Panel flutter suppression with an optimal controller based on the nonlinear model using piezoelectric materials

Abstract

This work intends to develop an optimal control strategy to suppress the flutter of a supersonic composite panel using piezoelectric actuators. In this study, an optimal control design based on the nonlinear model is investigated in order to obtain the higher maximum suppressible dynamic pressure with a lower control input as compared to a controller based on the linear model. The actuator for the suppression of panel flutter is implemented by using piezoceramic PZT and the shape and location of the PZT patches are determined by using genetic algorithms. The governing equations are derived through the use of the principle of virtual displacements and a finite element discretization is performed with the C1 conforming rectangular element. The discretized dynamic equations of motion are transformed into a nonlinear coupled-modal equation by using the proper modal coordinates and the nonlinear coupled-modal equations are then transformed into a state space model in order to design controller. Linear quadratic regulator (LQR) optimal control scheme is employed to determine the feedback gain. The flutter suppression results by an optimal controller based on the linear and nonlinear model are compared in the time domain using the Newmark-β method for a simply supported piezolaminated composite panel subjected to uniform thermal loading. As the time advances by the time integration, since the system matrix is the function of nonlinear modal stiffness matrix, the system matrix also is modified after each iteration within each time step. The results show that an optimal controller based on the nonlinear equation effectively attenuate the flutter to a relatively higher dynamic pressure with a lower control input as compared to a controller based on the linear model.