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 cylindrical shell is investigated. The middle layer is made of FGM and its integrated with two functionally graded piezoelectric (FGP) layers which act as sensor and actuator used for controlling the vibration of the system. Equations of motion are derived based on FSDT using Hamilton’s principle. The governing equations are derived as partial differential equations and then discretized by Navier method. The state space model is extracted and the state feedback strategy with optimized LQR gain vector is designed to control the vibration of the system. To validate this study the frequency parameter is compared with previously published results and great agreement is observed. Eventually controlled and uncontrolled response of the system is presented and the effect of non-homogeneous index of FG layer on the settling time of control system is discussed.