非线性气动弹性系统反演自适应控制

针对双自由度二元机翼,利用准定常气动力建立了非线性气动弹性方程,并以状态空间形式描述.双控制面非线性气动弹性系统中前后缘控制量相互耦合,不能直接应用反演自适应控制方法,为了解决这一问题,新定义了两个等效控制器.考虑俯仰方向立方非线性参数未知,根据Lyapunov稳定性理论设计了反演自适应控制律.通过Runge-Kutta数值方法对气动弹性方程进行求解,验证了控制律的有效性.仿真结果表明:所设计的控制器能够使开环不稳定的气动弹性系统稳定至零点,双控制面的作用提高了颤振临界速度.考虑到实际控制面的偏转限制,研究了单控制面失效问题,结果显示单后缘控制面比单前缘控制面对系统控制更有效.

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.