Optimal Vibration Control of a Rectangular Piezothermoelastic Plate

Marwan Abukhaled and Ibrahim Sadek


Optimal control, piezolectric, thermoelastic, time delay process, process interaction


This paper presents the vibration control of a thermoelastic rectangular plate subjected to sudden heat inputs. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time with the least expenditure of control forces. The solution method is a combination of a modal expansion and a variational approach. By modal expansion, the problem is converted from an optimal control of a distributed parameter system into an optimal control of a lumped parameter system. The variational approach will be employed to derive an explicit optimal control law and the determination of the corresponding displacement and velocity is obtained by solving a set of ordinary differential equation.

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