Optimal distributed control of transverse vibration of a plate

Distributed control is an effective method for controlling and suppressing excessive vibrations of continuous systems. Optimal distributed control for a plate problem is solved utilizing a maximum principle after the introduction of a quadratic index of performance in terms of displacement, velocity and a control force as well as an adjoint variable. The problem is reduced to solving a system of partial differential equations for the state variable and the adjoint variable subjected to boundary, initial and terminal conditions. A numerical algorithm is presented to solve the optimal distributed control problem in the space-time domain which reduces the computational effort required to solve the initial-terminal-boundary, value problem. Results obtained for a simply supported rectangular, thin plate are also presented.