We updated the L2P FF filter in BS M1 stage.

The resultant M1 L drive to BS oplev pitch TF is shown in the first attached image. The blue curves were for the old L2P FF (only a scalar with gain 0.002), and the red ones were for the new, freq-dependent FF at the M1 stage.

The measured FF filter = L2P/P2P appeared to be quite hard to fit, partly due to that I did not took a long enough measurement to integrate for good SNR. Thus for now we only focused on the main SUS resonance at ~ 0.5 Hz, and the microseismic band ~0.2-0.3 Hz, while sacrificing the earthquake band < 0.1 Hz. It should be fine in the full lock state when we could relying on the feedback to handle the <0.1 Hz band, but whether the current FF would be beneficial for the lock acquisition would still need to be tested.

Somehow in the coherence plot (top-right) the reduction in the main sus resonance was not apparent (it might be due to the fact that the DTT TF is a biased measurement, as the measurement noise term would not vanish in the auto-correlations used for computing coherence; see, e.g., Evan Hall's thesis, Appendix A). Nonetheless in the TF plot (top-left) we could see roughly an order of magnitude reduction at 0.5 Hz. The measurement used to fit the TF was done with the oplev damping off, and the attached plot showed the result with the oplev on. Thus it seemed that the FF should work in either case.

In the FF_fit_vs_data.pdf we show the fitted TF (blue) and the data (orange). The foton filter we use currently is:

zpk(
[
0.000000e+00+i*0.000000e+00; 
-1.400000e-01+i*0.000000e+00; 
-2.043560e+00+i*0.000000e+00; 
1.348996e+00+i*0.000000e+00; 
-1.028492e+00+i*8.718815e-01; 
-1.028492e+00-i*8.718815e-01; 
],
[
-5.000000e-03+i*0.000000e+00; 
-2.000000e-01+i*0.000000e+00; 
-1.720109e+00+i*0.000000e+00; 
-1.734806e+00+i*0.000000e+00; 
-2.301921e+01+i*0.000000e+00; 
-1.335285e-01+i*2.691426e+00; 
-1.335285e-01-i*2.691426e+00; 
-2.199115e+01+i*3.808979e+01; 
-2.199115e+01-i*3.808979e+01; 
],
4.584153e+02
)