Using wavelet multi-resolution nature to accelerate the identification of fractional order system

doi:10.1088/1674-1056/26/5/050201

中国物理B ›› 2017, Vol. 26 ›› Issue (5): 50201-050201.doi: 10.1088/1674-1056/26/5/050201

• GENERAL • 下一篇

Using wavelet multi-resolution nature to accelerate the identification of fractional order system

Yuan-Lu Li(李远禄), Xiao Meng(孟霄), Ya-Qing Ding(丁亚庆)

1 B-DAT, School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China;
2 Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044, China

收稿日期:2016-09-21 修回日期:2017-02-07 出版日期:2017-05-05 发布日期:2017-05-05
通讯作者: Yuan-Lu Li E-mail:lyl_nuist@nuist.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61271395) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161513).

Using wavelet multi-resolution nature to accelerate the identification of fractional order system

Yuan-Lu Li(李远禄)^1,2, Xiao Meng(孟霄)², Ya-Qing Ding(丁亚庆)²

1 B-DAT, School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China;
2 Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044, China

Received:2016-09-21 Revised:2017-02-07 Online:2017-05-05 Published:2017-05-05
Contact: Yuan-Lu Li E-mail:lyl_nuist@nuist.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61271395) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20161513).

摘要/Abstract

摘要： Because of the fractional order derivatives, the identification of the fractional order system (FOS) is more complex than that of an integral order system (IOS). In order to avoid high time consumption in the system identification, the least-squares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.

关键词: fractional order system, system identification, operational matrix, wavelet multi-resolution analysis

Abstract: Because of the fractional order derivatives, the identification of the fractional order system (FOS) is more complex than that of an integral order system (IOS). In order to avoid high time consumption in the system identification, the least-squares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.

Key words: fractional order system, system identification, operational matrix, wavelet multi-resolution analysis

中图分类号: (Partial differential equations)

02.30.Jr

02.60.Cb (Numerical simulation; solution of equations) 05.40.Ca (Noise) 05.45.-a (Nonlinear dynamics and chaos)

李远禄, 孟霄, 丁亚庆. Using wavelet multi-resolution nature to accelerate the identification of fractional order system[J]. 中国物理B, 2017, 26(5): 50201-050201.

Yuan-Lu Li(李远禄), Xiao Meng(孟霄), Ya-Qing Ding(丁亚庆). Using wavelet multi-resolution nature to accelerate the identification of fractional order system[J]. Chin. Phys. B, 2017, 26(5): 50201-050201.

参考文献 40

[1]	Zhang R X and Yang S P 2011 Chin. Phys. B 20 090512
[2]	Zhang D X, Zhao D, Guan Z H, Wu Y H and Chi M 2016 Phys. A: Stat. Mech. Appl. 461 299
[3]	Oldham K B 2010 Adv. Eng. Softw. 41 9
[4]	Magin R L 2010 Comput. Math. Appl. 59 1586
[5]	Li Y, Pan C, Meng X, Ding Y and Chen H 2015 Meas. Sci. Rev. 15 101
[6]	Li T Z, Wang Y and Luo M K 2014 Chin. Phys. B 23 080501
[7]	Chen J, Guan Z H, Li T, Zhang D X, Ge M F and Zheng D F 2015 Neurocomputing 168 698
[8]	Chen J, Guan Z H, Yang C, Li T, He D X and Zhang X H 2016 J. Frankl. Inst. 353 1672
[9]	Cao H L, Deng Z H, Li X, Yang J and Qin Y 2010 Int. J. Hydrogen Energy. 35 1749
[10]	Chen L F and Cheng L Y 2014 Sci. Technol. Eng. 14 54
[11]	Yao G J, Lv W G, Song R L, Cui Z W, Zhang X L and Wang K X 2010 Chin. Phys. B 19 074301
[12]	Poinot T and Trigeassou J C 2004 Nonlinear Dyn. 38 133
[13]	Jalloul A, Trigeassou J C, Jelassi K and Melchior P 2011 Int. J. Comput. Sci. Iss. 8 801
[14]	Malti R, Aoun M and Oustaloup A 2004 Proceedings of the 30th Chinese Control Conference, March 21-24, 2004, Hammamet, Tunisia, pp. 835-839
[15]	Malti R, Victor S and Oustaloup A 2008 17th IFAC World Congress, July, 2008, Seoul, Korea, pp. 14379-14384
[16]	Liao Z, Peng C and Wang Y 2011 30th Chinese Control Conference, July 22-24, 2011, Yantai, China, pp. 1636-1640
[17]	Wang Y, Liao Z, Peng C, Liang S and Zhu Z T 2013 Control. Decis. 28 67
[18]	Li X and Han Z 2011 Control. Decis. 26 1627
[19]	Zhou S X, Cao J Y and Chen Y Q 2013 Entropy 15 1624
[20]	Li D Z and Yu Z X 2008 J. Tsinghua University (Sci & Tech) 48 1742 (in Chinese)
[21]	Li Y L and Yu S L 2007 Acta Autom. Sin. 33 882
[22]	Thomassin M and Malti R 2009 15th IFAC Symposium on System Identification, July, 2009, Saint Malo, France, pp. TuA3. 6
[23]	Nazarian P, Haeri M and Tavazoei M S 2010 ISA Trans. 49 207
[24]	Li W, Peng C and Wang Y 2011 Int. J. Control Autom. Syst. 9 310
[25]	Valério D and Tejado I 2015 Signal Process. 107 254
[26]	Aoun M, Malti R, Levron F and Oustaloup A 2007 Automatica 43 1640
[27]	Tang Y G, Liu H F, Wang W W, Lian Q S and Guan X P 2015 Signal Process. 107 272
[28]	Li Y L and Sun N 2011 Comput. Math. Appl. 62 1046
[29]	Jafar H, Yousefi S A, Firoozjaee M A, Momani S and Khalique C M 2011 Comput. Math. Appl. 62 1038
[30]	Bhrawy A H, Doha E H, Ezz-Eldien S S and Abdelkawy M A 2016 Calcolo 53 2
[31]	Bhrawy A H and Alghamdi M A 2013 Adv. Differ. Equations 1 2
[32]	Bhrawy A H, Taha T M, Alzahrani E O, Baleanu D and Alzahrani A A 2015 PloS One 10 e0126620
[33]	Li Y L 2010 Commun. Nonlinear Sci. Numer. Simul. 15 2284
[34]	Seifollahi M and Shamloo A S 2013 Word Applied Program 3 85
[35]	Doha E H, Bhrawy A H and Ezz-Eldien S S 2012 Appl. Math. Model. 36 4931
[36]	Asgari M 2015 Iaeng Int. J. Appl. Math. 45 85
[37]	Li Y L and Zhao W W 2010 Appl. Math. Comput. 216 2276
[38]	Gao G and Gu S 2008 J. Tsinghua University (Sci & Tech) 48 1821 (in Chinese)
[39]	Li Y L, Meng X, Zheng B C and Ding Y Q 2015 ISA Trans. 59 79
[40]	Wu J L, Chen C H and Chen C F 2001 IEEE Trans. Circ. Syst I: Fund. Theor. Appl. 48 120

Using wavelet multi-resolution nature to accelerate the identification of fractional order system

Using wavelet multi-resolution nature to accelerate the identification of fractional order system

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 40

相关文章 1

Metrics

本文评价

推荐阅读 0