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		Ibrahim SADEK,Marwan ABUKHALED.[en_title][J].Control Theory and Technology,2013,11(3):463~467.[Copy]

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IbrahimSADEK,MarwanABUKHALED
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(Department of Mathematics and Statistics, American University of Sharjah)

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Received:October 04, 2011Revised:July 04, 2012

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Optimal control of thermoelastic beam vibrations by piezoelectric actuation

Ibrahim SADEK,Marwan ABUKHALED

(Department of Mathematics and Statistics, American University of Sharjah)

Abstract:

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a single piezoelectric actuator. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations. Numerical results are presented to demonstrate the effectiveness and the applicability of the proposed method.

Key words: Modal expansion approach Optimal control Thermoelastic beam Piezoelectric actuation Variational approach