Active control of nonlinear panel flutter under yawed supersonic flow

A coupled structural-electrical modal finite element formulation for composite panels with embedded piezoelectric sensors and actuators is presented for nonlinear panel flutter suppression under yawed supersonic flow. The first-order shear deformation theory for laminated composite plates, the von Karman nonlinear strain-displacement relations for large deflection response, the linear piezoelectricity constitutive relations, and the first-order piston theory of aerodynamics are employed. Nonlinear equations of motion are derived by extending the three-node triangular Mindlin (MIN3) plate element. Additional electrical degrees of freedom are introduced to model piezoelectric sensors and actuators. The system equations of motion are transformed and reduced to a set of nonlinear equations in modal coordinates. Analysis results for the effect of arbitrary flow yaw angle on nonlinear supersonic panel flutter are presented. The results show that the flow yaw angle has a major effect on the panel limit-cycle oscillation amplitude and deflection shape. Two different control methods are investigated for the suppression of nonlinear panel flutter. The first method is the linear quadratic Gaussian controller. The second method is the nonlinear output controller comprised of a linear quadratic regulator and an extended Kalman filter nonlinear state estimator. Closed-loop criteria based on the norm of feedback control gain and on the norm of Kalman filter estimator gain are used to determine the optimal location of piezoelectric actuators and sensors at different flow yaw angles. Optimal sensor and actuator locations for a range of yaw angles are determined by grouping the optimal locations for different angles within the range. The results demonstrate the effectiveness of piezoelectric materials and of the nonlinear output controller in suppressing nonlinear flutter of isotropic and composite panels at different flow yaw angles.