OPTIMAL OPEN CLOSED-LOOP CONTROL FOR SYSTEMS WITH DISTRIBUTED-PARAMETER

An optimal control problem for multi-dimensional structures es described by a system of partial differential equations is considered A combined open- and closed-loop mechanism is incorporated in to the formulation of the problem and a general method of solution is presented. Two performance indices are introduced and minimized with respect to the open-loop control functions and the closed-loop control parameters. The optimality condition for the open-loop control is derived in form of the integral equations by using the methods of eigen-function expansion and variational calculus. The closed-loop control parameters are numerically determined from the minimization of the energy of the system subject to a constraint on the maximum amount of closed-loop control force that can be applied. The proposed approach is applied to a shear deformable Beam excited by an initial disturbance. An explicit solution of the problem is obtained and numerical results are given to investigate the effectiveness of the proposed control mechanism.