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This paper considers position and attitude control of large flexible space structures composed of a number of subsystems(substructures) which are interconnected by flexible links modeled by springs and dampers. It is assumed that sensors and actuators are collocated in each subsystem. The purpose of the paper is to propose a decentralized control method by local proper controllers using only displacement/angular displacement output, which makes both each closed-loop subsystem and an overall closed-loop system not only robustly stable against uncertainty of characteristic parameters such as mass, damping, and stiffness, but also optimal for a quadratic cost function.

Decentralized control is considered for large space structures composed of a number of subsystems which are connected by springs and dampers. It is assumed that sensors and actuators are collocated. It has been known that the overall system is stable under any perturbations in mass, damping and stiffness if the control law for each subsystem is direct velocity and displacement feedback (DVDFB). In this paper, a condition on interconnections between subsystems is presented under which stability of the overall system is preserved even in case some local controllers fail. Furthermore, it is shown that with appropriately chosen gains, the decentralized DVDFB is optimal for a quadratic cost function.

SUMMARYThis paper solves the asymptotic stabilization problem for a magnetically levitated flexible beam using a nested-loop passivity-based controller design. Passivity analyses reveal that the system can be decomposed into two passive subsystems: a mechanical subsystem that consists of a flexible beam with both ends free and that defines a passive map from external forces to the velocity of the points on the flexible beam at which the external forces act; and an electrical subsystem that consists of a pair of electromagnets and that defines a strictly output-passive map from voltages applied across the electromagnets to magnetic fluxes. The standard method for designing passivity-based controllers leads to a nonlinear feed-forward controller for the electrical subsystem, which enables the electrical subsystem to generate given desired magnetic forces, and an output feedback compensator for the mechanical subsystem, which computes the desired forces required to regulate the position and vibration of the beam. The asymptotic stability of each controller may be proven using Lyapunov's stability theory and LaSalle's invariant set theorem. Numerical simulations confirm the asymptotic stability of the equilibrium configuration of the closed-loop system formed by the magnetically levitated flexible beam together with the proposed controllers.

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