Energy minimization of vibrating plates subject to constraints on open and closed loop control forces

Abstract The undesirable vibrations of a rectangular plate are suppressed by means of a combined open-closed loop control mechanism. The closed loop control mechanism is assumed to be proportional to displacement. The energy functional of the plate is minimized within a specified period of time with respect to both the open loop function and the displacement feedback parameter. The minimization is carried out subject to constraints on the open loop control force as well as on the closed loop force. For the open loop constraint a Lagrange multiplier is used to incorporate the contraint into an augmented energy functional. An explicit solution of the open loop control problem is obtained. Numerical results are given to indicate the effectiveness of the proposed control.