Limitations of Underactuated Modal Damping for Multistage Vibration Isolation Systems

The Laser Interferometer Gravitational-Wave Observatory 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. One control strategy likely to be employed in damping the high Q factor resonances of these systems is a modal damping technique. This technique simplifies the active damping design greatly by decoupling the system´s modal responses. However, the level of achievable damping is limited by the fact that these systems are underactuated and undersensed. This paper for the first time establishes the properties of these limitations when only a single degree of freedom is actuated and only velocity measurements are available.