Peter F, Rana, Kiwamu,
As a preparation for the full lock study, we experimentally tried adjusting good coefficients for decoupling MICH from the other two in the LSC output matrix. Here are the results.
Precision for the PR2 and SR2 coefficients seem to be roughly a few % and 10 % respectively.
(Adjusting coefficients using the realtime lockin oscillators and demodulators)
We used the LSC realtime lockin oscillators and demodulators to find out the good output matrix for MICH. We drove BS at 131 Hz with an amplitude of 1000 cnts. At first, in order to find out the coefficient for removing PRCL out of MICH, we locked the sideband PRMI. We shook the M2 stage of both BS and PR2 in the longitudinal while changing the coefficient for PR2 manually until in-phase signal vanished at REFLAIR_RF45. We, of course, assumed REFLAIR_RF45 to be well tuned in its demod phase. Before the measurement we copied BS's inversion filter over to PR2 such that their frequency responses as seen from the LSC frontend are identical. In PR2, all other filters should be off and gain should be just unity.
Moving onto DRMI, we then shook PR2, BS and SR2. The coefficients for PR2 and BS were set to 1.0 and 0.02 so that we shake MICH more purely. Experimentally adjusting the coefficient for SR2, we found it to -0.014. The sign is negative because the effect of BS onto PRCL and SRCL are different and therefore it makes sense. We don't know why the PRC and SRC coefficients are different by 40% or so.
(Some tricks in SR2 M2 stage)
So for the setup in SR2, since one of the coil actuators had been dead, we used only LL and UR coils such that they still actuate without a large cross-couplings to the angular degrees of freedom at a cost of losing the half of actuation efficiency. This factor of two was then compensated in the Euler matrix by increasing them by a factor of two. We also copied the same BS inversion filter to SR2.