It's taken a lot of trial and error, but I've found a path through MATLAB loops that seems like it may be stable at all points.
CAVEAT: This doesn't give any indication as to why we weren't able to turn up the AO gain more last night, as far as I can tell, so it's not all good news.
However, it's still ok to at least have a plan that works in simulation... 
Based on the location of the optical resonance peak in the CARM plant, we estimate our CARM offset to be 200pm. I haven't simulated TFs there exactly, but do have 100pm and 300pm TFs. This procedure works in MATLAB starting at either, though 100pm is a little nicer than 300. MATLAB data and code is attached in a zip.
The steps below correspond to the attached figures: Bode plots and step response of the Loop at each step.
0. [Not Plotted] DCTrans sensing, MCL actuation on CARM. FMs1,2,3,5,8; UGF = 120. (DARM not considered at all)
- AO path just turned on. Crossover with MCL path ~ 3.5kHz.
- AO gain increased. Crossover ~ 500 Hz. There are now multiple UGFs! Handling all of these in a stable manner is tricky.
- AO gain increased. Crossover = 150Hz. [No simulations with a higher crossover survived the next steps]
- Compensation filter applied to MCL path; 1 real Zero at 105Hz and a pole at 1k. From a TF point of view, this is sort of like switching to REFLDC, but the SNR at low frequencies is probably better in TR signals at this point.
- CARM offset reduced to 30pm. (This smoothens out the optical plant resonance.)
- Overall gain increased by factor of 3. There is now just one UGF at a few kHz, above the optical resonance. From here, gain can be further increased, boosts can go on, offset can go way down. In reality, we should switch to a single error signal once we're back to one UGF, and go from there.
 
#4 Seems like the most sticky part. While both sides of this look stable as far as I can tell. I feel that flipping from the red phase curve to the teal might not actually be ok, since they are on either side of the bad phase of 0 degrees. It isn't immediately evident to me how to easily model the transitions between steps, rather than just the stability of of each step in the steady state. |