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Entry  Thu Sep 29 16:19:29 2016, Lydia, Update, SUS, Free swing eigenmodes 05.pngSUS_eigenmodes.png
    Reply  Thu Oct 6 15:42:51 2016, Lydia, Update, SUS, Output matrix diagonalization 
       Reply  Fri Oct 7 20:56:15 2016, Koji, Update, SUS, Output matrix diagonalization 161007_P.pdf161007_Y.pdf
Message ID: 12540     Entry time: Fri Oct 7 20:56:15 2016     In reply to: 12536
Author: Koji 
Type: Update 
Category: SUS 
Subject: Output matrix diagonalization 

I wanted to see what is the reason to have such large coupling between pitch and yaw motions.

The first test was to check orthogonality of the bias sliders. It was done by monitoring the suspension motion using the green beam.
The Y arm cavity was aligned to the green. The damping of ITMY was all turned off except for SD.
Then ITMY was misaligned by the bias sliders. The ITMY face CCD view shows that the beam is reasonably orthogonally responding to the pitch and yaw sliders.
I also confirmed that the OPLEV signals also showed reasonablly orthogonal responce to the pitch and yaw misalignment.

=> My intuition was that the coils (including the gain balance) are OK for a first approximation.

Then, I started to excite the resonant modes. I agree that it is difficult to excite a pure picth motion with the resonance.

So I wanted to see how the mixing is frequency dependent.

The transfer functions between ITMY_ASCPIT/YAW_EXC to ITMY_OPLEV_PERROR/YERROR were measured.

The attached PDFs basically shows that the transfer functions are basically orthogonal (i.e. pitch exc goes to pitch, yaw exc goes to yaw) except at the resonant frequency.

I think the problem is that the two modes are almost degenerate but not completely. This elog shows that the resonant freq of the ITMY modes are particularly close compared to the other suspensions.
If they are completely degenerate, the motion just obeys our excitation. However, they are slightly split. Therefore, we suffer from the coupled modes of P and Y at the resonant freq.
However, the mirror motion obeys the exitation at the off resonance as these two modes are similar enough.

This means that the problem exists only at the resonant frequencies. If the damping servos have 1/f slope around the resonant freqs (that's the usual case), the antiresonance due to the mode coupling does not cause servo instability thank to the sufficient phase margin.

In conclusion, unfortunately we can't diagnalize the sensors and actuators using the natural modes because our assumption of the mode purity is not valid.
We can leave the pitch/yaw modes undiagnalized or just believe the oplevs as a relatively reliable reference of pitch and yaw and set the output matrix accordingly.


The figures will be rotated later.

Attachment 1: 161007_P.pdf  70 kB  | Hide | Hide all | Show all
Attachment 2: 161007_Y.pdf  69 kB  | Show | Hide all | Show all
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