Time-Delayed Feedback Control of 2-D Supersonic Flapped Wings

This paper is concerned with the time delayed active control of a three-degrees-offreedom supersonic lifting surface in the vicinity of the flutter boundary. Particular attention is given to the study of bifurcation and stability in the vicinity of critical flight speed at which Hopf bifurcation occurs. The critical flight speed is defined in terms of the eigenvalues of the linearized system. Hopf bifurcation is associated with one pair of purely imaginary eigenvalues. Linear analysis is used to consider the stability of equilibrium solutions and the onset of bifurcations. Center manifold theory and normal form reduction technique are used to investigate the stability in the post-flutter regime. The effects of the time-delayed linear/nonlinear feedback controls on the aeroelastic response are investigated. Numerical simulations are carried out to verify the analytical predictions.