > ; < span class = "org-comment" > % [Hz]< / span >
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< / pre >
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< p >
Then we define the windows that will be used to average the results.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > psd_window = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > fmin< span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgcb0a2db" class = "outline-2" >
< h2 id = "orgcb0a2db" > < span class = "section-number-2" > 4< / span > Coherence between the two vertical geophones on the Tilt Stage< / h2 >
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< div class = "outline-text-2" id = "text-4" >
< p >
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We first compute the coherence between the two geophones located on the tilt stage. The result is shown on figure < a href = "#org3d4d6fd" > 2< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > coh, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = mscohere< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "org3d4d6fd" class = "figure" >
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< p > < img src = "figs/coherence_vertical_tilt_sensors.png" alt = "coherence_vertical_tilt_sensors.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Coherence between the two vertical sensors positionned on the Tilt Stage< / p >
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< p >
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We then compute the transfer function from one sensor to the other (figure < a href = "#org62100a4" > 3< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > tf23, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = tfestimate< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "org62100a4" class = "figure" >
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< p > < img src = "figs/tf_vertical_tilt_sensors.png" alt = "tf_vertical_tilt_sensors.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Transfer function from one vertical geophone on the tilt stage to the other vertical geophone on the tilt stage< / p >
< / div >
< p >
Even though the coherence is not very good, we observe no resonance between the two sensors.
< / p >
< / div >
< / div >
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< div id = "outline-container-orgc619b39" class = "outline-2" >
< h2 id = "orgc619b39" > < span class = "section-number-2" > 5< / span > Data Post Processing< / h2 >
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< div class = "outline-text-2" id = "text-5" >
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< p >
When using two geophone sensors on the same tilt stage (measurements 1 and 2), we post-process the data to obtain the z displacement and the rotation of the tilt stage:
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > meas1_z = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-type" > +< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
meas1_tilt = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-type" > -< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1 = meas1_z;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_Y_Magnitude = < span class = "org-string" > 'Meter / second'< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_Name = < span class = "org-string" > 'Ry Z'< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2 = meas1_tilt;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_Y_Magnitude = < span class = "org-string" > 'Rad / second'< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_Name = < span class = "org-string" > 'Ry Tilt'< / span > ;
meas2_z = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-type" > +< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
meas2_tilt = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-type" > -< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1 = meas2_z;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_Y_Magnitude = < span class = "org-string" > 'Meter / second'< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_Name = < span class = "org-string" > 'Ry Z'< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2 = meas2_tilt;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_Y_Magnitude = < span class = "org-string" > 'Rad / second'< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_Name = < span class = "org-string" > 'Ry Tilt'< / span > ;
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< / pre >
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< div id = "outline-container-org03ef418" class = "outline-2" >
< h2 id = "org03ef418" > < span class = "section-number-2" > 6< / span > Normalization< / h2 >
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< div class = "outline-text-2" id = "text-6" >
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< p >
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Parameters of the geophone are defined below.
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The transfer function from geophone velocity to measured voltage is shown on figure < a href = "#org47ba141" > 4< / a > .
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< / p >
< p >
Measurements will be normalized by the inverse of this transfer function in order to go from voltage measurement to velocity measurement.
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > L4C_w0 = < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > ; < span class = "org-comment" > % [rad/s]< / span >
L4C_ksi = < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 28< / span > ;
L4C_G0 = < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ; < span class = "org-comment" > % [V/(m/s)]< / span >
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[Omitted long matching line]
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< div id = "org47ba141" class = "figure" >
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< p > < img src = "figs/L4C_bode_plot.png" alt = "L4C_bode_plot.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 4: < / span > Bode plot of the L4C Geophone< / p >
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< / div >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track4 = < span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track4< span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ./< / span > < span class = "org-highlight-numbers-number" > 276< / span > .< span class = "org-highlight-numbers-number" > 8< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1, t1< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2, t1< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3, t1< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1, t2< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2, t2< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3, t2< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1, t3< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2, t3< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3, t3< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1, t4< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2, t4< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3, t4< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track1_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1, t5< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track2_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2, t5< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track3_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3, t5< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
meas< span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > .Track4_norm = lsim< span class = "org-rainbow-delimiters-depth-1" > (< / span > inv< span class = "org-rainbow-delimiters-depth-2" > (< / span > L4C_G< span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track4, t5< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< / div >
< / div >
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< div id = "outline-container-org8583637" class = "outline-2" >
< h2 id = "org8583637" > < span class = "section-number-2" > 7< / span > Measurement 1 - Effect of Ty stage< / h2 >
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< div class = "outline-text-2" id = "text-7" >
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< p >
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The configuration for this measurement is shown table < a href = "#orgc1f3234" > 3< / a > .
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< / p >
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< table id = "orgc1f3234" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 3:< / span > Stages configuration - Measurement 1< / caption >
< colgroup >
< col class = "org-left" / >
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< col class = "org-left" / >
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< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Time< / th >
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< th scope = "col" class = "org-left" > 0-309< / th >
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< th scope = "col" class = "org-left" > 309-end< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Ty< / td >
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< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< / tr >
< tr >
< td class = "org-left" > Ry< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > SlipRing< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > Spindle< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > Hexa< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
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< / tr >
< / tbody >
< / table >
< p >
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We then plot the measurements in time domain (figure < a href = "#orgf931943" > 5< / a > ).
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< / p >
< div class = "important" >
< p >
We observe strange behavior when the Ty stage is turned on.
How can we explain that?
< / p >
< / div >
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< div id = "orgf931943" class = "figure" >
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< p > < img src = "figs/meas1.png" alt = "meas1.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 5: < / span > Time domain - measurement 1< / p >
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< / div >
< p >
To understand what is going on, instead of looking at the velocity, we can look at the displacement by integrating the data. The displacement is computed by integrating the velocity using < code > cumtrapz< / code > function.
< / p >
< p >
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Then we plot the position with respect to time (figure < a href = "#orgb6bceab" > 6< / a > ).
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< / p >
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< div id = "orgb6bceab" class = "figure" >
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< p > < img src = "figs/meas1_disp.png" alt = "meas1_disp.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 6: < / span > Y displacement of the Ty stage< / p >
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< / div >
< p >
We when compute the power spectral density of each measurement before and after turning on the stage.
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx111, f11< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 300< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx112, f12< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 350< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx121, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 300< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx122, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 350< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx131, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 300< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx132, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 350< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
< p >
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We finally plot the power spectral density of each track (figures < a href = "#org767e453" > 7< / a > , < a href = "#org8cd1899" > 8< / a > , < a href = "#org3030170" > 9< / a > ).
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< / p >
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< div id = "org767e453" class = "figure" >
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< p > < img src = "figs/meas1_ry_z_psd.png" alt = "meas1_ry_z_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 7: < / span > PSD of the Z velocity of Ry stage - measurement 1< / p >
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< / div >
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< div id = "org8cd1899" class = "figure" >
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< p > < img src = "figs/meas1_ry_tilt_psd.png" alt = "meas1_ry_tilt_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 8: < / span > PSD of the Rotation of Ry Stage - measurement 1< / p >
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< / div >
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< div id = "org3030170" class = "figure" >
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< p > < img src = "figs/meas1_ty_y_psd.png" alt = "meas1_ty_y_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 9: < / span > PSD of the Ty velocity in the Y direction - measurement 1< / p >
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< / div >
< div class = "important" >
< p >
Turning on the Y-translation stage increases the velocity of the Ty stage in the Y direction and the rotation motion of the tilt stage:
< / p >
< ul class = "org-ul" >
< li > at 20Hz< / li >
< li > at 40Hz< / li >
< li > between 80Hz and 90Hz< / li >
< / ul >
< p >
It does not seems to have any effect on the Z motion of the tilt stage.
< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org47192a7" class = "outline-2" >
< h2 id = "org47192a7" > < span class = "section-number-2" > 8< / span > Measurement 2 - Effect of Ry stage< / h2 >
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< div class = "outline-text-2" id = "text-8" >
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< p >
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The tilt stage is turned ON at around 326 seconds (table < a href = "#orgba0882e" > 4< / a > ).
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< / p >
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< table id = "orgba0882e" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 4:< / span > Stages configuration - Measurement 2< / caption >
< colgroup >
< col class = "org-left" / >
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< col class = "org-left" / >
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< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Time< / th >
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< th scope = "col" class = "org-left" > 0-326< / th >
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< th scope = "col" class = "org-left" > 326-end< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td class = "org-left" > Ty< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > Ry< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< / tr >
< tr >
< td class = "org-left" > SlipRing< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > Spindle< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > Hexa< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
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< / tr >
< / tbody >
< / table >
< p >
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We plot the time domain (figure < a href = "#org9bf6e90" > 10< / a > ) and we don't observe anything special in the time domain.
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< / p >
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< div id = "org9bf6e90" class = "figure" >
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< p > < img src = "figs/meas2.png" alt = "meas2.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 10: < / span > Time domain - measurement 2< / p >
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< / div >
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< div id = "org767f834" class = "figure" >
< p > < img src = "figs/meas2_disp.png" alt = "meas2_disp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > Time domain - measurement 2< / p >
< / div >
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< p >
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We compute the PSD of each track and we plot them (figures < a href = "#org23fbfb4" > 12< / a > , < a href = "#org7a18c86" > 13< / a > and < a href = "#orgdcf33e8" > 14< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx211, f21< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 326< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx212, f22< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 326< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx221, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 326< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx222, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 326< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx231, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 326< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx232, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 326< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "org23fbfb4" class = "figure" >
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< p > < img src = "figs/meas2_ry_z_psd.png" alt = "meas2_ry_z_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 12: < / span > PSD of the Z velocity of Ry Stage - measurement 2< / p >
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< / div >
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< div id = "org7a18c86" class = "figure" >
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< p > < img src = "figs/meas2_ry_tilt_psd.png" alt = "meas2_ry_tilt_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 13: < / span > PSD of the Rotation motion of Ry Stage - measurement 2< / p >
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< / div >
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< div id = "orgdcf33e8" class = "figure" >
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< p > < img src = "figs/meas2_ty_y_psd.png" alt = "meas2_ty_y_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 14: < / span > PSD of the Ty velocity in the Y direction - measurement 2< / p >
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< / div >
< div class = "important" >
< p >
We observe no noticeable difference when the Tilt-stage is turned ON expect a small decrease of the Z motion of the tilt stage around 10Hz.
< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org0c3a1d4" class = "outline-2" >
< h2 id = "org0c3a1d4" > < span class = "section-number-2" > 9< / span > Measurement 3 - Effect of the Hexapod< / h2 >
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< div class = "outline-text-2" id = "text-9" >
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< p >
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The hexapod is turned off after 406 seconds (table < a href = "#org8b4187d" > 5< / a > ).
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< / p >
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< table id = "org8b4187d" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 5:< / span > Stages configuration - Measurement 3< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Time< / th >
< th scope = "col" class = "org-left" > 0-406< / th >
< th scope = "col" class = "org-left" > 406-end< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td class = "org-left" > Ty< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > Ry< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< / tr >
< tr >
< td class = "org-left" > SlipRing< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< tr >
< td class = "org-left" > Spindle< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
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< / tr >
< tr >
< td class = "org-left" > Hexa< / td >
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< td class = "org-left" > < b > ON< / b > < / td >
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< td class = "org-left" > OFF< / td >
< / tr >
< / tbody >
< / table >
< p >
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The time domain result is shown figure < a href = "#org08fc17d" > 15< / a > .
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< / p >
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< div id = "org08fc17d" class = "figure" >
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< p > < img src = "figs/meas3.png" alt = "meas3.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 15: < / span > Time domain - measurement 3< / p >
< / div >
< div id = "org4ae7ca4" class = "figure" >
< p > < img src = "figs/meas3_disp.png" alt = "meas3_disp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 16: < / span > Time domain - measurement 3< / p >
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< / div >
< p >
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We then compute the PSD of each track before and after turning off the hexapod and plot the results in the figures < a href = "#org0c4287e" > 17< / a > , < a href = "#org899151a" > 18< / a > and < a href = "#org0fc8e31" > 19< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx311, f31< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 400< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx312, f32< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 420< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx321, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 400< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx322, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 420< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx331, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > :< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 400< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx332, < span class = "org-type" > ~< / span > < span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-highlight-numbers-number" > 420< / span > < span class = "org-type" > /< / span > dt< span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > :< / span > end< span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "org0c4287e" class = "figure" >
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< p > < img src = "figs/meas3_hexa_z_psd.png" alt = "meas3_hexa_z_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 17: < / span > PSD of the Z velocity of the Hexapod - measurement 3< / p >
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< / div >
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< div id = "org899151a" class = "figure" >
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< p > < img src = "figs/meas3_ry_z_psd.png" alt = "meas3_ry_z_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 18: < / span > PSD of the Z velocity of the Ry stage - measurement 3< / p >
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< / div >
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< div id = "org0fc8e31" class = "figure" >
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< p > < img src = "figs/meas3_ty_y_psd.png" alt = "meas3_ty_y_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 19: < / span > PSD of the Ty velocity in the Y direction - measurement 3< / p >
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< / div >
< div class = "important" >
< p >
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Turning ON induces some motion on the hexapod in the z direction (figure < a href = "#org0c4287e" > 17< / a > ), on the tilt stage in the z direction (figure < a href = "#org899151a" > 18< / a > ) and on the y motion of the Ty stage (figure < a href = "#org0fc8e31" > 19< / a > ):
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< / p >
< ul class = "org-ul" >
< li > at 17Hz< / li >
< li > at 34Hz< / li >
< / ul >
< / div >
< / div >
< / div >
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< div id = "outline-container-org1529580" class = "outline-2" >
< h2 id = "org1529580" > < span class = "section-number-2" > 10< / span > Measurement 4 - Effect of the Splip-Ring and Spindle< / h2 >
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< div class = "outline-text-2" id = "text-10" >
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< p >
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The slip ring is turned on at 300s, then the spindle is turned on at 620s (table < a href = "#org274f078" > 6< / a > ). The time domain signals are shown figure < a href = "#orgf0966f9" > 20< / a > .
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< / p >
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< table id = "org274f078" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 6:< / span > Stages configuration - Measurement 4< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Time< / th >
< th scope = "col" class = "org-left" > 0-300< / th >
< th scope = "col" class = "org-left" > 300-620< / th >
< th scope = "col" class = "org-left" > 620-end< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td class = "org-left" > Ty< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
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< td class = "org-left" > OFF< / td >
< / tr >
< tr >
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< td class = "org-left" > Ry< / td >
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< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< / tr >
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< tr >
< td class = "org-left" > SlipRing< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > < b > ON< / b > < / td >
< td class = "org-left" > < b > ON< / b > < / td >
< / tr >
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< tr >
< td class = "org-left" > Spindle< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
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< td class = "org-left" > < b > ON< / b > < / td >
< / tr >
< tr >
< td class = "org-left" > Hexa< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
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< / tr >
< / tbody >
< / table >
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< div id = "orgf0966f9" class = "figure" >
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< p > < img src = "figs/meas4.png" alt = "meas4.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 20: < / span > Time domain - measurement 4< / p >
< / div >
< p >
If we integrate this signal, we obtain Figure < a href = "#org62b5bdf" > 21< / a > .
< / p >
< div id = "org62b5bdf" class = "figure" >
< p > < img src = "figs/meas4_int.png" alt = "meas4_int.png" / >
< / p >
< p > < span class = "figure-number" > Figure 21: < / span > Time domain - measurement 4< / p >
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< / div >
< p >
The PSD of each track are computed using the code below.
< / p >
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< div id = "orgfd7f8ce" class = "figure" >
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< p > < img src = "figs/meas4_hexa_z_psd.png" alt = "meas4_hexa_z_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 22: < / span > PSD of the Z velocity of the Hexapod - measurement 4< / p >
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< / div >
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< p >
We plot the PSD of the displacement.
< / p >
< div id = "org917dbdc" class = "figure" >
< p > < img src = "figs/meas4_hexa_z_psd_int.png" alt = "meas4_hexa_z_psd_int.png" / >
< / p >
< p > < span class = "figure-number" > Figure 23: < / span > PSD< sub > INT< / sub > of the Z velocity of the Hexapod - measurement 4< / p >
< / div >
< p >
And we compute the Cumulative amplitude spectrum.
< / p >
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< div id = "orge4b6d59" class = "figure" >
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< p > < img src = "figs/meas4_ry_z_psd.png" alt = "meas4_ry_z_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 24: < / span > PSD of the Ry rotation in the Y direction - measurement 4< / p >
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< / div >
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< div id = "org08ad3dc" class = "figure" >
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< p > < img src = "figs/meas4_ty_y_psd.png" alt = "meas4_ty_y_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 25: < / span > PSD of the Ty velocity in the Y direction - measurement 4< / p >
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< / div >
< div class = "important" >
< p >
Turning ON the splipring seems to not add motions on the stages measured.
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It even seems to lower the motion of the Ty stage (figure < a href = "#org08ad3dc" > 25< / a > ): does that make any sense?
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< / p >
< p >
Turning ON the spindle induces motions:
< / p >
< ul class = "org-ul" >
< li > at 5Hz on each motion measured< / li >
< li > at 22.5Hz on the Z motion of the Hexapod. Can this is due to some 50Hz?< / li >
< li > at 62Hz on each motion measured< / li >
< / ul >
< / div >
< / div >
< / div >
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< div id = "outline-container-orga767d61" class = "outline-2" >
< h2 id = "orga767d61" > < span class = "section-number-2" > 11< / span > Measurement 5 - Transmission from ground to marble< / h2 >
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< div class = "outline-text-2" id = "text-11" >
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< p >
This measurement just consists of measurement of Y-Z motion of the ground and the marble.
< / p >
< p >
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The time domain signals are shown on figure < a href = "#orgc513617" > 26< / a > .
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< / p >
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< div id = "orgc513617" class = "figure" >
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< p > < img src = "figs/meas5.png" alt = "meas5.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 26: < / span > Time domain - measurement 5< / p >
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< / div >
< p >
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We compute the PSD of each track and we plot the PSD of the Z motion for the ground and marble on figure < a href = "#org28b0b94" > 27< / a > and for the Y motion on figure < a href = "#orgf797eae" > 28< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx51, f51< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx52, f52< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx53, f53< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx54, f54< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track4< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
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< div id = "org28b0b94" class = "figure" >
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< p > < img src = "figs/meas5_z_psd.png" alt = "meas5_z_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 27: < / span > PSD of the ground and marble in the Z direction< / p >
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< / div >
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< div id = "orgf797eae" class = "figure" >
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< p > < img src = "figs/meas5_y_psd.png" alt = "meas5_y_psd.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 28: < / span > PSD of the ground and marble in the Y direction< / p >
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< / div >
< p >
Then, instead of looking at the Power Spectral Density, we can try to estimate the transfer function from a ground motion to the motion of the marble.
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The transfer functions are shown on figure < a href = "#orgbb283a9" > 29< / a > and the coherence on figure < a href = "#orga357e58" > 30< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > tfz, fz< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = tfestimate< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > tfy, fy< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = tfestimate< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track4< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
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< div id = "orgbb283a9" class = "figure" >
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< p > < img src = "figs/meas5_tf.png" alt = "meas5_tf.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 29: < / span > Transfer function estimation - measurement 5< / p >
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< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > cohz, fz< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = mscohere< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track1< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track2< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > cohy, fy< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = mscohere< span class = "org-rainbow-delimiters-depth-1" > (< / span > meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track3< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , meas< span class = "org-rainbow-delimiters-depth-2" > {< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-2" > }< / span > .Track4< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , psd_window, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "orga357e58" class = "figure" >
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< p > < img src = "figs/meas5_coh.png" alt = "meas5_coh.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 30: < / span > Coherence - measurement 5< / p >
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< / div >
< div class = "important" >
< p >
The marble seems to have a resonance at around 20Hz on the Y direction.
But the coherence is not good above 20Hz, so it is difficult to estimate resonances.
< / p >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Thomas Dehaeze< / p >
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< p class = "date" > Created: 2019-04-02 mar. 10:39< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
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