控制面间隙对非线性二元机翼气动弹性响应的影响

Effect of Control Surface Freeplay on Nonlinear Aeroelastic Responses of an Airfoil

采用Theodorsen非定常气动力建立同时含有俯仰立方非线性和控制面间隙非线性二元机翼的运动方程,并以状态空间形式描述。基于状态依赖Riccati方程控制方法,设计了非线性颤振控制律。综合运用Runge-Kutta数值方法与Henon方法,研究了控制面间隙对系统开环/闭环响应的影响。其中Henon方法用以准确快速地确定间隙非线性的转折点,从而可以避免间隙非线性引起的数值不稳定现象。仿真结果显示,俯仰立方非线性可以使间隙非线性系统产生振幅稳定的极限环振荡;控制面间隙对开环响应的影响随着来流速度的升高而减弱;在速度较高的情况下,控制面间隙导致闭环系统响应产生过阻尼现象。

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.