Stability of a two-dimensional airfoil with time-delayed feedback control

This paper presents a systematic study on aeroelastic stability of a two-dimensional airfoil with a single or multiple time delays in the feedback control loops. Firstly, the delay-independent stability region of the aeroelastic system with a single time delay is determined on the basis of the generalized Sturm criterion for polynomials. Then, the stability switches with variations in time delay are analyzed when the system parameters fall out of the delay-independent stability region. Flutter boundaries of the controlled aeroelastic system as time delay varies are predicted in a continuous way by the predictor-corrector technique. Finally, two methods, the polynomial eigenvalue method and the infinitesimal generator method, are introduced to investigate the stability of the controlled aeroelastic system with multiple time delays. Numerical simulations are made to demonstrate the effectiveness of all the above approaches.