Modal control with state estimation for advanced LIGO quadruple suspensions

Abstract

Gravitational waves are predicted to exist by Einstein's General Theory of Relativity. These waves are distortions of space-time which until now have remained outside the realm of possible detection, due to their incredibly weak interactions. Now, due to newly built highly sensitive observatories, such as the Laser Interferometer Gravitational Wave Observatory (LIGO), these detections are now believed to be possible and may occur in the very near future. The research discussed here is on an active control system for the quadruple pendulum, from which the mirrors of the LIGO interferometer are suspended. This pendulum is a chain of four masses used to provide seismic isolation of the mirrors at the level of 10-19 m Hz-1/2 at 10 Hz. Because the pendulum is so quiet above 10 Hz, the sensor noise used in the active control is not trivial. Thus, the purpose of this research is to optimize a control scheme that has high gain at the resonant frequencies of the pendulum to provide damping while at the same time rolling the gain off to virtually zero at the limit of the gravitational wave detection band less than half a decade away. This requirement is very difficult to achieve with classical control design techniques. The alternative method explored here is a type of modal control with state estimation where incomplete sensor information is reconstructed and mathematically decomposed into modal responses. The modal responses can be thought of as simple single degree of freedom oscillators that are very easy to control. In this way, a few highly complicated controllers are traded for a larger collection of reasonably simple ones that are easy to design for each mode. Damping vs. noise injection can then be optimized by tailoring the control gain on each mode.