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< / 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 = "#org97f7c38" > 1. Importation of the data< / a > < / li >
< li > < a href = "#org8d71b56" > 2. Variables for analysis< / a > < / li >
< li > < a href = "#org8c58541" > 3. Measurement 1 - Effect of Ty stage< / a > < / li >
< li > < a href = "#orgedf4013" > 4. Measurement 2 - Effect of Ry stage< / a > < / li >
< li > < a href = "#org3e2fd81" > 5. Measurement 3 - Effect of the Hexapod< / a > < / li >
< li > < a href = "#org6fea2ed" > 6. Measurement 4 - Effect of the Splip-Ring and Spindle< / a > < / li >
< li > < a href = "#org3df0c76" > 7. 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 >
< div id = "outline-container-org97f7c38" class = "outline-2" >
< h2 id = "org97f7c38" > < span class = "section-number-2" > 1< / span > Importation of the data< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< p >
First, load all the measurement files:
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > meas = < span style = "color: #DCDCCC;" > {}< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #DCDCCC;" > }< / span > = load< span style = "color: #DCDCCC;" > (< / span > < span style = "color: #CC9393;" > './mat/Measurement1.mat'< / span > < span style = "color: #DCDCCC;" > )< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #DCDCCC;" > }< / span > = load< span style = "color: #DCDCCC;" > (< / span > < span style = "color: #CC9393;" > './mat/Measurement2.mat'< / span > < span style = "color: #DCDCCC;" > )< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #DCDCCC;" > }< / span > = load< span style = "color: #DCDCCC;" > (< / span > < span style = "color: #CC9393;" > './mat/Measurement3.mat'< / span > < span style = "color: #DCDCCC;" > )< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 4< / span > < span style = "color: #DCDCCC;" > }< / span > = load< span style = "color: #DCDCCC;" > (< / span > < span style = "color: #CC9393;" > './mat/Measurement4.mat'< / span > < span style = "color: #DCDCCC;" > )< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #DCDCCC;" > }< / span > = load< span style = "color: #DCDCCC;" > (< / span > < span style = "color: #CC9393;" > './mat/Measurement5.mat'< / span > < span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / 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 style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1_Name = 'Input < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > Hexa Z';
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 4< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1_Name = 'Input < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > Hexa Z';
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< / pre >
< / div >
< p >
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For the measurements 1 to 4, the measurement channels are shown table < a href = "#org5a4bbfa" > 1< / a > .
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< / p >
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< table id = "org5a4bbfa" 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 = "#org3cb3f90" > 2< / a > .
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< / p >
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< table id = "org3cb3f90" 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 >
< p >
When using two geophone sensors on the same tilt stage (measurements 1 and 2), we post-process the data to obtain the z displacement and the rotation of the tilt stage:
< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > meas1_z = < span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #7CB8BB;" > +< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #DCDCCC;" > )< / span > < span style = "color: #7CB8BB;" > /< / span > < span style = "color: #BFEBBF;" > 2< / span > ;
meas1_tilt = < span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #7CB8BB;" > -< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #DCDCCC;" > )< / span > < span style = "color: #7CB8BB;" > /< / span > < span style = "color: #BFEBBF;" > 2< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1 = meas1_z;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1_Y_Magnitude = < span style = "color: #CC9393;" > 'Meter / second'< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1_Name = < span style = "color: #CC9393;" > 'Ry Z'< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #DCDCCC;" > }< / span > .Track2 = meas1_tilt;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #DCDCCC;" > }< / span > .Track2_Y_Magnitude = < span style = "color: #CC9393;" > 'Rad / second'< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #DCDCCC;" > }< / span > .Track2_Name = < span style = "color: #CC9393;" > 'Ry Tilt'< / span > ;
meas2_z = < span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #7CB8BB;" > +< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #DCDCCC;" > )< / span > < span style = "color: #7CB8BB;" > /< / span > < span style = "color: #BFEBBF;" > 2< / span > ;
meas2_tilt = < span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #7CB8BB;" > -< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #DCDCCC;" > )< / span > < span style = "color: #7CB8BB;" > /< / span > < span style = "color: #BFEBBF;" > 2< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1 = meas2_z;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1_Y_Magnitude = < span style = "color: #CC9393;" > 'Meter / second'< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #DCDCCC;" > }< / span > .Track1_Name = < span style = "color: #CC9393;" > 'Ry Z'< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #DCDCCC;" > }< / span > .Track2 = meas2_tilt;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #DCDCCC;" > }< / span > .Track2_Y_Magnitude = < span style = "color: #CC9393;" > 'Rad / second'< / span > ;
meas< span style = "color: #DCDCCC;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #DCDCCC;" > }< / span > .Track2_Name = < span style = "color: #CC9393;" > 'Ry Tilt'< / span > ;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org8d71b56" class = "outline-2" >
< h2 id = "org8d71b56" > < span class = "section-number-2" > 2< / span > Variables for analysis< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< 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 style = "color: #BFEBBF;" > 256< / span > ; < span style = "color: #7F9F7F;" > % [Hz]< / span >
dt = < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > /< / span > < span style = "color: #DCDCCC;" > (< / span > Fs< span style = "color: #DCDCCC;" > )< / span > ;
t1 = dt< span style = "color: #7CB8BB;" > *< / span > < span style = "color: #DCDCCC;" > [< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > length< span style = "color: #BFEBBF;" > (< / span > meas< span style = "color: #D0BF8F;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #D0BF8F;" > }< / span > .Track1< span style = "color: #BFEBBF;" > )< / span > < span style = "color: #DCDCCC;" > ]< / span > ;
t2 = dt< span style = "color: #7CB8BB;" > *< / span > < span style = "color: #DCDCCC;" > [< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > length< span style = "color: #BFEBBF;" > (< / span > meas< span style = "color: #D0BF8F;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #D0BF8F;" > }< / span > .Track1< span style = "color: #BFEBBF;" > )< / span > < span style = "color: #DCDCCC;" > ]< / span > ;
t3 = dt< span style = "color: #7CB8BB;" > *< / span > < span style = "color: #DCDCCC;" > [< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > length< span style = "color: #BFEBBF;" > (< / span > meas< span style = "color: #D0BF8F;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #D0BF8F;" > }< / span > .Track1< span style = "color: #BFEBBF;" > )< / span > < span style = "color: #DCDCCC;" > ]< / span > ;
t4 = dt< span style = "color: #7CB8BB;" > *< / span > < span style = "color: #DCDCCC;" > [< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > length< span style = "color: #BFEBBF;" > (< / span > meas< span style = "color: #D0BF8F;" > {< / span > < span style = "color: #BFEBBF;" > 4< / span > < span style = "color: #D0BF8F;" > }< / span > .Track1< span style = "color: #BFEBBF;" > )< / span > < span style = "color: #DCDCCC;" > ]< / span > ;
t5 = dt< span style = "color: #7CB8BB;" > *< / span > < span style = "color: #DCDCCC;" > [< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > length< span style = "color: #BFEBBF;" > (< / span > meas< span style = "color: #D0BF8F;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #D0BF8F;" > }< / span > .Track1< span style = "color: #BFEBBF;" > )< / span > < span style = "color: #DCDCCC;" > ]< / span > ;
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< / pre >
< / div >
< 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 style = "color: #BFEBBF;" > 1< / span > ; < span style = "color: #7F9F7F;" > % [Hz]< / span >
fmax = < span style = "color: #BFEBBF;" > 100< / span > ; < span style = "color: #7F9F7F;" > % [Hz]< / span >
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< / pre >
< / div >
< 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 style = "color: #DCDCCC;" > (< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #7CB8BB;" > *< / span > fmin< span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org8c58541" class = "outline-2" >
< h2 id = "org8c58541" > < span class = "section-number-2" > 3< / span > Measurement 1 - Effect of Ty stage< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< p >
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The configuration for this measurement is shown table < a href = "#orgb1cd997" > 3< / a > .
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< / p >
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< table id = "orgb1cd997" 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" / >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Time< / th >
< th scope = "col" class = "org-right" > 0-309< / th >
< th scope = "col" class = "org-left" > 309-end< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Ty< / td >
< td class = "org-right" > OFF< / td >
< td class = "org-left" > ON< / td >
< / tr >
< / tbody >
< / table >
< p >
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We then plot the measurements in time domain (figure < a href = "#org86b888b" > 1< / 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 = "org86b888b" class = "figure" >
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< p > < img src = "Figures/meas1.png" alt = "meas1.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Time domain - measurement 1< / p >
< / 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 >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > tdisp = t1< span style = "color: #DCDCCC;" > (< / span > ceil< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 300< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #BFEBBF;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 340< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #BFEBBF;" > )< / span > < span style = "color: #DCDCCC;" > )< / span > ;
xdisp = cumtrapz< span style = "color: #DCDCCC;" > (< / span > tdisp, meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 300< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 340< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > < span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
< p >
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Then we plot the position with respect to time (figure < a href = "#org6e2029d" > 2< / a > ).
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< / p >
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< div id = "org6e2029d" class = "figure" >
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< p > < img src = "Figures/meas1_disp.png" alt = "meas1_disp.png" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Y displacement of the Ty stage< / p >
< / 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 style = "color: #DCDCCC;" > [< / span > pxx111, f111< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 300< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx112, f112< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 350< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< span style = "color: #DCDCCC;" > [< / span > pxx121, f121< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 300< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx122, f122< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 350< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< span style = "color: #DCDCCC;" > [< / span > pxx131, f131< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 300< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx132, f132< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 350< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
< p >
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We finally plot the power spectral density of each track (figures < a href = "#orgd40235d" > 3< / a > , < a href = "#org7bcf494" > 4< / a > , < a href = "#orga44d3ba" > 5< / a > ).
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< / p >
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< div id = "orgd40235d" class = "figure" >
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< p > < img src = "Figures/meas1_ry_z_psd.png" alt = "meas1_ry_z_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > PSD of the Z velocity of Ry stage - measurement 1< / p >
< / div >
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< div id = "org7bcf494" class = "figure" >
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< p > < img src = "Figures/meas1_ry_tilt_psd.png" alt = "meas1_ry_tilt_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > PSD of the Rotation of Ry Stage - measurement 1< / p >
< / div >
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< div id = "orga44d3ba" class = "figure" >
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< p > < img src = "Figures/meas1_ty_y_psd.png" alt = "meas1_ty_y_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > PSD of the Ty velocity in the Y direction - measurement 1< / p >
< / 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-orgedf4013" class = "outline-2" >
< h2 id = "orgedf4013" > < span class = "section-number-2" > 4< / span > Measurement 2 - Effect of Ry stage< / h2 >
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< div class = "outline-text-2" id = "text-4" >
< p >
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The tilt stage is turned ON at around 326 seconds (table < a href = "#orgd76c7d2" > 4< / a > ).
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< / p >
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< table id = "orgd76c7d2" 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" / >
< col class = "org-right" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Time< / th >
< th scope = "col" class = "org-right" > 0-326< / th >
< th scope = "col" class = "org-left" > 326-end< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Tilt< / td >
< td class = "org-right" > OFF< / td >
< td class = "org-left" > ON< / td >
< / tr >
< / tbody >
< / table >
< p >
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We plot the time domain (figure < a href = "#orga729884" > 6< / a > ) and we don't observe anything special in the time domain.
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< / p >
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< div id = "orga729884" class = "figure" >
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< p > < img src = "Figures/meas2.png" alt = "meas2.png" / >
< / p >
< p > < span class = "figure-number" > Figure 6: < / span > Time domain - measurement 2< / p >
< / div >
< p >
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We compute the PSD of each track and we plot them (figures < a href = "#org2e8116e" > 7< / a > , < a href = "#org4ac1f64" > 8< / a > and < a href = "#orge6191ed" > 9< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span style = "color: #DCDCCC;" > [< / span > pxx211, f211< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 326< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx212, f212< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 326< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< span style = "color: #DCDCCC;" > [< / span > pxx221, f221< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 326< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx222, f222< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 326< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< span style = "color: #DCDCCC;" > [< / span > pxx231, f231< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 326< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx232, f232< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 2< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 326< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
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< div id = "org2e8116e" class = "figure" >
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< p > < img src = "Figures/meas2_ry_z_psd.png" alt = "meas2_ry_z_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 7: < / span > PSD of the Z velocity of Ry Stage - measurement 2< / p >
< / div >
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< div id = "org4ac1f64" class = "figure" >
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< p > < img src = "Figures/meas2_ry_tilt_psd.png" alt = "meas2_ry_tilt_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 8: < / span > PSD of the Rotation motion of Ry Stage - measurement 2< / p >
< / div >
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< div id = "orge6191ed" class = "figure" >
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< p > < img src = "Figures/meas2_ty_y_psd.png" alt = "meas2_ty_y_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 9: < / span > PSD of the Ty velocity in the Y direction - measurement 2< / p >
< / 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-org3e2fd81" class = "outline-2" >
< h2 id = "org3e2fd81" > < span class = "section-number-2" > 5< / span > Measurement 3 - Effect of the Hexapod< / h2 >
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< div class = "outline-text-2" id = "text-5" >
< p >
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The hexapod is turned off after 406 seconds (table < a href = "#orgbfc2c48" > 5< / a > ).
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< / p >
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< table id = "orgbfc2c48" 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 >
< td class = "org-left" > Tilt< / td >
< td class = "org-left" > ON< / td >
< td class = "org-left" > ON< / td >
< / tr >
< tr >
< td class = "org-left" > Hexa< / td >
< td class = "org-left" > ON< / td >
< td class = "org-left" > OFF< / td >
< / tr >
< / tbody >
< / table >
< p >
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The time domain result is shown figure < a href = "#org7cabb1b" > 10< / a > .
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< / p >
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< div id = "org7cabb1b" class = "figure" >
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< p > < img src = "Figures/meas3.png" alt = "meas3.png" / >
< / p >
< p > < span class = "figure-number" > Figure 10: < / span > Time domain - measurement 3< / p >
< / 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 = "#org54b060a" > 11< / a > , < a href = "#orgd849a63" > 12< / a > and < a href = "#org99c4085" > 13< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span style = "color: #DCDCCC;" > [< / span > pxx311, f311< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 400< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx312, f312< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 420< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< span style = "color: #DCDCCC;" > [< / span > pxx321, f321< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 400< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx322, f322< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 420< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< span style = "color: #DCDCCC;" > [< / span > pxx331, f331< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #BFEBBF;" > 1< / span > < span style = "color: #7CB8BB;" > :< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 400< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx332, f332< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 3< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > ceil< span style = "color: #D0BF8F;" > (< / span > < span style = "color: #BFEBBF;" > 420< / span > < span style = "color: #7CB8BB;" > /< / span > dt< span style = "color: #D0BF8F;" > )< / span > < span style = "color: #7CB8BB;" > :< / span > end< span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
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< div id = "org54b060a" class = "figure" >
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< p > < img src = "Figures/meas3_hexa_z_psd.png" alt = "meas3_hexa_z_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 11: < / span > PSD of the Z velocity of the Hexapod - measurement 3< / p >
< / div >
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< div id = "orgd849a63" class = "figure" >
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< p > < img src = "Figures/meas3_ry_z_psd.png" alt = "meas3_ry_z_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 12: < / span > PSD of the Z velocity of the Ry stage - measurement 3< / p >
< / div >
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< div id = "org99c4085" class = "figure" >
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< p > < img src = "Figures/meas3_ty_y_psd.png" alt = "meas3_ty_y_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 13: < / span > PSD of the Ty velocity in the Y direction - measurement 3< / p >
< / div >
< div class = "important" >
< p >
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Turning ON induces some motion on the hexapod in the z direction (figure < a href = "#org54b060a" > 11< / a > ), on the tilt stage in the z direction (figure < a href = "#orgd849a63" > 12< / a > ) and on the y motion of the Ty stage (figure < a href = "#org99c4085" > 13< / 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-org6fea2ed" class = "outline-2" >
< h2 id = "org6fea2ed" > < span class = "section-number-2" > 6< / span > Measurement 4 - Effect of the Splip-Ring and Spindle< / h2 >
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< div class = "outline-text-2" id = "text-6" >
< p >
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The slip ring is turned on at 300s, then the spindle is turned on at 620s (table < a href = "#org1c4a2a2" > 6< / a > ). The time domain signals are shown figure < a href = "#org5185258" > 14< / a > .
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< / p >
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< table id = "org1c4a2a2" 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 >
< td class = "org-left" > SlipRing< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > ON< / td >
< td class = "org-left" > ON< / 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 >
< / tr >
< tr >
< td class = "org-left" > Spindle< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > OFF< / td >
< td class = "org-left" > ON< / td >
< / tr >
< / tbody >
< / table >
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< div id = "org5185258" class = "figure" >
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< p > < img src = "Figures/meas4.png" alt = "meas4.png" / >
< / p >
< p > < span class = "figure-number" > Figure 14: < / span > Time domain - measurement 4< / p >
< / div >
< p >
The PSD of each track are computed using the code below.
< / p >
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< div id = "org69ec074" class = "figure" >
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< p > < img src = "Figures/meas4_hexa_z_psd.png" alt = "meas4_hexa_z_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 15: < / span > PSD of the Z velocity of the Hexapod - measurement 4< / p >
< / div >
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< div id = "org16cfff3" class = "figure" >
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< p > < img src = "Figures/meas4_ry_z_psd.png" alt = "meas4_ry_z_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 16: < / span > PSD of the Ry rotation in the Y direction - measurement 4< / p >
< / div >
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< div id = "org4abdc85" class = "figure" >
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< p > < img src = "Figures/meas4_ty_y_psd.png" alt = "meas4_ty_y_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 17: < / span > PSD of the Ty velocity in the Y direction - measurement 4< / p >
< / div >
< div class = "important" >
< p >
Turning ON the splipring seems to not add motions on the stages measured.
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It even seems to lower the motion of the Ty stage (figure < a href = "#org4abdc85" > 17< / 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-org3df0c76" class = "outline-2" >
< h2 id = "org3df0c76" > < span class = "section-number-2" > 7< / span > Measurement 5 - Transmission from ground to marble< / h2 >
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< div class = "outline-text-2" id = "text-7" >
< 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 = "#orgca564a5" > 18< / a > .
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< / p >
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< div id = "orgca564a5" class = "figure" >
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< p > < img src = "Figures/meas5.png" alt = "meas5.png" / >
< / p >
< p > < span class = "figure-number" > Figure 18: < / span > Time domain - measurement 5< / p >
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< 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 = "#orgcdb2199" > 19< / a > and for the Y motion on figure < a href = "#org7b5e2b5" > 20< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span style = "color: #DCDCCC;" > [< / span > pxx51, f51< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx52, f52< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx53, f53< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > pxx54, f54< span style = "color: #DCDCCC;" > ]< / span > = pwelch< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track4< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
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< div id = "orgcdb2199" class = "figure" >
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< p > < img src = "Figures/meas5_z_psd.png" alt = "meas5_z_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 19: < / span > PSD of the ground and marble in the Z direction< / p >
< / div >
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< div id = "org7b5e2b5" class = "figure" >
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< p > < img src = "Figures/meas5_y_psd.png" alt = "meas5_y_psd.png" / >
< / p >
< p > < span class = "figure-number" > Figure 20: < / span > PSD of the ground and marble in the Y direction< / p >
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< 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 = "#org56ece37" > 21< / a > and the coherence on figure < a href = "#org8a2c451" > 22< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span style = "color: #DCDCCC;" > [< / span > tfz, fz< span style = "color: #DCDCCC;" > ]< / span > = tfestimate< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > tfy, fy< span style = "color: #DCDCCC;" > ]< / span > = tfestimate< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track4< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
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< div id = "org56ece37" class = "figure" >
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< p > < img src = "Figures/meas5_tf.png" alt = "meas5_tf.png" / >
< / p >
< p > < span class = "figure-number" > Figure 21: < / span > Transfer function estimation - measurement 5< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span style = "color: #DCDCCC;" > [< / span > cohz, fz< span style = "color: #DCDCCC;" > ]< / span > = mscohere< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track1< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track2< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
< span style = "color: #DCDCCC;" > [< / span > cohy, fy< span style = "color: #DCDCCC;" > ]< / span > = mscohere< span style = "color: #DCDCCC;" > (< / span > meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track3< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , meas< span style = "color: #BFEBBF;" > {< / span > < span style = "color: #BFEBBF;" > 5< / span > < span style = "color: #BFEBBF;" > }< / span > .Track4< span style = "color: #BFEBBF;" > (< / span > < span style = "color: #7CB8BB;" > :< / span > < span style = "color: #BFEBBF;" > )< / span > , psd_window, < span style = "color: #BFEBBF;" > []< / span > , < span style = "color: #BFEBBF;" > []< / span > , Fs< span style = "color: #DCDCCC;" > )< / span > ;
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< / pre >
< / div >
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< div id = "org8a2c451" class = "figure" >
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< p > < img src = "Figures/meas5_coh.png" alt = "meas5_coh.png" / >
< / p >
< p > < span class = "figure-number" > Figure 22: < / span > Coherence - measurement 5< / p >
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< 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: 2019-03-15 ven. 11:42< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
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