基于反步法非线性纯反馈系统的控制器设计

doi:10.11772/j.issn.1001-9081.2017061365

计算机应用 ›› 2018, Vol. 38 ›› Issue (1): 300-304.DOI: 10.11772/j.issn.1001-9081.2017061365

• 应用前沿、交叉与综合 • 上一篇

基于反步法非线性纯反馈系统的控制器设计

贾付金, 蒋沅

南昌航空大学信息工程学院, 南昌 330000

收稿日期:2017-06-05 修回日期:2017-07-24 出版日期:2018-01-10 发布日期:2018-01-22
通讯作者: 贾付金
作者简介:贾付金(1988-),男,安徽阜阳人,硕士研究生,主要研究方向:非线性系统理论、输出调节理论;蒋沅(1982-),男,浙江金华人,副教授,博士,主要研究方向:飞行器控制设计、电机控制及优化。
基金资助:
国家自然科学基金资助项目（61663030，61663032）；江西省自然科学基金资助项目（20142BAB207021）；江西省教育厅科技项目（GJJ150753）；无损检测技术教育部重点实验室（南昌航空大学）开放基金资助项目（ZD29529005）；南昌航空大学研究生创新专项资金项目（YC2016-S350）；南昌航空大学第十二届三小重点项目（2017ZD021）。

Design of controller based on backstepping nonlinear pure feedback system

JIA Fujin, JIANG Yuan

School of Information Engineering, Nanchang Hangkong University, Nanchang Jiangxi 330000, China

Received:2017-06-05 Revised:2017-07-24 Online:2018-01-10 Published:2018-01-22
Supported by:
This work is partially supported by the National Natural Science Foundation of China (61663030, 61663032), the Natural Science Foundation of Jiangxi Province (20142BAB207021), the Scientific and Technological Project of Jiangxi Educational Committee (GJJ150753), the Open Foundation of Key Laboratory of Nondestructive Testing (Nanchang Hangkong University), Ministry of Education (ZD29529005), the Innovaion Fund Designated for Graduate Students of Nanchang Hangkong University (YC2016-S350), the "Small Invention, Small Manufacture, Small Creation" Key Projects of the Twelfth of Nanchang Hangkong University (2017ZD021).

摘要/Abstract

摘要： 针对由于非线性纯反馈系统存在非仿射性结构使得用以往的坐标变换难以设计出控制器的问题，提出了一种新的坐标变换，并引入了一阶控制输入的辅助系统来处理非线性纯反馈系统。首先，结合新提出的坐标变换，计算出新状态方程；然后，基于反步法在每一步中设计出正定的Lyapunov函数；最后，通过设计虚拟控制器和实际的辅助控制器使得Lyapunov的导数负定，这样从理论上解决了非线性纯反馈系统的跟踪问题。仿真实验表明所设计的辅助控制器能使得纯反馈闭环系统所有状态信号有界，控制输出能跟踪到给定信号，跟踪误差渐近地趋于稳定，从而达到要求。

关键词: 纯反馈系统, 坐标变换, 反步法, Lyapunov函数

Abstract: To solve the problem that it is difficult to design a controller by previous coordinate transformation because there is nonaffine structure in nonlinear pure feedback system, a new coordinate transformation was proposed and a first-order control input auxiliary system was introduced to deal with the nonlinear pure feedback systems. Firstly, a new state equation was calculated by combining the new coordinate transformation. Secondly, positive definite Lyapunov function was designed for each step based on the backstepping method. Finally, the derivatives of Lyapunov functions were made negative by designing virtual controllers and auxiliary controller, so the tracking problem of nonlinear pure feedback systems was theoretically solved. The experimental results show that the designed auxiliary controller is able to make the state of the nonlinear system bounded globally, and the control output can track the given signal, and the tracking error becomes asymptotically stable.

Key words: pure feedback system, coordinate transformation, backstepping method, Lyapunov function

中图分类号:

TP271.6

贾付金, 蒋沅. 基于反步法非线性纯反馈系统的控制器设计[J]. 计算机应用, 2018, 38(1): 300-304.

JIA Fujin, JIANG Yuan. Design of controller based on backstepping nonlinear pure feedback system[J]. Journal of Computer Applications, 2018, 38(1): 300-304.

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基于反步法非线性纯反馈系统的控制器设计

Design of controller based on backstepping nonlinear pure feedback system

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