If we use a digital PLL for locking the frequency of the PSL and END green lasers then we can expect a UGF of around 1kHz (assuming a sampling rate of 16kHz). Let's assume a simple 1/f loop giving a loop gain of ~1000x at 1Hz. If the free-swinging ETM pendulum motion at 1Hz is of the order of 1 micron, then the residual motion at 1Hz, once we lock the digital PLL by actuating on the ETM position, will be of the order of 1nm. This is bordering on too high.
Alternatively, is we use an analogue PLL then we can expect a much higher UGF and many orders of magnitude more gain at 1Hz (see here). So we would expect the residual motion of the pendulum to be much smaller - probably limited by some other noise source somewhere in the system (I doubt it's going to be reduced by 12 orders of magnitude).
RA: I think ballpark's not good enough for this. To see what's good enough, we need to to an analysis similar to what Bram has for the ALS. Get the 40m seismic spectrum from the arm locking spectrum or the green laser feedback signal and then correct it for a realistic loop shape.
KA: For this purpose I have made the simulink model for the green locking more than a year ago, but the entire green team has consistently neglected its presence...
Agreed. It doesn't completely rule out the digital PLL. I'll check out Kiwamu's model.