Free swing MI differential length is 86 nm RMS and residual length when locked is 0.045 nm RMS(in-loop).
Looks very quiet. Comparison with PRMI is the next step.
Openloop transfer function:
OLTF of simple MI lock using AS55_Q_ERR as error signal and ITMs as actuators is below.
UGF ~ 90 Hz, phase margin ~ 40deg
I added 16 Hz resonant gain to suppress bounce mode.
MI differential length spectra:
Below. Calibration was done using calibrated AS55_Q_ERR and actuator response(elog #8242)
Expected free swing is calculated using
x_free = (1+G)/G * A * fb
where G is openloop transfer function, A is actuator response, fb is feedback signal(C1:LSC_ITMX/Y_IN1) spectrum. I used A as simple pendulum with resonant frequency at 1 Hz, Q = 5. Since free swing RMS is dominated by this resonance, RMS depends on this Q assumption.