Modal damping of a quadruple pendulum for advanced gravitational wave detectors

The Laser Interferometer Gravitational-Wave Observatory (LIGO) has begun a major set of upgrades to reach a sensitivity better than 10^-19 m/√(Hz) in the 10Hz to 10 kHz frequency band. This advance is expected to bring gravitational wave observations of relativistic astrophysical events such as black hole mergers and supernovae into the realm of regular astronomy. These upgrades require complex vibration isolation systems to better decouple the test masses from ground disturbances. These high performance systems require correspondingly more complex and aggressive active control loops to meet the increased demand in instrument sensitivity. This paper applies a modal damping technique with state estimation to optimize the trade-off between disturbance rejection and sensor noise amplification. The state estimator design applies a customized cost function around the Linear Quadratic Regulator (LQR) algorithm.