A Feedback Linearization Approach for Panel Flutter Suppression with Piezolectric Actuation

Abstract

A panel is subject to dynamic instability when induced aerodynamic loads under the supersonic/hypersonic environment result in a self-excited oscillation called panel flutter. The panel of an aircraft that flies at supersonic speed or a structural panel that is in fluid flow at such regime may experience panel flutter. A plate with highly distributed piezoelectric actuators and sensors connected to processing networks, referred to as intelligent plate can actively control its vibrations. The objective of this research is to analytically demonstrate panel flutter suppression using piezoelectric actuation based on feedback linearization controllers. A nonlinear control system is formulated using the nonlinear dynamic equations for a simply supported rectangular panel with piezoelectric layers based on Galerkin’s method with modal expansions of nonlinear partial differential equation obtained from von Kárman large-deflection plate theory, which accounts for the structure nonlinearity. The nonlinear equations also account for loads such as externally applied in-plane loads, aerodynamic loads, and electrical displacements. The aerodynamic loads are given by the first-order piston theory or the quasi-steady supersonic theory. The control inputs are given by the electric fields required to drive the actuators based on piezoelectric actuation, which is modeled by linear piezoelectric constitutive relations. Outputs of the nonlinear system are feedback and used to transform it into an equivalent controllable linear system in new coordinates by formulating nonlinear feedback control laws, which cancel the nonlinear dynamics resulting in a linear system. The pole placement technique is then employed to make the states of the feedback linearized models locally asymptotically stable at a given equilibrium. Numerical simulations are carried out for the closed-loop systems at dynamic pressures higher than the critical dynamic pressures for the onset of panel flutter, where limit-cycle motions are generated. The simulated systems show that the closed-loop systems based on the controllers effectively suppress panel flutter limit-cycle motions with the generated piezoelectric bending actuations as control inputs. Therefore, with the feedback linearization controllers developed, the limit-cycle motion of panel flutter can be completely suppressed or the panel can be made flutter free if the controller gains are carefully selected.