Adaptive backstepping control of a nonlinear aeroelastic system

For a two-dimensional airfoil with leading-edge and trailing-edge control surfaces, the nonlinear aeroelastic equations under the supposition of quasi-steady aerodynamic forces were established and were described in state space form. The control variables of the leading and trailing edges were coupled resulting that the backstepping control method could not be used directly. To solve the problem, two equivalent control laws were newly defined. Supposing that the system has parametric uncertainty in the cubic nonlinearity in pitch, an adaptive control law was designed based on Lyapunov stability theory. In order to verify the validation of the control law, the dynamic equations were solved numerically by using Runge-Kutta method. The simulation results show that the open-loop aeroelastic system is unstable with limit cycle oscillation, while the close-loop system reaches to stable as a result of the adaptive control law. With double control surfaces, the flutter critical velocity is improved after the control design. Taking the limits of the control surface deflection in reality into account, the invalidation problems of the single control surface are discussed. Just considering the effectiveness of the single control surface, the system using the trailing edge control surface is better than that of using the leading edge control surface.