Optimal open/closed-loop control for systems with distributed parameter

• Published in: Journal of the Franklin Institute Vol. 332; no. 1; pp. 5 - 19
• Main Authors: Sadek, Ibrahim S., Yürekli, Osman
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1995
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/0016-0032(94)00018-F

An optimal control problem for multi-dimensional structures described by a system of partial differential equations is considered. A combined open- and closed-loop mechanism is incorporated into 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 eigenfunction 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.