Active optimal control of functionally graded laminated sandwich cylindrical shells integrated with functionally graded piezoelectric layers using LQR

In this paper active optimal control of sandwich cylindricalshell is investigated. The middle layer is made of FGM andits integrated with two functionally graded piezoelectric(FGP) layers which act as sensor and actuator used forcontrolling the vibration of the system. Equations of motionare derived based on FSDT using Hamilton’s principle. Thegoverning equations are derived as partial differentialequations and then discretized by Navier method. The statespace model is extracted and the state feedback strategy withoptimized LQR gain vector is designed to control thevibration of the system. To validate this study the frequencyparameter is compared with previously published results andgreat agreement is observed. Eventually controlled anduncontrolled response of the system is presented and theeffect of non-homogeneous index of FG layer on the settlingtime of control system is discussed.