Time-delayed feedback control of subcritical limit cycle oscillations in aeroelastic systems
摘要
This study presents the time-delayed feedback control for suppressing subcritical limit cycle oscillations of an elastically-mounted airfoil. The nonlinear aeroelastic model of a two-degree-of-freedom airfoil equipped with a trailing-edge control surface, where concentrated structural nonlinearity exists in the pitch degree of freedom, is established based on the quasi-steady aerodynamic model. The performance of time-delayed feedback control concerning the flutter onset speed is investigated through linear stability analysis. The method of multiple scales is employed to derive an analytical expression for the vibration amplitude under nonlinear time-delayed feedback, and the criticality curve representing the boundary between subcritical and supercritical bifurcation regions is established. The numerical results demonstrate that the proposed time-delayed feedback control of the nonlinear aeroelastic system can successfully convert the subcritical Hopf bifurcation to supercritical, and reduce the amplitude of limit-cycle oscillations.