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

计量
- 文章访问数: 3248
- HTML全文浏览量: 274
- PDF下载量: 624
- 被引次数: 0
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

参考文献(32)

[1]	Albertos P, Crespo A. Real-time control of non-uniformly sampled systems. Control Engineering Practice, 1999, 7(4): 445-458 doi: 10.1016/S0967-0661(99)00005-2
[2]	Cuenca A, Salt J. RST controller design for a non-uniform multi-rate control system. Journal of Process Control, 2012, 22(10): 1865-1877 doi: 10.1016/j.jprocont.2012.09.010
[3]	刘强, 秦泗钊.过程工业大数据建模研究展望.自动化学报, 2016, 42(2): 161-171 http://www.aas.net.cn/CN/abstract/abstract18807.shtml Liu Qiang, Qin S J. Perspectives on big data modeling of process industries. Acta Automatica Sinica, 2016, 42(2): 161-171 http://www.aas.net.cn/CN/abstract/abstract18807.shtml
[4]	Ding F, Qiu L, Chen T W. Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica, 2009, 45(2): 324-332 doi: 10.1016/j.automatica.2008.08.007
[5]	Wang H W, Liu T. Recursive state-space model identification of non-uniformly sampled systems using singular value decomposition. Chinese Journal of Chemical Engineering, 2014, 22(11-12): 1268-1273 doi: 10.1016/j.cjche.2014.09.028
[6]	邱爱兵, 吉虹钢, 顾菊平.非均匀采样数据系统时变故障估计与调节最优集成设计.自动化学报, 2014, 40(7): 1493-1504 http://www.aas.net.cn/CN/abstract/abstract18418.shtml Qiu Ai-Bing, Ji Hong-Gang, Gu Ju-Ping. Optimal integrated design of time-varying fault estimation and accommodation for nonuniformly sampled data systems. Acta Automatica Sinica, 2014, 40(7): 1493-1504 http://www.aas.net.cn/CN/abstract/abstract18418.shtml
[7]	杜大军, 商立立, 漆波, 费敏锐.一种不完全信息下递推辨识方法及收敛性分析.自动化学报, 2015, 41(8): 1502-1515 http://www.aas.net.cn/CN/abstract/abstract18724.shtml Du Da-Jun, Shang Li-Li, Qi Bo, Fei Min-Rui. Convergence analysis of an online recursive identification method with uncomplete communication constraints. Acta Automatica Sinica, 2015, 41(8): 1502-1515 http://www.aas.net.cn/CN/abstract/abstract18724.shtml
[8]	Ni B, Xiao D. Identification of non-uniformly sampled multirate systems with application to process data compression. IET Control Theory & Applications, 2010, 4(6): 970-984 https://www.researchgate.net/publication/224143985_Identification_of_non-uniformly_sampled_multirate_systems_with_application_to_process_data_compression
[9]	郭东亮, 张铁军, 戴宪华.基于非均匀采样的信号频率、幅值和相位检测.系统工程与电子技术, 2012, 34(4): 662-665 http://www.cnki.com.cn/Article/CJFDTOTAL-XTYD201204007.htm Guo Dong-Liang, Zhang Tie-Jun, Dai Xian-Hua. Methods of signal frequency, amplitude and phase measurement based on non-uniform sampling. Systems Engineering and Electronics, 2012, 34(4): 662-665 http://www.cnki.com.cn/Article/CJFDTOTAL-XTYD201204007.htm
[10]	Pillai A K M, Johansson H. Efficient recovery of sub-Nyquist sampled sparse multi-band signals using reconfigurable multi-channel analysis and modulated synthesis filter banks. IEEE Transactions on Signal Processing, 2015, 63(19): 5238-5249 doi: 10.1109/TSP.2015.2451104
[11]	Cuenca Á, Salt J, Albertos P. Implementation of algebraic controllers for non-conventional sampled-data systems. Real-Time Systems, 2007, 35(1): 59-89 https://www.researchgate.net/publication/220414231_Implementation_of_algebraic_controllers_for_non-conventional_sampled-data_systems
[12]	Khan S, Goodall R M, Dixon R. Non-uniform sampling strategies for digital control. International Journal of Systems Science, 2013, 44(12): 2234-2254 doi: 10.1080/00207721.2012.687785
[13]	Zhu Y C, Telkamp H, Wang J H, Fu Q L. System identification using slow and irregular output samples. Journal of Process Control, 2009, 19(1): 58-67 doi: 10.1016/j.jprocont.2008.02.002
[14]	Ding F, Liu G J, Liu X P. Parameter estimation with scarce measurements. Automatica, 2011, 47(8): 1646-1655 doi: 10.1016/j.automatica.2011.05.007
[15]	Raghavan H, Tangirala A K, Gopaluni R B, Shah S L. Identification of chemical processes with irregular output sampling. Control Engineering Practice, 2006, 14(5): 467-480 doi: 10.1016/j.conengprac.2005.01.015
[16]	Gopaluni R B. Nonlinear system identification under missing observations: the case of unknown model structure. Journal of Process Control, 2010, 20(3): 314-324 doi: 10.1016/j.jprocont.2009.12.008
[17]	Tulsyan A, Huang B, Gopaluni R B, Fraser F J. On simultaneous on-line state and parameter estimation in non-linear state-space models. Journal of Process Control, 2013, 23(4): 516-526 doi: 10.1016/j.jprocont.2013.01.010
[18]	倪博溢, 萧德云.非均匀采样系统的一种递推辨识方法.自动化学报, 2009, 35(12): 1520-1527 http://www.aas.net.cn/CN/abstract/abstract13610.shtml Ni Bo-Yi, Xiao De-Yun. A recursive identification method for non-uniformly sampled systems. Acta Automatica Sinica, 2009, 35(12): 1520-1527 http://www.aas.net.cn/CN/abstract/abstract13610.shtml
[19]	李大海, 李天石.非均匀采样系统的支持向量回归建模与控制.西安交通大学学报, 2011, 45(3): 65-69 doi: 10.7652/xjtuxb201103012 Li Da-Hai, Li Tian-Shi. Modeling and control of non-uniformly sampled systems using support vector regression. Journal of Xi'an Jiaotong University, 2011, 45(3): 65-69 doi: 10.7652/xjtuxb201103012
[20]	丁锋, 陈通文, 萧德云.非均匀周期采样多率系统的一种辨识方法.电子学报, 2004, 32(9): 1414-1420 http://www.cnki.com.cn/Article/CJFDTOTAL-DZXU200409001.htm Ding Feng, Chen Tong-Wen, Xiao De-Yun. Identification of non-uniformly periodically sampled multirate systems. Acta Electronica Sinica, 2004, 32(9): 1414-1420 http://www.cnki.com.cn/Article/CJFDTOTAL-DZXU200409001.htm
[21]	王宏伟, 孙爽.基于子空间方法的非均匀多采样率系统辨识.大连理工大学学报, 2014, 54(5): 575-580 doi: 10.7511/dllgxb201405014 Wang Hong-Wei, Sun Shuang. Subspace-based method for identification of non-uniformly multirate sampling systems. Journal of Dalian University of Technology, 2014, 54(5): 575-580 doi: 10.7511/dllgxb201405014
[22]	王宏伟, 王佳, 夏浩.基于子空间方法的非均匀周期刷新和采样系统辨识.控制与决策, 2014, 29(5): 901-906 http://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201405023.htm Wang Hong-Wei, Wang Jia, Xia Hao. Identification of non-uniform period refresh and sampling system via subspace method. Control and Decision, 2014, 29(5): 901-906 http://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201405023.htm
[23]	Ding J, Lin J X. Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Systems & Signal Processing, 2014, 33(5): 1439-1449 https://www.researchgate.net/publication/278155807_Modified_Subspace_Identification_for_Periodically_Non-uniformly_Sampled_Systems_by_Using_the_Lifting_Technique
[24]	王涛, 林卫星, 包建孟.基于协同PSO算法的非均匀采样系统辨识.计算机工程与应用, 2013, 49(24): 32-37 doi: 10.3778/j.issn.1002-8331.1303-0473 Wang Tao, Lin Wei-Xing, Bao Jian-Meng. Method of non-uniformly sampled-data system identification based on cooperative PSO. Computer Engineering and Applications, 2013, 49(24): 32-37 doi: 10.3778/j.issn.1002-8331.1303-0473
[25]	Xie L, Liu Y J, Yang H Z, Ding F. Modelling and identification for non-uniformly periodically sampled-data systems. IET Control Theory & Applications, 2010, 4(5): 784-794 https://www.researchgate.net/publication/224137614_Modelling_and_identification_for_non-uniformly_periodically_sampled-data_systems
[26]	Ding F, Liu G, Liu X P. Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Transactions on Automatic Control, 2010, 55(8): 1976-1981 doi: 10.1109/TAC.2010.2050713
[27]	Liu Y J, Ding F, Shi Y. Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle. Circuits Systems & Signal Processing, 2012, 31(6): 1985-2000 https://www.researchgate.net/publication/257319009_Least_squares_estimation_for_a_class_of_non-uniformly_sampled_systems_based_on_the_hierarchical_identification_principle
[28]	Jing S X, Pan T H, Li Z M. Recursive Bayesian algorithm with covariance resetting for identification of Box-Jenkins systems with non-uniformly sampled input data. Circuits Systems & Signal Processing, 2016, 35(3): 919-932 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7162643
[29]	Zhou L C, Li X L, Pan F. Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling. Nonlinear Dynamics, 2014, 76(1): 627-634 doi: 10.1007/s11071-013-1156-5
[30]	刘冉冉, 潘天红, 李正明.非均匀Hammerstein-Wiener系统的递阶随机梯度辨识算法.控制与决策, 2015, 30(8): 1491-1496 http://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201508023.htm Liu Ran-Ran, Pan Tian-Hong, Li Zheng-Ming. Hierarchical stochastic gradient identification for Hammerstein-Wiener systems with non-uniformly sampling. Control and Decision, 2015, 30(8): 1491-1496 http://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201508023.htm
[31]	Xie L, Yang H Z, Ding F, Huang B. Novel model of non-uniformly sampled-data systems based on a time-varying backward shift operator. Journal of Process Control, 2016, 43: 38-52 doi: 10.1016/j.jprocont.2016.04.010
[32]	Xie L, Yang H Z, Ding F. Identification of non-uniformly sampled-data systems with asynchronous input and output data. Journal of the Franklin Institute, 2017, 354(4): 1974-1991 doi: 10.1016/j.jfranklin.2016.12.026