Sheila, Hang

We tried to do the PRM local length to pitch decoupling, similar to what LLO had done (LLO:31459). We measured both the M2L -> M3P and M2P -> M3P transfer functions, and fitted them using Lee's IIRrational.  The filters were loaded into the PRM_M2_DRIVEALIGN_L2P filter bank. To engage the L2A, we should put a gain of -1. 

The first and second plots were measured TFs. They were left in [ct/ct] as this was sufficient for filter design. 

We also tested the effectiveness of the filter using past data (starting gps: 1186963218; duration: 2048 s). We used the fitted coefficients to filter SUS-PRM_M2_LOCK_L_OUT16 and then subtracted the results from SUS-PRM_M3_WIT_P_DQ. We further computed the residual coherence between PRM_PIT and CHARD_PIT. The result was shown in the third plot. The blue trace was the original coherence between PRM_PIT and CHARD_PIT and the red trace was after the M2_L decoupling. It seemed to reduced the coherence around 1 Hz significantly.

However, the measured suspension M2L->M3P did not quite match the optimal Wiener filter computed for the L2P decoupling from the past data with the full ifo locked, whose result was shown in the light cyan curve (the reason we start with M2 instead of M1 was that the M1 suspension L2A deviated from the Wiener result even more than M2). We might want to switch to the Wiener results in the future for better decoupling...