A Lower Limit on Controls Noise in LIGO's Suspended Optic

Since the first version of the Laser Interferometer Gravitational-wave Observatory (LIGO), suspended optics have proved vital to decoupling seismic noise from optical motion. In the 10-20Hz band, the control loop that steadies these optics introduces significant controls noise, which is amplified sensing noise. While this noise currently does not hinder LIGO's ability to detect gravitational waves, upgrades like frequency dependent squeezing incorporate more suspended optics which could benefit from lower controls noise. We model a new control system design using Kalman filters and modern optimal control methods to estimate the lower limit on the controls noise in LIGO's suspensions. Since controls noise is a limiting noise in other processes in the LIGO detectors, having a lower limit of this noise can inform how well essential processes, like LIGO's arm-length stabilization, can perform. We also look at how an improvement in the sensor array can improve the overall state estimation of the suspension and help to improve the controls design and decrease extraneous noise.