Over the last days, we did several measurements of the DSOFT and DHARD loops to investigate the oscillations that lead to loose lock. In particular 0.47 Hz and 1.1 Hz oscillations are seen frequently.

With the angular controls offloaded to M0, we first checked the cross-over frequency between M0 and L1. We drove the two stages through the hierarchical path and measured the angular signals with the oplevs. The model is in very good agreement with the measurements and we can extrapolate that the cross-over frequency is slightly above 0.1 Hz (see figure 1). We also check the angular LOCK filters in all test masses are the same, which is mostly true, expect for a gain difference in M0 ETMX P (see figure 2 and 3).

DSOFT P: The loop was measured at 20W without the Radiation Pressure Compensation (RPC) and without the RESG filter. We observed an unexpected phase shift around 0.46 Hz.

• When modeling the loop, a possible way to reproduce this feature is to consider a coupling of few % of DHARD with DSOFT in the sensing (see figure 4). (edit: Sheila pointed out that this particular measurement is not trustworthy). Improving the sensing decoupling (see alog 46816) didn't change the feature, as seen in figure 5 where we measured the loop at 30W in the nominal low noise configuration.
• Using the same filters, I modeled the loop at different input powers (see figure 6), we can see that a similar feature also appears at low power, but we know that the circulating power is around 140kW.
• I also modeled the loop at 30W input with a 8% imbalance between the arms (see figure 7). This doesn't explain the feature.
• When increasing the M0 contribution by a factor 3, the phase variation is between 0.4 and 0.5 Hz matches better the measurement (see figure 8). This also increases the dip at 0.46Hz that drives the instability.

I would suggest to decrease the M0 gain by a factor 3 to decrease the crossover, and remeasure the loop to see if this removes the instability.  I would also recommend to increase the gain if this is compatible with the noise coupling in the IFO.