非均匀采样数据系统的新型模型描述方法

谢莉; 杨慧中; 丁锋

doi:10.16383/j.aas.2017.c150787

非均匀采样数据系统的新型模型描述方法

doi: 10.16383/j.aas.2017.c150787

谢莉^1,2, ,,
杨慧中^1,2,,
丁锋^1,2,

1.
江南大学轻工过程先进控制教育部重点实验室无锡 214122
2.
江南大学物联网工程学院无锡 214122

基金项目:

国家自然科学基金 61403166

中央高校基本科研业务费专项资金 JUSRP11561

江苏省自然科学基金 BK20140164

中央高校基本科研业务费专项资金 JUSRP51510

详细信息

作者简介:
杨慧中江南大学物联网工程学院教授.2001年获得华东理工大学博士学位.主要研究方向为复杂工业过程的建模与优化.E-mail:yhz@jiangnan.edu.cn

丁锋江南大学物联网工程学院教授.1994年获得清华大学博士学位.主要研究方向为系统辨识与过程控制.E-mail:fding@jiangnan.edu.cn

通讯作者:
谢莉江南大学物联网工程学院讲师.2013年获得江南大学控制理论与控制工程专业博士学位.主要研究方向为多率系统辨识.E-mail:xieli@jiangnan.edu.cn

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出版历程
- 收稿日期: 2015-11-23
- 录用日期: 2016-03-02
- 刊出日期: 2017-05-01

Novel Input-output Representation of Non-uniformly Sampled-data Systems

XIE Li^{1,2
, ,},
YANG Hui-Zhong^{1,2
,},
DING Feng^{1,2
,}

1.
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education, Jiangnan University, Wuxi 214122
2.
School of Internet of Things Engineering, Jiangnan University, Wuxi 214122

Funds:

National Natural Science Foundation of China 61403166

Fundamental Research Funds for the Central Universities JUSRP11561

Natural Science Foundation of Jiangsu Province BK20140164

Fundamental Research Funds for the Central Universities JUSRP51510

More Information

Author Bio:
Professor at the School of Internet of Things Engineering, Jiangnan University. She received her Ph. D. degree from East China University of Science and Technology in 2001. Her research interest covers modeling and optimization of complex industrial process

Professor at the School of Internet of Things Engineering, Jiangnan University. He received his Ph. D. degree from Tsinghua University in 1994. His research interest covers system identiflcation and process control

Corresponding author: XIE Li Lecturer at the School of Internet of Things Engineering, Jiangnan University. She received her Ph. D. degree in control theory and control engineering from Jiangnan University in 2013. Her research interest covers identiflcation of multirate systems. Corresponding author of this paper

摘要

摘要: 提升技术是处理非均匀采样数据（Non-uniformly sampled-data，NUSD）系统的标准工具.然而，提升状态空间模型存在因果约束问题，相应的提升传递函数模型结构复杂，且参数数目过多.因此，它们不便于非均匀采样数据系统的辨识与控制.通过引入时变后移算子，本文提出了一种输入输出表达的新型模型描述方法.该模型能够克服提升系统模型的缺点，使得传统单率系统的辨识和控制方法能够推广到非均匀采样数据系统中.仿真结果表明了新模型的优越性和有效性.
- 非均匀采样 /
- 多率系统 /
- 系统模型 /
- 传递函数模型
Abstract: The lifting technique is a benchmark tool to deal with non-uniformly sampled-data (NUSD) systems. However, the lifted state space model suffers from the causality constraint problem, and the corresponding lifted transfer function model is complex and involves a large number of parameters. Therefore, they are inconvenient for the identification and control purposes. By introducing a time-varying backward shift operator, this paper proposes a novel input-output representation of NUSD systems. The proposed model can overcome the limitation of the lifted models, and make traditional identification methods and control strategies of single-rate systems applicable to NUSD systems. The simulation results illustrate the advantages and effectiveness of the novel model.
- Non-uniform sampling /
- multirate system /
- system model /
- transfer function model
注释:

1) 本文责任编委方海涛

HTML全文

图 1 非均匀采样数据系统的结构图

Fig. 1 The schematic of the non-uniformly sampled-data systems

下载: 全尺寸图片幻灯片

图 2 非均匀刷新与采样方式

Fig. 2 The non-uniform updating and sampling pattern

下载: 全尺寸图片幻灯片

图 3 模型预测输出与非均匀采样输出

Fig. 3 The predicted output and the non-uniformly sampled output

下载: 全尺寸图片幻灯片

表 1 模型参数数目比较

Table 1 The parameter number comparison of different models

模型	参数数目	(n = 2, r = 10)
提升状态空间模型	n² + 2nr + r²	144
提升传递函数模型	nr² + n + r	212
基于时变后移算子的传递函数模型	2 nr + r	50

下载: 导出CSV

表 2 提升传递函数模型

Table 2 The lifted transfer function model

j	α(z)	β_0，j
1	1-0.3695z^-1+0.2865z^-2	0.1038z^-1 + 0.005038z^-2
2		0.1279z^-1 + 0.02207z^-2
3		0.1406z^-1 + 0.05318z^-2
4		0.126z^-1 + 0.1034z^-2
5		0.05919z^-1 + 0.1758z^-2
j	β_1，j	β_2，j(z)
1	0.01573 + 0.09557z^-1	0.04951 + 0.07633z^-1
2	0.1297z^-1 + 0.007972z^-2	0.02422 + 0.1171z^-1
3	0.1511z^-1 + 0.03344z^-2	0.1555z^-1 + 0.01162z^-2
4	0.152z^-1 + 0.0775z^-2	0.1723z^-1 + 0.04747z^-2
5	0.109z^-1 + 0.145z^-2	0.156z^-1 + 0.1069z^-2
j	β_3，j	β_4，j(z)
1	0.07863 + 0.05338z^-1	0.098 + 0.02866^-1
2	0.07226 + 0.08816z^-1	0.1089 + 0.05529z^-1
3	0.03435 + 0.1376z^-1	0.09796 + 0.09715z^-1
4	0.1812z^-1 + 0.01602z^-2	0.04604 + 0.1572z^-1
5	0.1911z^-1 + 0.06427z^-2	0.2066z^-1 + 0.02117z^-2

下载: 导出CSV

表 3 基于时变后移算子的传递函数模型

Table 3 The time-varying backward shift operator based transfer function model

i	A_i(δ)	B_i(δ)
0	1-1.7269δ^-1+ 0.83267δ^-2	0.059191δ^-1 +0.046547δ^-2
1	1-1.3497δ^-1+ 0.3946δ^-2	0.015735δ^-1 + 0.029157δ^-2
2	1-1.9913δ^-1+ 1.0337δ^-2	0.02422δ^-1 +0.018176δ^-2
3	1-1.8905δ^-1+ 0.95134δ^-2	0.034349δ^-1 +0.026472δ^-2
4	1-1.8047δ¹+ 0.88668δ^-2	0.046035δ^-1 +0.035974δ^-2

下载: 导出CSV

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