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< h1 class = "title" > Measurement Analysis< / h1 >
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< h2 > Table of Contents< / h2 >
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< li > < a href = "#org4b89ca1" > 1. Measurement Description< / a > < / li >
< li > < a href = "#orga8fd9ad" > 2. Importation of the data< / a > < / li >
< li > < a href = "#orgd2f3c71" > 3. Variables for analysis< / a > < / li >
< li > < a href = "#org5c64001" > 4. Coherence between the two vertical geophones on the Tilt Stage< / a > < / li >
< li > < a href = "#org61ba96a" > 5. Data Post Processing< / a > < / li >
< li > < a href = "#org1d3ae96" > 6. Normalization< / a > < / li >
< li > < a href = "#org381ee31" > 7. Measurement 1 - Effect of Ty stage< / a > < / li >
< li > < a href = "#orgde80036" > 8. Measurement 2 - Effect of Ry stage< / a > < / li >
< li > < a href = "#org340fbde" > 9. Measurement 3 - Effect of the Hexapod< / a > < / li >
< li > < a href = "#orgeaf345c" > 10. Measurement 4 - Effect of the Splip-Ring and Spindle< / a > < / li >
< li > < a href = "#org743054f" > 11. Measurement 5 - Transmission from ground to marble< / a > < / li >
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< div class = "note" id = "orgbc54efa" >
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< p >
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All the files (data and Matlab scripts) are accessible < a href = "data/meas_analysis_geophones.zip" > here< / a > .
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< h2 id = "org4b89ca1" > < span class = "section-number-2" > 1< / span > Measurement Description< / h2 >
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< div id = "org18a91b9" class = "figure" >
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< p > < img src = "./figs/setup_picture.png" alt = "setup_picture.png" width = "500px" / >
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< p > < span class = "figure-number" > Figure 1: < / span > Picture of the setup for the measurement< / p >
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< 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.
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< p >
The goal is to see what noise is injected in the system due to the regulation loop of each stage.
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< h2 id = "orga8fd9ad" > < span class = "section-number-2" > 2< / span > Importation of the data< / h2 >
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< p >
First, load all the measurement files:
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< pre class = "src src-matlab" > meas = {};
meas{1} = load(< span class = "org-string" > './mat/Measurement1.mat'< / span > );
meas{2} = load(< span class = "org-string" > './mat/Measurement2.mat'< / span > );
meas{3} = load(< span class = "org-string" > './mat/Measurement3.mat'< / span > );
meas{4} = load(< span class = "org-string" > './mat/Measurement4.mat'< / span > );
meas{5} = load(< span class = "org-string" > './mat/Measurement5.mat'< / span > );
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< p >
Change the track name for measurements 3 and 4.
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< pre class = "src src-matlab" > meas{3}.Track1_Name = < span class = "org-string" > 'Input 1: Hexa Z'< / span > ;
meas{4}.Track1_Name = < span class = "org-string" > 'Input 1: Hexa Z'< / span > ;
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< p >
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For the measurements 1 to 4, the measurement channels are shown table < a href = "#orgd9ddfba" > 1< / a > .
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< / p >
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< table id = "orgd9ddfba" 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 >
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< 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 >
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< 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 >
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< 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 >
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< p >
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For the measurement 5, the channels are shown table < a href = "#orgf39e86b" > 2< / a > .
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< / p >
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< table id = "orgf39e86b" 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 >
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< 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 >
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< 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 >
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< h2 id = "orgd2f3c71" > < span class = "section-number-2" > 3< / span > Variables for analysis< / h2 >
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< p >
We define the sampling frequency and the time vectors for the plots.
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< pre class = "src src-matlab" > Fs = 256; < span class = "org-comment" > % [Hz]< / span >
dt = 1< span class = "org-type" > /< / span > (Fs);
t1 = dt< span class = "org-type" > *< / span > (0< span class = "org-type" > :< / span > length(meas{1}.Track1)< span class = "org-type" > -< / span > 1);
t2 = dt< span class = "org-type" > *< / span > (0< span class = "org-type" > :< / span > length(meas{2}.Track1)< span class = "org-type" > -< / span > 1);
t3 = dt< span class = "org-type" > *< / span > (0< span class = "org-type" > :< / span > length(meas{3}.Track1)< span class = "org-type" > -< / span > 1);
t4 = dt< span class = "org-type" > *< / span > (0< span class = "org-type" > :< / span > length(meas{4}.Track1)< span class = "org-type" > -< / span > 1);
t5 = dt< span class = "org-type" > *< / span > (0< span class = "org-type" > :< / span > length(meas{5}.Track1)< span class = "org-type" > -< / span > 1);
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< p >
For the frequency analysis, we define the frequency limits for the plot.
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< pre class = "src src-matlab" > fmin = 1; < span class = "org-comment" > % [Hz]< / span >
fmax = 100; < span class = "org-comment" > % [Hz]< / span >
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< p >
Then we define the windows that will be used to average the results.
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< pre class = "src src-matlab" > psd_window = hanning(2< span class = "org-type" > *< / span > fmin< span class = "org-type" > /< / span > dt);
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< h2 id = "org5c64001" > < 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 = "#org51857d1" > 2< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [coh, f] = mscohere(meas{1}.Track1(< span class = "org-type" > :< / span > ), meas{1}.Track2(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
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< / div >
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< div id = "org51857d1" 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 >
< / div >
< p >
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We then compute the transfer function from one sensor to the other (figure < a href = "#orgb667db6" > 3< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [tf23, f] = tfestimate(meas{1}.Track1(< span class = "org-type" > :< / span > ), meas{1}.Track2(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
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< / pre >
< / div >
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< div id = "orgb667db6" 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 >
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< p >
Even though the coherence is not very good, we observe no resonance between the two sensors.
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< h2 id = "org61ba96a" > < 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 = (meas{1}.Track1< span class = "org-type" > +< / span > meas{1}.Track2)< span class = "org-type" > /< / span > 2;
meas1_tilt = (meas{1}.Track1< span class = "org-type" > -< / span > meas{1}.Track2)< span class = "org-type" > /< / span > 2;
meas{1}.Track1 = meas1_z;
meas{1}.Track1_Y_Magnitude = < span class = "org-string" > 'Meter / second'< / span > ;
meas{1}.Track1_Name = < span class = "org-string" > 'Ry Z'< / span > ;
meas{1}.Track2 = meas1_tilt;
meas{1}.Track2_Y_Magnitude = < span class = "org-string" > 'Rad / second'< / span > ;
meas{1}.Track2_Name = < span class = "org-string" > 'Ry Tilt'< / span > ;
meas2_z = (meas{2}.Track1< span class = "org-type" > +< / span > meas{2}.Track2)< span class = "org-type" > /< / span > 2;
meas2_tilt = (meas{2}.Track1< span class = "org-type" > -< / span > meas{2}.Track2)< span class = "org-type" > /< / span > 2;
meas{2}.Track1 = meas2_z;
meas{2}.Track1_Y_Magnitude = < span class = "org-string" > 'Meter / second'< / span > ;
meas{2}.Track1_Name = < span class = "org-string" > 'Ry Z'< / span > ;
meas{2}.Track2 = meas2_tilt;
meas{2}.Track2_Y_Magnitude = < span class = "org-string" > 'Rad / second'< / span > ;
meas{2}.Track2_Name = < span class = "org-string" > 'Ry Tilt'< / span > ;
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< / pre >
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< h2 id = "org1d3ae96" > < 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 = "#orgb09443d" > 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 = 2< span class = "org-type" > *< / span > < span class = "org-constant" > pi< / span > ; < span class = "org-comment" > % [rad/s]< / span >
L4C_ksi = 0.28;
L4C_G0 = 276.8; < span class = "org-comment" > % [V/(m/s)]< / span >
L4C_G = L4C_G0< span class = "org-type" > *< / span > (s< span class = "org-type" > /< / span > L4C_w0)< span class = "org-type" > ^< / span > 2< span class = "org-type" > /< / span > ((s< span class = "org-type" > /< / span > L4C_w0)< span class = "org-type" > ^< / span > 2 < span class = "org-type" > +< / span > 2< span class = "org-type" > *< / span > L4C_ksi< span class = "org-type" > *< / span > (s< span class = "org-type" > /< / span > L4C_w0) < span class = "org-type" > +< / span > 1);
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< / pre >
< / div >
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< div id = "orgb09443d" 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" >
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< pre class = "src src-matlab" > meas{1}.Track1 = (meas{1}.Track1)< span class = "org-type" > ./< / span > 276.8;
meas{1}.Track2 = (meas{1}.Track2)< span class = "org-type" > ./< / span > 276.8;
meas{1}.Track3 = (meas{1}.Track3)< span class = "org-type" > ./< / span > 276.8;
meas{2}.Track1 = (meas{2}.Track1)< span class = "org-type" > ./< / span > 276.8;
meas{2}.Track2 = (meas{2}.Track2)< span class = "org-type" > ./< / span > 276.8;
meas{2}.Track3 = (meas{2}.Track3)< span class = "org-type" > ./< / span > 276.8;
meas{3}.Track1 = (meas{3}.Track1)< span class = "org-type" > ./< / span > 276.8;
meas{3}.Track2 = (meas{3}.Track2)< span class = "org-type" > ./< / span > 276.8;
meas{3}.Track3 = (meas{3}.Track3)< span class = "org-type" > ./< / span > 276.8;
meas{4}.Track1 = (meas{4}.Track1)< span class = "org-type" > ./< / span > 276.8;
meas{4}.Track2 = (meas{4}.Track2)< span class = "org-type" > ./< / span > 276.8;
meas{4}.Track3 = (meas{4}.Track3)< span class = "org-type" > ./< / span > 276.8;
meas{5}.Track1 = (meas{5}.Track1)< span class = "org-type" > ./< / span > 276.8;
meas{5}.Track2 = (meas{5}.Track2)< span class = "org-type" > ./< / span > 276.8;
meas{5}.Track3 = (meas{5}.Track3)< span class = "org-type" > ./< / span > 276.8;
meas{5}.Track4 = (meas{5}.Track4)< span class = "org-type" > ./< / span > 276.8;
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< / pre >
< / div >
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< pre class = "src src-matlab" > meas{1}.Track1_norm = lsim(inv(L4C_G), meas{1}.Track1, t1);
meas{1}.Track2_norm = lsim(inv(L4C_G), meas{1}.Track2, t1);
meas{1}.Track3_norm = lsim(inv(L4C_G), meas{1}.Track3, t1);
meas{2}.Track1_norm = lsim(inv(L4C_G), meas{2}.Track1, t2);
meas{2}.Track2_norm = lsim(inv(L4C_G), meas{2}.Track2, t2);
meas{2}.Track3_norm = lsim(inv(L4C_G), meas{2}.Track3, t2);
meas{3}.Track1_norm = lsim(inv(L4C_G), meas{3}.Track1, t3);
meas{3}.Track2_norm = lsim(inv(L4C_G), meas{3}.Track2, t3);
meas{3}.Track3_norm = lsim(inv(L4C_G), meas{3}.Track3, t3);
meas{4}.Track1_norm = lsim(inv(L4C_G), meas{4}.Track1, t4);
meas{4}.Track2_norm = lsim(inv(L4C_G), meas{4}.Track2, t4);
meas{4}.Track3_norm = lsim(inv(L4C_G), meas{4}.Track3, t4);
meas{5}.Track1_norm = lsim(inv(L4C_G), meas{5}.Track1, t5);
meas{5}.Track2_norm = lsim(inv(L4C_G), meas{5}.Track2, t5);
meas{5}.Track3_norm = lsim(inv(L4C_G), meas{5}.Track3, t5);
meas{5}.Track4_norm = lsim(inv(L4C_G), meas{5}.Track4, t5);
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< / pre >
< / div >
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< / div >
< / div >
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< div id = "outline-container-org381ee31" class = "outline-2" >
< h2 id = "org381ee31" > < 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 = "#org671285c" > 3< / a > .
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< / p >
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< table id = "org671285c" 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 = "#orgf997195" > 5< / a > ).
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< / p >
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< div class = "important" id = "org6b8cc61" >
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< 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 = "orgf997195" 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 = "#org28db150" > 6< / a > ).
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< / p >
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< div id = "org28db150" 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" > [pxx111, f11] = pwelch(meas{1}.Track1(1< span class = "org-type" > :< / span > ceil(300< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx112, f12] = pwelch(meas{1}.Track1(ceil(350< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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[pxx121, < span class = "org-type" > ~< / span > ] = pwelch(meas{1}.Track2(1< span class = "org-type" > :< / span > ceil(300< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx122, < span class = "org-type" > ~< / span > ] = pwelch(meas{1}.Track2(ceil(350< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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[pxx131, < span class = "org-type" > ~< / span > ] = pwelch(meas{1}.Track3(1< span class = "org-type" > :< / span > ceil(300< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx132, < span class = "org-type" > ~< / span > ] = pwelch(meas{1}.Track3(ceil(350< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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< / pre >
< / div >
< p >
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We finally plot the power spectral density of each track (figures < a href = "#orgd3d8ddd" > 7< / a > , < a href = "#org8e55c40" > 8< / a > , < a href = "#org545f29f" > 9< / a > ).
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< / p >
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< div id = "orgd3d8ddd" 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 = "org8e55c40" 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 = "org545f29f" 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 >
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< div class = "important" id = "org28ce135" >
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< 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-orgde80036" class = "outline-2" >
< h2 id = "orgde80036" > < 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 = "#org4205d55" > 4< / a > ).
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< / p >
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< table id = "org4205d55" 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 = "#orgcd4b5b2" > 10< / a > ) and we don’ t observe anything special in the time domain.
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< / p >
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< div id = "orgcd4b5b2" 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 = "orgc1cada2" class = "figure" >
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< 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 = "#orgc533b05" > 12< / a > , < a href = "#org76fd0d7" > 13< / a > and < a href = "#org26db023" > 14< / a > ).
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [pxx211, f21] = pwelch(meas{2}.Track1(1< span class = "org-type" > :< / span > ceil(326< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx212, f22] = pwelch(meas{2}.Track1(ceil(326< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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[pxx221, < span class = "org-type" > ~< / span > ] = pwelch(meas{2}.Track2(1< span class = "org-type" > :< / span > ceil(326< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx222, < span class = "org-type" > ~< / span > ] = pwelch(meas{2}.Track2(ceil(326< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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[pxx231, < span class = "org-type" > ~< / span > ] = pwelch(meas{2}.Track3(1< span class = "org-type" > :< / span > ceil(326< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx232, < span class = "org-type" > ~< / span > ] = pwelch(meas{2}.Track3(ceil(326< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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< / pre >
< / div >
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< div id = "orgc533b05" 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 = "org76fd0d7" 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 = "org26db023" 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 >
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< div class = "important" id = "orga669a8e" >
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< 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-org340fbde" class = "outline-2" >
< h2 id = "org340fbde" > < 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 = "#orge03bb03" > 5< / a > ).
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< / p >
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< table id = "orge03bb03" 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 = "#org69167fd" > 15< / a > .
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< / p >
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< div id = "org69167fd" 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 >
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< div id = "org1e22f4d" class = "figure" >
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< 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 = "#orgd9bf904" > 17< / a > , < a href = "#orgb63f3f3" > 18< / a > and < a href = "#orgba7de7a" > 19< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [pxx311, f31] = pwelch(meas{3}.Track1(1< span class = "org-type" > :< / span > ceil(400< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx312, f32] = pwelch(meas{3}.Track1(ceil(420< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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[pxx321, < span class = "org-type" > ~< / span > ] = pwelch(meas{3}.Track2(1< span class = "org-type" > :< / span > ceil(400< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx322, < span class = "org-type" > ~< / span > ] = pwelch(meas{3}.Track2(ceil(420< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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[pxx331, < span class = "org-type" > ~< / span > ] = pwelch(meas{3}.Track3(1< span class = "org-type" > :< / span > ceil(400< span class = "org-type" > /< / span > dt)), psd_window, [], [], Fs);
[pxx332, < span class = "org-type" > ~< / span > ] = pwelch(meas{3}.Track3(ceil(420< span class = "org-type" > /< / span > dt)< span class = "org-type" > :< / span > end), psd_window, [], [], Fs);
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< / pre >
< / div >
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< div id = "orgd9bf904" 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 = "orgb63f3f3" 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 = "orgba7de7a" 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 >
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< div class = "important" id = "org8bfd785" >
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< p >
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Turning ON induces some motion on the hexapod in the z direction (figure < a href = "#orgd9bf904" > 17< / a > ), on the tilt stage in the z direction (figure < a href = "#orgb63f3f3" > 18< / a > ) and on the y motion of the Ty stage (figure < a href = "#orgba7de7a" > 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-orgeaf345c" class = "outline-2" >
< h2 id = "orgeaf345c" > < 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 = "#org77ba68a" > 6< / a > ). The time domain signals are shown figure < a href = "#org7698f96" > 20< / a > .
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< / p >
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< table id = "org77ba68a" 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 = "org7698f96" 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 >
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If we integrate this signal, we obtain Figure < a href = "#orgf1cd229" > 21< / a > .
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< / p >
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< div id = "orgf1cd229" class = "figure" >
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< 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 = "orgd5f35e4" 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 >
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< div id = "org9c071ce" class = "figure" >
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< p > < img src = "figs/meas4_hexa_z_psd_int.png" alt = "meas4_hexa_z_psd_int.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 23: < / span > PSD_INT of the Z velocity of the Hexapod - measurement 4< / p >
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< / div >
< p >
And we compute the Cumulative amplitude spectrum.
< / p >
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< div id = "org4133016" 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 = "org9270d4d" 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 >
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< div class = "important" id = "org773be49" >
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< 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 = "#org9270d4d" > 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-org743054f" class = "outline-2" >
< h2 id = "org743054f" > < 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 = "#orgaadb200" > 26< / a > .
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< / p >
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< div id = "orgaadb200" 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 = "#orgb195b4d" > 27< / a > and for the Y motion on figure < a href = "#org37af53b" > 28< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [pxx51, f51] = pwelch(meas{5}.Track1(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
[pxx52, f52] = pwelch(meas{5}.Track2(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
[pxx53, f53] = pwelch(meas{5}.Track3(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
[pxx54, f54] = pwelch(meas{5}.Track4(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
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< / pre >
< / div >
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< div id = "orgb195b4d" 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 = "org37af53b" 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 = "#org2043690" > 29< / a > and the coherence on figure < a href = "#org96fb839" > 30< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > [tfz, fz] = tfestimate(meas{5}.Track1(< span class = "org-type" > :< / span > ), meas{5}.Track2(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
[tfy, fy] = tfestimate(meas{5}.Track3(< span class = "org-type" > :< / span > ), meas{5}.Track4(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
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< / pre >
< / div >
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< div id = "org2043690" 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" > [cohz, fz] = mscohere(meas{5}.Track1(< span class = "org-type" > :< / span > ), meas{5}.Track2(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
[cohy, fy] = mscohere(meas{5}.Track3(< span class = "org-type" > :< / span > ), meas{5}.Track4(< span class = "org-type" > :< / span > ), psd_window, [], [], Fs);
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< / pre >
< / div >
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< div id = "org96fb839" 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 >
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< div class = "important" id = "org8b62548" >
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< 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 >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
2019-07-05 11:35:40 +02:00
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2020-11-12 jeu. 10:27< / p >
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< / div >
< / body >
< / html >
