Lipschitz非线性系统未知输入观测器设计

杨俊起 1; 2; 张良 1; 朱芳来 1; 张登辉 3

doi:10.7652/xjtuxb201308015

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Lipschitz非线性系统未知输入观测器设计

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- Lipschitz非线性系统未知输入观测器设计
- Design of Observer with Unknown Input for Lipschitz Nonlinear Systems
- 西安交通大学学报 2013年47卷第8期页码：87-92
- 作者机构：
  
  1. 同济大学电子与信息工程学院,上海,201804
  2. 河南理工大学电气工程与自动化学院,河南,焦作,454000
- 作者简介：
- 基金信息：
  
  : 2013-01-18。作者简介: 杨俊起(1979—),男,博士生;朱芳来(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(61074009);教育部高等学校博士学科点专项科研基金资助项目(20110072110013);上海市重点学科资助项目(B004);河南省教育厅科学技术研究重点资助项目(13B413035,13B413028)
- DOI：10.7652/xjtuxb201308015
  中图分类号： TN927
- 网络首发：2013-08-10，
  
  纸质出版：2013
- 稿件说明：
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杨俊起 1, 2, 张良 1, 等. Lipschitz非线性系统未知输入观测器设计[J]. 西安交通大学学报, 2013,47(8):87-92.

Design of Observer with Unknown Input for Lipschitz Nonlinear Systems[J]. 2013, 47(8): 87-92.
杨俊起 1, 2, 张良 1, 等. Lipschitz非线性系统未知输入观测器设计[J]. 西安交通大学学报, 2013,47(8):87-92. DOI： 10.7652/xjtuxb201308015.

Design of Observer with Unknown Input for Lipschitz Nonlinear Systems[J]. 2013, 47(8): 87-92. DOI： 10.7652/xjtuxb201308015.

摘要

针对观测器匹配条件不满足情况下的Lipschitz非线性系统状态估计和未知输入重构问题

提出了一种未知输入观测器设计方法。首先

通过构造辅助输出向量

突破了观测器匹配条件的限制

并设计高阶、高增益滑模微分器实现对辅助输出向量及其微分的精确估计; 之后

在辅助输出及其微分精确估计的基础上

设计具有滑模控制律和自适应调节律的自适应鲁棒滑模观测器

并提出了一种未知输入重构方法。该观测器设计方法不需知道Lipschitz常数

其大小可通过自适应调节律调节

且信息重构具有避免直接使用系统输出微分的优点。仿真结果表明

所设计的未知输入观测器不仅在观测器匹配条件不满足情况下可以实现对状态的渐进估计以及对未知输入重构之目的

而且自适应调节律能够在约5 s时间内实现对Lipschitz常数的自适应调节。

Abstract

A scheme to design observer with unknown input and unknown input reconstruction for Lipschitz nonlinear systems is proposed when the observer matching condition is not satisfied. An auxiliary output vector is constructed to satisfy the observer matching condition

and a high-order sliding mode differentiator with high-gain is designed to exactly estimate the auxiliary output vector and its derivative. Then

an adaptive robust sliding mode observer which complies with a robust sliding mode control law and an adaptation law is developed based on the estimations of the auxiliary output vector and its derivative

and an unknown input reconstruction method is derived without using the derivative information of system's output vector. The Lipschitz constant does not need to be known and is adjusted using the adaptive law. The method of unknown input reconstruction avoids the direct use of the derivative information of system's output. Simulation results show that states and unknown inputs can be gradually estimated by the proposed unknown input observer when the observer matching condition is not satisfied

and that the Lipschitz constant can be adjusted within 5 seconds by the proposed adaptation law.

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Keywords

references

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BAR-SHALOM Y. Optimal simultaneous state estimation and parameter identification in linear discrete-time system [J]. IEEE Transactions on Automatic Control, 1972,17(3):308-319.

YAN Xinggang, EDWARDS C. Adaptive sliding-mode observer-based fault reconstruction for nonlinear systems with parametric uncertainties [J]. IEEE Transactions on Industrial Electronics, 2008,35(11):4029-4036.

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LI Jianmin, ZHENG Yunfeng, SHEN Zhipeng. Nonlinear observer design for a class of nonlinear systems with non-Lipschitz nonlinearities of the unmeasured states [C]∥Proceeding of the 29th Chinese Control Conference. Beijing, China: Chinese Association of Automation, 2010:3531-3533.

SHEN Zhongyu, ZHAO Jin, XU Jie, et al. Nonlinear unknown input observer design by LMI for Lipschitz nonlinear systems [C]∥Proceeding of the 8th World Congress on Intelligent Control and Automation. Beijing, China: Chinese Association for Artificial Intelligence, 2010:3450-3453.

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FlOQUET T, EDWARDS C, SPRUGEON S K. On sliding mode observers for systems with unknown inputs [J]. International Journal of Adaptive Control and Signal Processing, 2007,21(8/9):638-656.

LEVANT A. High-order sliding modes: differentiation and output-feedback control [J]. International Journal of Control, 2003,76(9/10):924-941.

朱芳来,韩正之. 非线性系统降维观测器设计 [J]. 自动化学报, 2004,30(4):613-618.

ZHU Fanglai, HAN Zhengzhi. The design of reduced-order observers for Lipschitz nonlinear systems [J]. Acta Automatica Sinica, 2004,30(4):613-618.

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