Element and system design for active and passive vibration isolation

Abstract

This thesis focusses on broadband vibration isolation, with an emphasis on control of absolute payload motion for ultra-precision instruments such as the MIT/Caltech Laser-Interferometric Gravitational Wave Observatory (LIGO), which is designed to measure spatial strains on the order of 10-²¹. We develop novel passive elements and control strategies as well as a framework for concurrent design of the passive and active elements of single-stage and multi-stage isolation systems. In many applications, it is difficult to construct passive isolation systems compliant enough to achieve specifications on low-frequency ground transmission without introducing hysteresis as well as high-frequency transmission resonances. We develop and test a compliant support that employs a post-buckled structure in con- junction with a compliant spring to attain a low-frequency, low-static-sag mount in a compact package with a large range of travel and very clean dynamics. Most passive damping techniques increase ground transmission at high frequency, but tuned-mass dampers are decoupled from the ground. We explore the tuned-mass damper as a passive realization of the skyhook damper, obtain the optimal designs for multiple-SDOF systems of dampers, propose the concept of a multi-DOF damper, and show that MDOF dampers that couple translational and rotational motion have the potential to provide performance many times better than that traditional tuned-mass dampers. Active control can be used to improve low-frequency performance, but high-gain control can amplify sensor and actuator noise or cause instability. We study several control strategies for uncertain plants with high-order dynamics.

(cont.) In particular, we develop a novel control strategy, "model-reaching" adaptive control, that drives the system onto a dynamic manifold defined directly in terms of the states of the target. The method can be used to robustly increase the apparent compliance of an isolation mount and maintain a -40 dB/decade roll-off above the resulting corner frequency.