J. Kissel, O. Patane, B. Weaver, I. Abouelfettouh

Executive Summary: For now, we can damp the BBSS Glass BS with BOSEMs and old Level 2 BSFM Glass BS damping loops as long as the L and P EPICs gains are -0.5, all other DOFs are -1.0, and we turn OFF all DOFs of the BSFM bounce/roll mode notches.

Debugging damping loops for BBSS with BOSEMs mounted to the table cloth, we found that with direct copy of "old" level 2 damping loops for BS (a BSFM) was unstable, ringing up in L and P at 2.668 Hz (measured with t-cursors on an ndscope session). 

This is not a huge surprise; we'd already modeled the phase margin with this direct copy SWG:12301 has very low phase margin (modeled to be 23.8 [deg], with the highest upper unity gain frequency crossing at ~2.5 Hz; see dampingfilters_BBSS_2025-07-09.pdf page 33). Plus, experience has taught us that measured TFs often have more phase loss than models, so the phase margin of the loops is likely even less -- hence instability from 1/(1+G) gain peaking.

Ibrahim took some preliminary undamped TFs to confirm the (undamped) dynamical TFs of the BBSS with a glass optic. With what poor coherence we have in air, we can at least eye-ball confirm that they're not substantially different from the metal build on the test stand. Good! Great! We'll try to get these TFs better and Ibrahim will post for reference.

OK, with the dynamics checked out, on to the damping loops. Thus far the team had just rammed all the Level 2 BSFM loops on with a gain of -1.0, as we'd run them for years with the BSFM BS.

So, we did the dumb things first: 
    - We turned OFF the BSFM's BS highest bounce ("SB17.79" FM8) and roll ("SB26.06" FM9) mode frequency notch filters. We know these are the wrong frequency, and they're just eating up phase. (We plotted them, and it's not much at ~2 Hz, but they're the wrong frequency for a BBSS, so we just turned them OFF.) 
    - Turned on DOFs one or two at a time to narrow down which DOF(s) are problematic. T, V, R, and Y close fine and are stable with the old BSFM filters with a gain of -1.0. L and P are the loops that buzz at the 2.625 Hz (0.005 Hz resolution ASD with DTT).
    - Just reduce the overall gain of the loop(s) -- tried P at -0.5 and -0.25 with L still at -1.0. That was still unstable. But, L, P = -0.5, -0.5, is nicely stable, and damps stuff.

Getting slightly smarter, we checked in with the hard work of Vlad from LHO:81178 and found that the L and P filters have an EPICs gain of -1.0, and are identical in frequency response -- but the *filter* overall gain is a factor of 1.88x lower (i.e. essentially a factor of 2.0x). So -- he had to do essentially the same thing we did (though if I know Vlad, he actually measured this factor of 1.88x rather than blind guess like we did). Note that LLO's already using QOSEMs.

So, for now, we have something stable. Over time, we'll work on improving it, but this'll do. Once we have time, we'll take open loop gains, see exactly where we need phase, and adjust. Smart: Shouldn't need that much, change honestly. 
Just as I said in the acceptance review; Slides 33 and 34 of E2500057, we can easily relax the P low-pass filter and then regain the on-resonance pitch damping that we lost from dropping the overall gain by 2.0x.