Abstract:

I designed a new filter to improve PRCL control.
The unity gain frequency (UGF) will shift from 20 Hz to 40 Hz, and the phase margin at the UGF will increase from 30 degrees to 45 degrees.

Detail:

Although the reason for the low coherence between DARM and PRCL is not understood well, it is likely that PRCL displacement dominates the DARM sensitivity in the 10–30 Hz range, as discussed in klog:33357.
This is primarily because the current PRCL feedback filter provides a limited phase margin of approximately 30 deg around the UGF at 20 Hz, which leads to an enhancement of PRCL displacement in this frequency band.
As shown in the bottom right panel of Fig.1, which displays the closed-loop transfer function 1/(1 + G), the displacement at 30 Hz is amplified by roughly 9 dB.

Given that the PRCL displacement can now be measured clearly up to 50 Hz, due to increased optical power compared to O4a, it is feasible to increase the UGF without injecting significant sensing noise at high frequencies.
Based on this, I have designed a new PRCL feedback filter.

I temporarily updated FM1 in PRCL2 (named "temp"), which previously contained a simple gain(10 dB) filter.
The new filter consists of a straightforward zero-pole configuration: zpk([1; 2; 2; 10], [0; 0.05; 0.05; 100], 1, n) zpk([], [1000], 1, n) gain(111 dB).
To avoid displacement enhancement near the UGF, no sharp filters were introduced to suppress high-frequency feedback of the sensing noise.

Figure 2 compares the current (blue) and proposed (red) PRCL open-loop transfer functions.
The new UGF and phase margin will be 40 Hz and 45 degrees, respectively.
This modification is expected to yield an improvement of approximately 5–10 dB in DARM sensitivity in the 10–30 Hz band.

Next, I will produce a projection plot showing the expected PRCL contribution with the new filter and confirm that feedback of the sensing noise will not become a limiting factor for the DARM sensitivity.