PID controller design for second order nonlinear uncertain systems

作     者：Cheng ZHAO Lei GUO 

作者机构：Institute of Systems Science Academy of Mathematics and Systems Science (AMSS)Chinese Academy of Sciences 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2017年第60卷第2期

页      面：5-17页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0802[工学-机械工程] 080201[工学-机械制造及其自动化] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 11688101) by National Center for Mathematics and Interdisciplinary Sciences, CAS 

主　　题：PID controller nonlinear uncertain systems global stability Lyapunov function asymptotic regulation 

摘      要：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 *** 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.