OPTIMAL ACTIVE CONTROL OF DISTRIBUTED-PARAMETER SYSTEMS WITH APPLICATIONS TO A RAYLEIGH BEAM

A class of control problems for self-adjoint systems described by linear partial differential equations is considered. Problems of this type are of significant practical interest, for example, in controlling flexible or very large space structures. A method is proposed to damp the undesirable vibrations in the structures actively by means of open-loop and closed-loop control. Necessary and sufficient conditions of optimality are derived in the form of integral equations which lead to explicit expressions for the open-loop control. The feedback parameters of the closed-loop control are numerically determined from the solution of a minimization problem. The proposed approach is illustrated by a numerical example on a vibrating Rayleigh beam subject to certain initial conditions, in which the effectiveness of the control and the amount of force spent in the process are investigated. © 1990 Oxford University Press.