J. Kissel, P. Fritschel

We have recently been reminded that, in the past (prior science runs with the initial detectors), the inverse actuation filter did not include inverse of all the necessary notch filters in the DARM actuation function. This reminder came from early ER8 analysis (LHO aLOG 20893 and subsequent comments). All of these notch filters live in one digital filter bank in the actuation chain, up-stream of the DARM filter bank. Remember that the injection point for hardware injections is currently just up-stream of the DARM filter bank, in the LSC portion of the OMC front end model, passed in from the CAL-CS front-end model over IPC.

In studying this a little more carefully, Peter pointed out that if we don't include the notches, the phase distortion (with respect to a perfect inversion of the actuation function) will be quite significant (10s of degrees), even well-out-side the frequency region that one might niavely think is impacted when only looking at the magnitude.

I attach several plots of the same thing in various formats to show this affect.

H1 Mini-run Filter LHO aLOG 18115
H1 ER7 Filter LHO aLOG 18997 (not installed until halfway through ER7, and known to have problems: )

In the mini-run design, I had slapped something quickly together because we were strapped for time, that quick approximation did not include any notches -- but mostly because we hadn't yet started nothing these features out of the DARM loop yet. In ER7, we had installed some of our notches, and I took my time to tailor the inverse filter to be very close to the full model of the inverse actuation filter. 

LLO has replicated the inverse actuation function without notch filters for ER7 LLO aLOG 18499. 
ER6 design was similar to LHO's Mini-run's design -- something simply to get us started LLO aLOG 16129.

We intend to discuss this with the hardware injection team, and more appropriately with the search groups as to how we should proceed.