北京航空航天大学学报 ›› 2019, Vol. 45 ›› Issue (7): 1444-1450.doi: 10.13700/j.bh.1001-5965.2018.0688

• 论文 • 上一篇    下一篇

一类反馈型非线性系统的跟踪控制

虞江航, 徐军, 黄雨可   

  1. 北京理工大学 宇航学院, 北京 100081
  • 收稿日期:2018-11-22 出版日期:2019-07-20 发布日期:2019-07-25
  • 通讯作者: 徐军 E-mail:xujun2324@x263.Net
  • 作者简介:虞江航 男,硕士研究生。主要研究方向:飞行动力学与控制;徐军 男,博士,副教授。主要研究方向:飞行动力学与控制、非线性微分几何控制、飞行控制系统原型技术;黄雨可 男,硕士研究生。主要研究方向:飞行器总体设计。

Tracking control for a class of nonlinear systems in feedback form

YU Jianghang, XU Jun, HUANG Yuke   

  1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
  • Received:2018-11-22 Online:2019-07-20 Published:2019-07-25

摘要: 为了完成对一类反馈型非线性系统的控制,研究了该类非线性系统。首先,根据LaSalle不变性原理论证了一类自治系统收敛的引理。然后,引入误差函数,通过误差函数的Lyapunov函数寻找使得误差函数渐近稳定的控制器,再根据引理得出系统状态所跟踪的轨迹全部收敛,从而使得系统状态均有界,系统的输出趋于输入;论述了控制器使系统状态稳定的条件,给出了闭环系统稳定性的证明。最后,给出了一个固定翼飞机纵向运动飞行控制系统的算例,并且按照所提的方法设计了控制器,在MATLAB的Simulink模块下进行了仿真验证。结果表明,对于阶跃信号和正弦信号,所提出的控制方法能够使得飞机俯仰角快速收敛跟踪指令。

关键词: 非线性系统, 反馈, Lyapunov方法, 系统稳定性, 飞行控制系统

Abstract: In order to achieve the control of a class of nonlinear systems in feedback form, the system is studied. First, according to LaSalle's invariance principle, the convergence of a class of autonomous systems is proved. The error function is introduced, and the Lyapunov function of the error function is used to find the controller which makes the error function asymptotically stable. Then, according to the lemma, the trajectories tracked by the system states are all converged, so that the system states are bounded and the output of the system converges to input. The condition and the proof of the stability of the closed-loop system are given. Finally, an example of longitudinal dynamics of an fixed-wing aircraft flight control system is presented, and the controller is designed according to the proposed method. The simulation is verified under the Simulink module of MATLAB. The results show that, for step signals and sinusoidal signals, the proposed controller can enable the pitch angle of aircraft to quickly converge the tracking command.

Key words: nonlinear systems, feedback, Lyapunov methods, system stability, flight control systems

中图分类号: 


版权所有 © 《北京航空航天大学学报》编辑部
通讯地址:北京市海淀区学院路37号 北京航空航天大学学报编辑部 邮编:100191 E-mail:jbuaa@buaa.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发