Using a Rayleigh-Ritz approximation to model the transverse vibration of the Poisson-Kirchoff plate an energy based linear coupling control (LCC) strategy, for free and forced vibrations of the plate, is developed. The controller seeks to minimize a quadratic control objective and is implemented for a reduced order model by coupling a virtual second order system with each critical mode in the quadratic control objective. The energy transfer phenomena between each mode and the controller is maximized by coupling the appropriate states of the plant and the controller. Energy is transfered from the plant to the controller where it is dissipated via linear damping.

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