Towards a theoretical foundation of PID control for uncertain nonlinear systems

doi:10.1016/j.automatica.2022.110360

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	Towards a theoretical foundation of PID control for uncertain nonlinear systems
	Zhao, Cheng; Guo, Lei
	2022-08-01
发表期刊	AUTOMATICA
ISSN	0005-1098
卷号	142 页码:12
摘要	As is well-known, the classical PID control plays a dominating role in various control loops of industrial processes. However, a theory that can explain the rationale why the linear PID can successfully deal with the ubiquitous uncertain nonlinear dynamical systems and a method that can provide explicit design formulae for the PID parameters are still lacking. This paper is a continuation of the authors recent endeavor towards establishing a theoretical foundation of PID for nonlinear uncertain systems. In contrary to most of the existing literature on linear or affine nonlinear systems, we will consider a class of non-affine nonlinear uncertain systems, and will show that a three dimensional parameter set can be constructed explicitly, such that whenever the PID parameters are chosen from this set, the closed-loop systems will be globally stable and the regulation error will converge to zero exponentially fast, under some suitable conditions on the system uncertainties. Moreover, we will also consider the simpler PI and PD control, and provide a necessary and sufficient condition for the choice of the PI parameters for a class of one dimensional non-affine uncertain systems, by applying the Markus-Yamabe theorem in differential equations. These theoretical results show explicitly that the ubiquitous PID control does indeed have strong robustness with respect to both the system nonlinear uncertainties and the selection of the controller parameters. (C) 2022 Elsevier Ltd. All rights reserved.
关键词	PID control Uncertain nonlinear systems Non-affine systems Global stabilization Asymptotic regulation
DOI	10.1016/j.automatica.2022.110360
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12288201]
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000830850700022
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61167
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, Lei
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhao, Cheng,Guo, Lei. Towards a theoretical foundation of PID control for uncertain nonlinear systems[J]. AUTOMATICA,2022,142:12.
APA	Zhao, Cheng,&Guo, Lei.(2022).Towards a theoretical foundation of PID control for uncertain nonlinear systems.AUTOMATICA,142,12.
MLA	Zhao, Cheng,et al."Towards a theoretical foundation of PID control for uncertain nonlinear systems".AUTOMATICA 142(2022):12.