Dynamics and control of high precision magnetically levitated vibration isolation systems

Vibration control of flexible structures has received a great deal of interest in recent years. Several authors have investigated this topic in the areas of robot manipulators, space structures, and flexible rotors. Key issues associated with the dynamics and control of vibration isolation systems are addressed. Among other important issues to consider in the control of such systems, the location and number of actuators and sensors are essential to effectively control and suppress vibration. We first address the selection of proper actuator and sensor locations leading to a controllable and observable system. The Rayleigh-Ritz modal analysis method is used to develop a lumped-parameter model of a flexible vibration isolation table top. This model is then used to investigate the system's controllability and observability including the coupling effects introduced by the magnetic bearing. This analysis results in necessary and sufficient conditions for proper selection of actuator and sensor locations. These locations are also important for both controller system's complexity and stability of point of views. A favorable pole-zero plot of the open loop transfer functions is presented. Necessary and sufficient conditions for reducing the controller complexity are derived. The results are illustrated by examples using approximate mode shape functions.