[1] Liu Lu, Shan Liang, Jiang Chao, Dai Yuewei, et al. Parameter identification of the fractional-order systemsbased on a modified PSO algorithm [J]. Journal of Southeast University (English Edition), 2018, 34 (1): 6-14. [doi:10.3969/j.issn.1003-7985.2018.01.002]

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Parameter identification of the fractional-order systemsbased on a modified PSO algorithm()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

34

Issue:

2018 1

Page:

6-14

Research Field:

Computer Science and Engineering

Publishing date:

2018-03-20

Info

Title:

Parameter identification of the fractional-order systemsbased on a modified PSO algorithm

Author(s):

Liu Lu¹;  Shan Liang¹;  Jiang Chao²;  Dai Yuewei¹;  Liu Chenglin³;  Qi Zhidong¹

¹School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
²Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA
³Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi 214122, China

Keywords:

particle swarm optimization;  Tent mapping;  parameter identification;  fractional-order systems;  passive congregation

PACS:

TP301.6

DOI:

10.3969/j.issn.1003-7985.2018.01.002

Abstract:

In order to better identify the parameters of the fractional-order system, a modified particle swarm optimization(MPSO)algorithm based on an improved Tent mapping is proposed. The MPSO algorithm is validated with eight classical test functions, and compared with the POS algorithm with adaptive time varying accelerators(ACPSO), the genetic algorithm(GA), and the improved PSO algorithm with passive congregation(IPSO). Based on the systems with known model structures and unknown model structures, the proposed algorithm is adopted to identify two typical fractional-order models. The results of parameter identification show that the application of average value of position information is beneficial to making full use of the information exchange among individuals and speeds up the global searching speed. By introducing the uniformity and ergodicity of Tent mapping, the MPSO avoids the extreme value of position information, so as not to fall into the local optimal value. In brief, the MPSO algorithm is an effective and useful method with a fast convergence rate and high accuracy.

References:

[1] Diethelm K. An efficient parallel algorithm for the numerical solution of fractional differential equations[J].Fractional Calculus and Applied Analysis, 2011, 14(3): 475-490. DOI:10.2478/s13540-011-0029-1.
[2] Gepreel K A. Explicit Jacobi elliptic exact solutions for nonlinear partial fractional differential equations [J]. Advances in Difference Equations, 2014, 2014(1): 1-14. DOI:10.1186/1687-1847-2014-286.
[3] Laskin N. Fractional market dynamics[J]. Physica A: Statistical Mechanics and Its Applications, 2000, 287(3): 482-492. DOI:10.1016/s0378-4371(00)00387-3.
[4] Ionescu C, Machado J T, de Keyser R. Fractional-order impulse response of the respiratory system[J]. Computers & Mathematics with Applications, 2011, 62(3): 845-854. DOI:10.1016/j.camwa.2011.04.021.
[5] Badri V, Tavazoei M S. Fractional order control of thermal systems: Achievability of frequency-domain requirements[J]. Nonlinear Dynamics, 2014, 80(4): 1773-1783. DOI:10.1007/s11071-014-1394-1.
[6] Vikhram Y R, Srinivasan L. Decentralised wide-area fractional order damping controller for a large-scale power system[J]. IET Generation, Transmission & Distribution, 2016, 10(5): 1164-1178. DOI:10.1049/iet-gtd.2015.0747.
[7] Safarinejadian B, Asad M, Sadeghi M S. Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise [J]. International Journal of Control, 2016, 89(11): 2277-2296.
[8] Taleb M A, Béthoux O, Godoy E. Identification of a PEMFC fractional order model[J]. International Journal of Hydrogen Energy, 2017, 42(2): 1499-1509. DOI:10.1016/j.ijhydene.2016.07.056.
[9] Storn R, Price K. Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces [J]. Journal of Global Optimization, 1997, 11(4): 341-359.
[10] Tao C, Zhang Y, Jiang J J. Estimating system parameters from chaotic time series with synchronization optimized by a genetic algorithm [J]. Physical Review E, 2007, 76(2): 016209. DOI:10.1103/PhysRevE.76.016209.
[11] Kennedy J, Eberhart R. Particle swarm optimization[J]. Proceedings of ICNN’95—International Conference on Neural Networks. Perth, Australia, 1995: 1942-1948. DOI:10.1109/icnn.1995.488968.
[12] Gupta R, Gairola S, Diwiedi S. Fractional order system identification and controller design using PSO [C]//2014 Innovative Applications of Computational Intelligence on Power, Energy and Controls with Their Impact on Humanity. Ghaziabad, India, 2015: 149-153. DOI:10.1109/cipech.2014.7019053.
[13] Hammar K, Djamah T, Bettayeb M. Fractional hammerstein system identification using particle swarm optimization [C]//2015 7th IEEE International Conference on Modelling, Identification and Control. Sousse, Tunisia, 2015: 1-6. DOI:10.1109/icmic.2015.7409483.
[14] Shi Y, Eberhart R C. A modified particle swarm optimizer [C]//1998 IEEE International Conference on Evolutionary Computation. Anchorage, USA, 1998: 69-73. DOI:10.1109/icec.1998.699146.
[15] Koulinas G, Kotsikas L, Anagnostopoulos K. A particle swarm optimization based hyper-heuristic algorithm for the classic resource constrained project scheduling problem [J]. Information Sciences, 2014, 277: 680-693. DOI:10.1016/j.ins.2014.02.155.
[16] Gong Y J, Li J J, Zhou Y, et al. Genetic learning particle swarm optimization[J]. IEEE Trans Cybern, 2016, 46(10): 2277-2290. DOI:10.1109/TCYB.2015.2475174.
[17] Aghababa M P. Optimal design of fractional-order PID controller for five bar linkage robot using a new particle swarm optimization algorithm[J]. Soft Computing, 2016, 20(10): 4055-4067. DOI:10.1007/s00500-015-1741-2.
[18] He S, Wu Q H, Wen J Y, et al. A particle swarm optimizer with passive congregation[J]. Biosystems, 2004, 78(1/2/3): 135-147. DOI:10.1016/j.biosystems.2004.08.003.
[19] Rossikhin Y A, Shitikova M V. Application of fractional calculus for dynamic problems of solid mechanics: Novel trends and recent results [J]. Applied Mechanics Reviews, 2009, 63(1): 010801. DOI:10.1115/1.4000563.
[20] Hartley T T, Lorenzo C F. Fractional-order system identification based on continuous order-distributions[J].Signal Processing, 2003, 83(11): 2287-2300. DOI:10.1016/s0165-1684(03)00182-8.
[21] Gaing Z L. A particle swarm optimization approach for optimum design of PID controller in AVR system[J].IEEE Transactions on Energy Conversion, 2004, 19(2): 384-391. DOI:10.1109/tec.2003.821821.

Memo

Memo:

Biographies: Liu Lu(1990—), male, Ph.D. candidate; Shan Liang(corresponding author), male, doctor, associate professor, shanliang@njust.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.61374153, 61473138, 61374133), the Natural Science Foundation of Jiangsu Province(No.BK20151130), Six Talent Peaks Project in Jiangsu Province(No.2015-DZXX-011), China Scholarship Council Fund(No.201606845005).
Citation: Liu Lu, Shan Liang, Jiang Chao, et al. Parameter identification of the fractional-order systems based on a modified PSO algorithm[J].Journal of Southeast University(English Edition), 2018, 34(1):6-14.DOI:10.3969/j.issn.1003-7985.2018.01.002.

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