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Message ID: 13393     Entry time: Wed Oct 18 19:17:42 2017
Author: gautam 
Type: Update 
Category: General 
Subject: PRC angular feedforward 

Last night, I collected ~30mins of data for the vertex seismometer channels and the POP QPD PIT/YAW signals with the PRMI locked on carrier (angular FF OFF). The ITM Oplev loops weren't DC coupled, as they are in the full IFO locking sequence, but I feel like the angular FF filters can be improved - there are frequent sharp dives in the AS110 signal level which are correlated with large amplitude motion of the POP spot on the control room CCD monitor.

Repeating the frequency domain multicoherence analysis using BS_X and BS_Y seismometer channels as witnesses suggest that we can win significantly (see Attachment #1).

I've never really implemented feedforward filters - I was planning on using ericq's latest entry on this subject as a guide. From what I gather, the procedure is as follows:

  1. Pre-filter the target (POP QPD PIT or YAW) and witness (BS_X, BS_Y) channels
    • Downsample the 2k target data and 256Hz witness data to 32 Hz (how to choose this?)
    • Detrend (linear?)
    • Apply elliptic low pass filter (previously, a 3rd order Elliptic Low pass with 3dB ripple, 40dB stopband attenuation, corner at 5Hz was used).
  2. Filter the target signal (i.e. POP QPD PIT/YAW) by the inverse actuator TF.
    • This "actuator TF" is a measurement of how actuating on the angular DoFs of the PRM affects the POP QPD spot.
    • So by pre-filtering the target signal through the inverse actuator TF, we get a measure of how much the PRM angular motion is.
    • The reason we want to do this is to give the FIR filter that produces optic motion (output) given ground motion sensed by the seismometer (input) fewer poles/zeros to fit (?).
    • The actual actuator TF has to be measured using DTT, and fit - is there anything critical about this fitting? Seems like this should be just a simple pendulum transfer function so a pair of complex poles should be sufficient?
  3. The actual Wiener filter is calculated by the function miso_firlev.m. There are many versions of this floating around from what I can gather.
    • This function requires 3 input parameters.
      • Order of filter to be fit
      • Witness channels (can be multiple)
      • Target channel (has to be single, hence the "miso" in the function name).
    • Today, at the meeting, we talked about weighting the cost function that the optimal Wiener filter calculator minimizes.
    • The canonical wiener filter minimizes the mean squared error between the output of the filter and the desired signal profile (which for this particular problem is the angular motion of the PRM, calculated by dividing the target signal by the actuator TF, knowing which we can cancel it out).
    • But as seen in Attachment #1, the main reduction in RMS comes below f=5Hz.
    • So can we weight the cost function more heavily at lower frequencies? From what I can find in previous calculations, it looks like this weighting happens in the pre-filtering stage, which is not the same thing as including the frequency dependent weighting in the calculation of the Weiner filter? The PSD and acf are F.T. pairs per the Wiener-Khinchin theorem so intuitively I would think that weighting in the frequency domain corresponds to weighting on the lags at which the acf is calculated, but I need to think about this.
    • What kind of low-pass filter do we use to prevent noise injection at higher frequencies? Does the optimal filter calculation automatically roll-off the filter response at high frequencies?
  4. As I write this, seems like there is another level of optimization of "meta-parameters" possible in this whole process - e.g. what is the optimal order of filter to fit? what is the optimal pre-filtering of training data? Not sure how much we can gain from this though.

Some notes from Rana from some years ago: https://nodus.ligo.caltech.edu:8081/40m/11519

If anyone has pointers / other considerations I should take into account, please post here.

Attachment 1: pop_feedforward_potential.pdf  405 kB  | Hide | Hide all
pop_feedforward_potential.pdf
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