分数阶广义线性系统观测器设计

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1529-1544.

分数阶广义线性系统观测器设计

冯再勇^1,²(),陈宁^3,*(),台永鹏⁴,向峥嵘²()

¹ 南京铁道职业技术学院基础部南京 210031
² 南京理工大学自动化学院南京 210094
³ 南京林业大学机械电子工程学院南京 210037
⁴ 南京林业大学汽车与交通工程学院南京 210037

收稿日期:2020-09-24 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 陈宁 E-mail:zyfeng-97040@163.com;chenning@njfu.edu.cn
作者简介:冯再勇, E-mail: zyfeng-97040@163.com|向峥嵘, E-mail: zyfeng-97040@163.com
基金资助:
国家自然科学基金(61873128);江苏省高等学校自然科学研究面上项目(17KJB120008);江苏省轨道交通控制工程技术研究开发中心项目(KFJ2010);江苏省高校"青蓝工程"项目;南京铁道职业技术学院"青蓝工程"项目

On the Observer Design for Fractional Singular Linear Systems

Zaiyong Feng^1,²(),Ning Chen^3,*(),Yongpeng Tai⁴,Zhengrong Xiang²()

¹ Department of Basic Sciences, Nanjing Institute of Railway Technology, Nanjing 210031
² School of Automation, Nanjing University of Science and Technology, Nanjing 210094
³ College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037
⁴ College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037

Received:2020-09-24 Online:2021-10-26 Published:2021-10-08
Contact: Ning Chen E-mail:zyfeng-97040@163.com;chenning@njfu.edu.cn
Supported by:
the NSFC(61873128);the NSF of the Jiangsu Higher Education Institution of China(17KJB120008);the Jiangsu Rail Transit Control Engineering Technology Research and Development Center(KFJ2010);the Qing Lan Project of the Jiangsu Higher Education Institutions;Qing Lan Project of Nanjing Institute of Railway Technology

摘要/Abstract

摘要：

研究了脉冲函数$\delta(t)$的Caputo导数${^C_0}{D}_t^\alpha\delta(t) $及其Laplace变换, 由此得到含脉冲项的分数阶广义线性系统的分布解. 阐明了分布解如何反映分数阶系统的"记忆特性". 以系统的分布解为基础, 证明了含脉冲项的分数阶广义线性系统的渐近稳定性定理. 据此, 给出了具有分数阶广义线性系统形式的状态观测器存在定理. 研究并总结了仅针对慢子系统进行极点配置, 得到系统全维状态观测器的简单设计方法. 最后, 针对具体实例, 设计了状态观测器, 验证了所给方法的有效性.

关键词: 分数阶广义线性系统, Caputo导数, 分布解, 渐近稳定性, 状态观测器

Abstract:

The paper discussed the Caputo fractional derivatives of impulse function $\delta(t) $, i.e., ${^C_0}{D}_t^\alpha\delta(t) $ and its Laplace transform, the distributional solution of Fractional Singular Linear Systems (FSLS) was consequently obtained. Based on the distributional solution of the system, the asymptotic stability theorem for FSLS was given, and the existence theorem of state observer for FSLS was proved. A simplified design method of full state observer for FSLS was investigated and summarized by pole assignment only for the slow subsystem. Finally, a state observer as an example was designed to verify the effectiveness of the proposed method.

Key words: Fractional singular linear system, Caputo fractional derivatives, Distributional solution, Asymptotic stability, State observer

中图分类号:

TP13

冯再勇,陈宁,台永鹏,向峥嵘. 分数阶广义线性系统观测器设计[J]. 数学物理学报, 2021, 41(5): 1529-1544.

Zaiyong Feng,Ning Chen,Yongpeng Tai,Zhengrong Xiang. On the Observer Design for Fractional Singular Linear Systems[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1529-1544.

图/表 4

参考文献 26

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