Closed-loop Grammians of flexible space structures

The control of flexible space structures (FSS) is often analyzed in a centralized framework, where the outputs of all sensors on the structure are fed back to all of the actuators. This paper studies how much a decentralized controller can shift closed-loop poles for a given control effort. This question is analogous to the centralized control problem of determining the degree of controllability of each mode of a system. Exploitation of the special form of the equations of motion of flexible structures has permitted simple results to be obtained for this problem for the case of widely-spaced natural frequencies. A new closed loop controllability Grammian is developed. This matrix is defined for the FSS with a constant output feedback loop closed around it, and so reflects any decentralised structure that is imposed on the gain matrix