Finite element analysis and design of control system with feedback output using piezoelectric sensor/actuator for panel flutter suppression

A general finite element formulation of an optimal control scheme such as a linear quadratic regulator (LQR) with output feedback is presented for the nonlinear flutter suppression of a composite panel with piezoelectric actuators and sensors. Most of the studies on panel flutter suppression have been based on LQR full state feedback control law where all the state components are assumed to be available and thus the previous LQR controllers cannot be suitable for actual applications. This work intends to develop output feedback control law that provides a more meaningful design approach in practice for panel flutter suppression. The governing equations are derived through the use of the principle of virtual displacements and a finite element discretization is performed with the C1C1 conforming four-node rectangular element. Additional electrical degrees of freedom are introduced to model piezoelectric actuators and sensors. The discretized dynamic equations of motion are transformed into a nonlinear coupled-modal equation by using the proper modal coordinates and then the equation is transformed into a state space model in order to design controller. For maximum control effect, the shape and location of the actuators and sensors are determined by using genetic algorithms. The flutter suppression results are presented in the time domain using the Newmark-ββ method.