Approximately two weeks ago I diagonalized the LSC output matrix for the DRMI locking.
Since actuation on the position of BS changes not only MICH but also PRC and SRC, we needed to diagonalize the output matrix.
- What I did :
(1) The DRMI was locked. At this point PRC, MICH and SRC was controlled by PRM, BS and SRC actuators respectively.
(2) I injected excitation signal on C1:LSC-MICH_EXC by awg. The excitation was at about 200 Hz, which is above the UGF of all the LSC loops.
At this point the excitation only shakes the position of BS.
(3) I looked at spectra of REFL11_I, AS55_Q, AS55_I, that were used to sense PRC, MICH and SRC respectively.
At the beginning I was able to see the peak due to the excitation in those spectra. This means BS shakes the other DOFs (i.e. PRC and SRC) as well as MICH.
(4) To minimize the coupling from MICH to PRC (or SRC), I tuned a number on an element of the output matrix, which transfers the signal from MICH to PRM (or SRM).
This business was done by looking at the peak on REFL11_I (or AS55_I) and minimizing it. Since this technique was too naive the tuning was done only in second decimal place.