Optimal distributed control of transverse vibration of a plate

Authors: Bazezew, A.; Bruch, J.C.; Sloss, J.M.

Source: Engineering Computations: Int J for Computer-Aided Engineering, Volume 16, Number 6, 1999 , pp. 659-676(18)

Publisher: Emerald Group Publishing Limited

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Abstract:

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.

Keywords: Continuous systems; Maximum principle; Optimal control; Space-time domain; Vibration

Document Type: Research article

DOI: http://dx.doi.org/10.1108/02644409910281226

Publication date: 1999-09-01