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PID controller design for second order nonlinear uncertain systems

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Although the classical PID (proportional-integral-derivative) controller is most widely and successfully used in engineering systems which are typically nonlinear with various uncertainties,almost all the existing investigations on PID controller focus on linear systems.The aim of this paper is to present a theory on PID controller for nonlinear uncertain systems,by giving a simple and analytic design method for the PID parameters together with a mathematic proof for the global stability and asymptotic regulation of the closed-loop control systems.To be specific,we will construct a 3-dimensional manifold within which the three PID parameters can be chosen arbitrarily to globally stabilize a wide class of second order nonlinear uncertain dynamical systems,as long as some knowledge on the upper bound of the derivatives of the nonlinear uncertain function is available.We will also try to make the feedback gains as small as possible by investigating the necessity of the manifold from which the PID parameters are chosen,and to establish some necessary and sufficient conditions for global stabilization of several special classes of nonlinear uncertain systems.

PID controllernonlinear uncertain systemsglobal stabilityLyapunov functionasymptotic regulation

Cheng ZHAO、Lei GUO

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Institute of Systems Science, Academy of Mathematics and Systems Science(AMSS), Chinese Academy of Sciences, Beijing 100190, China

This work was supported by National Natural Science Foundation of Chinaby National Center for Mathematics and Interdisciplinary Sciences,CAS

11688101

2017

10.1007/s11432-016-0879-3

中国科学:信息科学(英文版)
中国科学院

中国科学:信息科学(英文版)

CSCDEI
影响因子：0.715
ISSN：1674-733X
年,卷(期)：2017.60(2)
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