J. Kissel, S. Dwyer, A. Staley, N Smith

Continuing Shiela's investigations from last night (see LHO aLOG 14883), we put our heads together to figure out why we're having so much trouble with the ALS DIFF control. I attach plots comparing what is currently installed against when I last was involved with the ALS DIFF design (see G1400146, and the subsequent design that was used never got published, but was designed using ${SusSVN}/trunk/QUAD/Common/FilterDesign/HierarchicalControl/DARMmodel_ALS_20140428.m). Note this is also around the time that we increased the UIM driver strength by a factor of 4, and this WAS included in my 2014-04-28 design.

Some Comments and History that I think has caused in the current badness:
- After initial installation by Kiwamu (see LHO aLOG 11665), Stefan, Sheila and Kiwamu had lowered the UIM / TST crossover a bit, from 2-ish [Hz] to 1.5-ish [Hz] (see LHO aLOG 11899). From that entry, "These tweaks served to (1) to move the elliptic filter's gain peaking bump out of the way of the 10 [Hz] features in the input noise, and (2) roll off the low-frequency end of the test mass drive faster." These adjusted filters are shown on pg 3 and 4 of the attached, shown in solid lines. The dashed lines are the original filters. One can see there's a good amount of phase action and amplitude ripple around 10 [Hz]. The cross-over action happens over a wide frequency range from 0.6 to 20 [Hz].
- At the time, we were mystified why we were never able to get to the 15 [Hz] UGF I'd designed, but we moved on before figuring it out. With some finagling, one could only get the UGFs to 5 to 10 [Hz].
- Over the course of a few weeks, Stefan, Sheila, Arnaud, and Keita began to add tweaks and patches to the plant-inversion portion of the distributed hierarchical design. This is the source of the "invL2LNEW," "patch," "LISOfit" "invL2L1," "invL2L2," "MatchedinvL2L" filters that are now used. It's unclear if this completely solved the stability problems, but it tweaked the phase in the right regions enough to certainly help. Sometimes.
- This was followed by Arnaud pioneering the length-to-pitch decoupling filters, but those installs never really went well (see, e.g. LHO aLOGs 11952, 11849, 11832).
So -- as we left ALS DIFF before the summer vent, we could only ever get the UGF up to 5 to 10 [Hz], had trouble with its stability and cross-coupling to pitch, had installed a whole bunch of high-Q plant compensation filters. Indeed, these very-precise compensation filters were measured specifically for ETMX, and then copied and pasted over to ETMY (dubious).

- Quite a bit after this, after the summer vent, we (discovered / became confident) that the actuation strength or the ESDs were lower than I modeled by a factor of 2-to-4 (see, .e.g. LHO aLOG 12220) due to charge plaguing the electrostatic drive system. 
- Further, not only is it weaker by a factor of 2-4, but the strength of the ESD *varies* on the hour timescale because of continuous charge noise from ion pumps, requiring the cross-over between the UIM and TST to constantly need adjustment (needed both at LLO and LHO, but never really reported), and (I believe) occasionally moving the cross-over into instability.
- Further, further, because the charge on the quadrants evolve differently, which mean the length-to-pitch coupling is constantly evolving for this stage. We currently do not have *any* compensation for it (frequency dependent or independent).
- Distracted elsewhere, I never got back to modeling whether one could get a stable, 10 [Hz] UGF ALS DIFF loop, that did not saturate the SUS DACs. Not to mention, ground motion / SEI performance has evolved. As such, we haven't changed the cross-over of the distribution filters for the weaker, time-dependent, ESD drive.
- After finding that the highest vertical and roll modes were getting rung up with lock-acquisition, and saturating actuators, high-Q notches were added at 9 and 13 [Hz]. First to the DARM filter bank, and then moved to the UIM stage (LHO aLOG 14672). These are the "BandstopBR" that are now used in the UIM plant inversion filters. These cause substantial phase distortion near (a) the constantly evolving UIM / TST cross-over, and (b) the unity gain frequency of the loop depending on where they lived. NOTE: Sheila did NOT include these notches in her open loop gain plot (pg 1).

So things we know now that should aide new design considerations:
- The ESD actuators are weaker by a factor of 2-4, and they vary in time. 
- So we need lots of gain margin both at the cross-over and the overall loop UGF.
- We should try to decrease the wide-frequency range impact of the UIM / TST distribution filters.
- We need 9 and 13 [Hz] notches in the length control path, because lock acquisition impulses cause them to ring up.
- Length-to-angle, though probably does not play a roll in the ALS DIFF loop stability at 10 [Hz], it does play a roll in the slow alignment fluctuations. In this case "slow" is both at 0.15 [Hz] as well as on the "DC drift," minute time-scale. It's unclear which stage is causing the problem.