摘要
文章针对一类具有参数不确定性和未知扰动项的非仿射非线性系统,提出了一种基于奇异摄动理论的鲁棒自适应控制方法.首先,通过控制输入构建了一个快变子系统,为原系统引入时标分离特性,使闭环系统可以在快变和慢变时间尺度上分解为两个降阶子系统:边界层子系统和降阶慢变子系统.在快时间尺度上,通过设计边界层子系统的结构使其在平衡点处指数稳定;在慢时间尺度上,针对含有参数不确定性和未知扰动项的降阶慢变子系统设计鲁棒自适应控制器.根据奇异摄动理论,闭环系统的跟踪性能可由降阶慢变子系统近似.文章提出的控制方法同时考虑了参数不确定性和未知扰动项的影响,在不忽略非仿射结构的前提下实现控制目标,不依赖于原系统的时标分离特性,且避免了反步法中的“复杂性爆炸”问题.两组与参考文献控制方法的对比仿真结果验证了文章控制方法的有效性.
In this paper,we propose a robust adaptive control method based on singular perturbation theory for a class of non-afine nonlinear systems with parame-ter uncertainties and unknown disturbance terms.Firstly,a fast dynamic subsystem is constructed for the system through the control input to introduce time-scale separation.Then,the closed-loop system can be decomposed into two order-reduced subsystems:A boundary layer subsystem and a reduced slow subsystem,on the fast and slow time scales,respectively.On the fast time scale,the structure of the boundary layer subsystem is designed to make it exponentially stable around the equilibrium point.On the slow time scale,a robust adaptive controller is designed for the reduced slow subsystem with parameter uncertainties and unknown disturbance.According to singular perturbation theory,the tracking performance of the closed-loop system can be approximated by the reduced slow subsystem.The proposed control method considers the effects of parameter uncertainties and disturbance terms,achieves the control goal without ignoring the non-affine structure,does not rely on the time-scale separation of the original system,and avoids the"complexity explosion problem"in backstepping method.Simulation results with comparisons to reference control methods verify the effectiveness of the proposed control method.
作者
苟鑫攀
杨浩
宋海鹰
蒋海翔
GOU Xinpan;YANG Hao;SONG Haiying;JIANG Haixiang(School of Automation,Guangdong Polytechnic Normal University,Guangzhou 510665)
出处
《系统科学与数学》
CSCD
北大核心
2023年第11期2820-2835,共16页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金会科学仪器发展计划项目(61527810)
广州市基础与应用基础研究项目(202201011133)
广东技术师范大学人才引进项目(2021SDKYA028)资助课题。
关键词
鲁棒自适应控制
奇异摄动理论
非仿射非线性系统
参数不确定
未知扰动
Robust adaptive control
singular perturbation theory
non-affine non-linear system
parameter uncertainty
unknown disturbance
