Passivity‐based control of a magnetically levitated flexible beam

This 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. Copyright © 2008 John Wiley & Sons, Ltd.