Actuator sizing 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 10 Hz 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. Appropriately sized actuators are essential to achieving the necessary control performance while limiting the cost, noise, and complexity associated with larger actuators. This paper applies the plant´s pseudoinverse transfer function to analyze the least squares dynamic range required by the actuators to reject the stochastic disturbances exciting the Advanced LIGO quadruple pendulum isolation systems.