I have taken EricQ's simulation results for the CARM plant change vs. CARM offset, and put that together with the CM and CARM digital control loops, to see what we have.
The overall gains here aren't meaningful yet (I haven't set a UGF), but we can certainly look at the phases, and how the magnitude of the signals change with CARM offset.
First, the analog CM servo. I use the servo shape from Den's elog from December, but only what he calls "BOOST", the regular servo shape, not any of the super boosts, "BOOST 1-3". No normalization.
Next, the digital LSC CARM servo (same filters as XARM and YARM). I have used FM4 and FM5, which are the 2 filters that we use to acquire regular LSC arm lock. For the actuator, I just use a 1Hz pendulum as if I'm pushing only on the ETMs.
I also used the exact same setups as above, but normalized the transfer functions by a DC photodiode output. The analog CM loops change the least (around a few kHz) if I use POPDC. The digital CARM loops change the least (around 100Hz) if I use TRX (or, equivalently, TRX + TRY).
Here are the normalized plots:
Either way, with or without normalization, the digital CARM loop will go unstable between 0-10pm, for both the REFL RF photodiodes. We need to figure out how to get a realistic transfer function out for the 1/sqrt(TRANS) signals, and see what happens with those. If those also look unstable, then maybe we should consider a DC signal for the analog CM servo to start, since that could have a wider linear range.