A comb of line spaced by 50Hz is present in the PSTAB spectrum, and the projection of those lines in the sensitivity show that the 250Hz line, and maybe some other are dominating the contribution of 50Hz harmonics to the sensitivity. The real solution will be to have fully differential calbing from the PSTAB photodiodes, instead of single ended calbing inside the vacuum as is currently the case. In the mean time, a feed forward of the 50Hz and its harmonics could be tried to reduce those lines.
https://git.ligo.org/virgo/commissioning/commissioning-tasks/-/work_items/8
Paola has kindly explained how the 50Hz feed-forward into DARM is implemented in the DSP and I have replicated the method in Acl. The environmental channel is bandpassed around 50Hz and then a variable delay+gain filter is applied to the environmental channel with two continuously updated parameters. The filter gain is a simple product by a parameter, and the dephasing is formed by implementing an (s-s0)/(s+s0) filter manually in Acl retaining in a separate channel the previous value of a channel.
To obtain error signals for those two parameters the PSTAB channel after after adding the feed-forward correction is band passed at 50Hz, and multiplied by the environmental channel band passed around 50Hz and filtered by the dephasing filter. After low passing the result this yields the error signal for the gain parameter of the feedforward.
To obtain the delay parameter error signal, the environmental channel is first filtered by a pole at 1Hz, to dephase it by 90 degrees before multplying it with the PSTAB channel band passed at 50Hz and low-passing. In this way the other quadrature of the demodulation of the PSTAB by the environmental channel is obtained.
To test the Acl implementation Alain has setup a test process Acl17_INJ in the test instance of VPM: https://vpm.virgo.infn.it:40010/main.html?subsystem=Tests&process=Acl17_INJ
To access the data from it one needs to change the Cmdomain using the command "cmdomain CascinaTest" before starting dataDisplay, and then choosing the FbmMainTestUsers online server.
Figure 1 shows that after fixing many mistakes the 50Hz feed-back works in a test, reducing the 50Hz line in the target PSTAB channel by two orders of magnitude. FF_product_I/Q are the two error signals, while FF_gain and FF_z0 are the two variable parameters of the feed-forward filter. The adjustment of those filters is done using a simple pure integrator of the error signals, and the adjustment loop UGF is around 0.2Hz, I haven't tried to increase the UGF further.
One important aspect was to do the demodulation for calculating the FF_product_I/Q error signals after applying the dephasing signal to the environmental channel, so that the loop automatically tunes the demodulation phase. Initially the loop was not working at all, as the 50Hz line in the PSTAB channel was ~90 degree out of phase with the line in the environmental channel, which was swapping the two error signals.
This could be tested at some point on the actual PSTAB, starting from next week, to see if that idea works in practice. The code naming need to be first cleaned up, added into the ISYSnoise process to include it into the existing PSTAB_NOISE channel, and eventually replicated for all of the lines in the 50Hz harmanics comb.
