On Feb 18, 2023 I was able to grab some low-coherence measurements of all of our ASC loops. Here is the DHARD Pitch OLG, and the associated digital filters for DHARD_P and RPC_DHARD_P at the time of the measurement. There are potentially seven UGFs (looking at the 0.05 Hz binwidth plot. 1) 0.47 Hz 2) 0.80 Hz 3) 1.40 Hz 4) 1.96 Hz 5) 2.17 Hz 6) 2.24 Hz 7) 4.55 Hz There is definitely significant peak splitting observed in this plant, even at the wide binwidth it is clear in the lower suspension peak. At the peak splits there is rapid phase rotation as one might expect, this is even well-resolved in the 0.02 Hz plant. Again, there are two unintended UGFs (the ones at 2.17 Hz and 2.24 Hz). The phase here is not too bad, so this does not necessarily hurt our stability too badly in this loop. 2.2 Hz is a particularly troubling frequency for us in many loops, so it is not necessarily surprising that we see some unexpected loop dynamics here. Hard to say which loop is the true cause of our troubles here. However, the controller for this loop is well-designed to counter this plant (last PDF). It suppresses the region between the suspension resonances, enforcing decently low gain at the phase zero-crossings (like at 0.64 Hz and 1.66 Hz). The RPC feedback does not dominate in very many locations, and is mostly out of phase with the regular controller at those frequencies where is does dominate. This mostly adjusts the phase response of the controller between 0.6 and 2 Hz.
Here is a plot comparing the 0.05Hz binwidth measurement with a model. Similar to other arm ASC models, this is best fit assuming 290 kW of circulating power. I have not made a measurement of the DHARD P optical gain, but before this measurement, I have been assuming roughly 4e10 ct/rad for DHARD P. In order to match the measurement, I found that I needed to scale the OLG by 1.25, suggesting that the DHARD P optical gain is about 5e10 ct/rad.
Similar to my other models, I am using only the L2 and L3 stages, no effect from M0.
The appearance of right-half-plane zeros here (and similarly in the cHard pitch compensation) is perhaps not surprising. The point of the digital radiation-pressure compensation is to soften the optomechanical plant back to its O(1 Hz) dynamics at low power, while the point of the remaining digital loop-shaping compensation is to produce a closed-loop response with a few hertz bandwidth, which is a stiffening of the system dynamics and hence should tend to have an opposite sign to the radiation pressure compensation. Since both dynamical effects have roughly similar time constants for the hard loops, they also have similar magnitudes, and thus produce RHP zeros.
You may be able to eliminate these RHP zeros with more gain in the loop-shaping compensator (i.e., do you really have to invert the 10 W optomechanical plant so precisely?), but they might recur when the circulating arm power (and hence the radiation pressure compensation) increases in the future.