Effect of control surface freeplay on nonlinear aeroelastic responses of an airfoil

Dynamic equations of a two-dimensional airfoil with cubic nonlinearity in pitching degree-of-freedom and freeplay in the control surface are derived, where Theodorsen unsteady aerodynamics is adopted. Then the equations are rewritten in state space form. Based on the state-dependent Riccati equation method, a nonlinear control law is designed for its flutter control. The Runge-Kutta numerical approach in conjunction with Henon's method is used to investigate the effect of the control surface freeplay on the open/closed-loop system responses. In order to avoid instability, switching points of the freeplay are located by using Henon's method. Simulation results are presented. Because of the existence of cubic nonlinearity in pitch, the flutter responses of a freeplay system become limit cycle oscillations with a stable amplitude. With the increase of the flow speed, the control surface freeplay has less influence on the open-loop response. When the flow velocity is higher, the control surface freeplay may cause overdamping responses of the closed-loop system.