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非线性机械系统PID控制渐近稳定性分析
引用本文:苏玉鑫,郑春红,Peter C.Müller.非线性机械系统PID控制渐近稳定性分析[J].自动化学报,2008,34(12):1544-1548.
作者姓名:苏玉鑫  郑春红  Peter C.Müller
作者单位:1.西安电子科技大学机电工程学院 西安 710071
基金项目:国家自然科学基金,高等学校全同优秀博士学位论文件者专项资金,教育部跨世纪优秀人才培养计划
摘    要:应用Lyapunov直接稳定性理论和LaSalle不变性原理, 证明了不确定非线性机械系统常用线性PID控制的半全局渐近稳定性. 同时证明了为提高系统的响应速度而发展的一种非线性PI加D (NPI-D)控制系统的全局渐近稳定性. 两自由度机器人系统的数值仿真结果验证了NPI-D控制的良好性能.

关 键 词:PID控制    非线性PID控制    半全局渐近稳定    全局渐近稳定    非线性机械系统
收稿时间:2007-10-29
修稿时间:2008-7-2

Asymptotic Stability of PID Controller for Nonlinear Mechanical Systems
SU Yu-Xin,ZHENG Chun-Hong,Peter C.Müller.Asymptotic Stability of PID Controller for Nonlinear Mechanical Systems[J].Acta Automatica Sinica,2008,34(12):1544-1548.
Authors:SU Yu-Xin  ZHENG Chun-Hong  Peter CMüller
Affiliation:1.School of Electro-Mechanical Engineering, Xidian University, Xi'an 710071, P.R.China;2.School of Electronic Engineering, Xidian University, Xi'an 710071, P.R.China;3.Safety Control Engineering, University of Wuppertal D-42097 Germany
Abstract:In this paper,we provide an answer to the long- standing question of designing global asymptotically stable proportional-integral-derivative(PID)regulators for uncertain nonlinear mechanical systems.Our main contribution is to es- tablish the semiglobal asymptotic stability of the controlled sys- tem with the commonly used linear PID controller by using Lya- punov direct method and LaSalle invariance principle.Further- more,an improved nonlinear proportional-integral plus deriva- tive(NPI-D)controller is proposed to speed up the transient and achieve the global asymptotic stability of the closed-loop system. Simulations performed on a two degree-of-freedom(DOF)robot manipulator demonstrate the improved performance of the pro- posed NPI-D controller.
Keywords:PID control  nonlinear PID control  semiglobalasymptotic stability  global asymptotic stability  nonlinear mechanical systems
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