第 39 卷 第 6 期 自 动 化 学 报 Vol. 39, No. 6
2013 年 6 月 ACTA AUTOMATICA SINICA June, 2013
具有输入死区的非线性系统的鲁棒
重复控制
朱 胜
1
孙明轩
2
王雪洁
1
李艳君
1
方志刚
1
摘 要 针对一类输入含死区非线性特性的周期时变系统, 在周期时变
参数不可参数化的情形下设计鲁棒重复控制器. 采用微分自适应律估计
未知死区参数, 剩余的有界项通过鲁棒方法予以消除, 为避免出现颤振现
象, 采用饱和函数替代符号函数. 在系统输出跟踪周期轨迹的情形下, 将
非参数化不确定项转化为含周期时变参数的形式, 以达到利用周期学习
律进行估计的目的. 理论分析与仿真结果表明, 采用部分饱和或全饱和
学习算法均能实现输出误差有界收敛, 并保证闭环系统所有信号有界.
关键词 输入死区, 非参数化, 周期时变参数, 鲁棒重复控制
引用格式 朱胜, 孙明轩, 王雪洁, 李艳君, 方志刚. 具有输入死区的非
线性系统的鲁棒重复控制. 自动化学报, 2013, 39(6): 908−912
DOI 10.3724/SP.J.1004.2013.00908
Robust Repetitive Control for a Class of
Nonlinear Systems with Input Deadzone
ZHU Sheng
1
SUN Ming-Xuan
2
WANG Xue-Jie
1
LI Yan-Jun
1
FANG Zhi-Gang
1
Abstract This paper deals with the robust repetitive con-
troller design for a class of nonlinear systems with input dead-
zone, without the assumption that the periodic uncertainties
can be parameterized. The unknown parameters involved in the
deadzone nonlinearity are estimated by using integral adaptive
algorithms, while the bounded term is treated by a robust ap-
proach, and the saturation function is adopted to avoid the pos-
sible chattering phenomenon. The non-parametric uncertainty
is expressed with a periodically time-varying function, to which
the periodic learning approach can be applied for estimation pur-
pose. It is shown by theoretical and numerical results that both
partially- and fully-saturated learning algorithms are effective to
ensure asymptotic convergence of the tracking error, as well as
boundedness of all the signals in the closed-loop system.
Key words Input deadzone, non-parametrization, periodi-
cally time-varying parameter, robust rep etitive control
Citation Zhu Sheng, Sun Ming-Xuan, Wang Xue-Jie, Li Yan-
Jun, Fang Zhi-Gang. Robust repetitive control for a class of non-
linear systems with input deadzone. Acta Automatica Sinica,
2013, 39(6): 908−912
对于很多物理装置, 在输入的大小达到某个特定值之前,
它们的输出为零. 这种输入输出特性称为死区. 死区是重
收稿日期 2012-08-13 录用日期 2013-01-28
Manuscript received August 13, 2012; accepted January 28, 2013
国 家 自 然 科 学 基 金 (61174034, 61104149), 浙 江 省 自 然 科 学 基 金
(LQ12F03005), 浙江大学城市学院教师基金 (J12011) 资助
Supported by National Natural Science Foundation of China
(61174034, 61104149), Natural Science Foundation of Zhejiang
Province (LQ12F03005), and the Teacher Foundation of Zhejiang
University City College (J12011)
本文责任编委 刘允刚
Recommended by Associate Editor LIU Yun-Gang
1. 浙江大学城市学院 杭州 310015 2. 浙江工业大学信息工程学院 杭州
310023
1. Zhejiang University City College, Hangzhou 310015 2. Insti-
tute of Information and Control, College of Information Engineering,
Zhejiang University of Technology, Hangzhou 310023
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