北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (6): 1128-1134.doi: 10.13700/j.bh.1001-5965.2014.0423

• 论文 • 上一篇    下一篇

非线性气动弹性系统反演自适应控制

刘送丹, 李道春, 向锦武   

  1. 北京航空航天大学 航空科学与工程学院, 北京 100191
  • 收稿日期:2014-07-17 出版日期:2015-06-20 发布日期:2015-07-30
  • 通讯作者: 向锦武(1964—),男,湖南平江人,教授,xiangjw@buaa.edu.cn,主要研究方向为飞机总体设计、结构设计技术. E-mail:xiangjw@buaa.edu.cn
  • 作者简介:刘送丹(1991—),女,湖南常德人,硕士研究生,lsdmm2012@163.com
  • 基金资助:
    国家自然科学基金(91216102,11402014); 中央高校基本科研业务费专项资金(YWF-14-HKXY-026)

Adaptive backstepping control of a nonlinear aeroelastic system

LIU Songdan, LI Daochun, XIANG Jinwu   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-07-17 Online:2015-06-20 Published:2015-07-30

摘要: 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.

关键词: 二元机翼, 非线性气动弹性, 颤振, Lyapunov稳定性理论, 反演自适应控制

Abstract: 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.

Key words: two-dimensional airfoil, nonlinear aeroelasticity, flutter, Lyapunov stability theory, adaptive backstepping control

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