A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 3 Issue 4
Oct.  2016

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 6.171, Top 11% (SCI Q1)
    CiteScore: 11.2, Top 5% (Q1)
    Google Scholar h5-index: 51, TOP 8
Turn off MathJax
Article Contents
Zhuoyun Nie, Qingguo Wang, Ruijuan Liu and Yonghong Lan, "Identification and PID Control for a Class of Delay Fractional-order Systems," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 463-476, Oct. 2016.
Citation: Zhuoyun Nie, Qingguo Wang, Ruijuan Liu and Yonghong Lan, "Identification and PID Control for a Class of Delay Fractional-order Systems," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 463-476, Oct. 2016.

Identification and PID Control for a Class of Delay Fractional-order Systems


National Natural Science Foundation of China 61403149, 6157329

Natural Science Foundation of Fujian Province 2015J01261, 2016J05165

Foundation of Huaqiao University Z14Y0002

More Information
  • In this paper, a new model identification method is developed for a class of delay fractional-order system based on the process step response. Four characteristic functions are defined to characterize the features of the normalized fractionalorder model. Based on the time scaling technology, two identification schemes are proposed for parameters' estimation. The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly. The other scheme employs optimal searching method to adjust the fractional order for the best model identification. The proposed two identification schemes are both applicable to any stable complex process, such as higher-order, under-damped/over-damped, and minimum-phase/nonminimum-phase processes. Furthermore, an optimal PID tuning method is proposed for the delay fractionalorder systems. The requirements on the stability margins and the negative feedback are cast as real part constraints (RPC) and imaginary part constraints (IPC). The constraints are implemented by trigonometric inequalities on the phase variable, and the optimal PID controller is obtained by the minimization of the integral of time absolute error (ITAE) index. Identification and control of a Titanium billet heating process is given for the illustration.


  • loading
  • [1]
    Zhao C N, Xue D Y, Chen Y Q. A fractional order PID tuning algorithm for a class of fractional order plants. In:Proceedings of the 2005 IEEE International Conference Mechatronics and Automation. Canada:IEEE, 2005. 216-221
    Manabe S. A suggestion of fractional-order controller for flexible spacecraft attitude control. Nonlinear Dynamics, 2002, 29(1-4):251-268 http://cn.bing.com/academic/profile?id=121642006&encoded=0&v=paper_preview&mkt=zh-cn
    Torvik P J, Bagley R L. On the appearance of the fractional derivative in the behavior of real materials. Journal of Applied Mechanics, 1984, 51(2):294-298 doi: 10.1115/1.3167615
    Nakagawa M, Sorimachi K. Basic characteristics of a fractance device. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 1992, E75-A(12):1814-1819 http://cn.bing.com/academic/profile?id=1734093257&encoded=0&v=paper_preview&mkt=zh-cn
    Özbay H, Bonnet C, Fioravanti A R. PID controller design for fractional-order systems with time delays. Systems and Control Letters, 2012, 61(1):18-23 doi: 10.1016/j.sysconle.2011.09.011
    Caponetto R, Dongola G, Pappalardo F L, Tomasello V. Autotuning method for PIλDμ controllers design. International Journal of Innovative Computing, Information and Control, 2013, 9(10):4043-4055
    Caponetto R, Dongola G, Pappalardo F, Tomasello V. Auto-tuning and fractional order controller implementation on hardware in the loop system. Journal of Optimization Theory and Applications, 2013, 156(1):141-152 doi: 10.1007/s10957-012-0235-y
    Monje C A, Vinagre B M, Feliu V, Chen Y Q. Tuning and autotuning of fractional order controllers for industry applications. Control Engineering Practice, 2008, 16(7):798-812 doi: 10.1016/j.conengprac.2007.08.006
    Monje C A, Chen Y Q, Vinagre B M, Xue D Y, Feliu-Batlle V. Fractional-Order Systems and Controls:Fundamentals and Applications. London:Springer-Verlag, 2010.
    Tavazoei M S. Time response analysis of fractional-order control systems:a survey on recent results. Fractional Calculus and Applied Analysis, 2014, 17(2):440-461 http://cn.bing.com/academic/profile?id=2061898553&encoded=0&v=paper_preview&mkt=zh-cn
    Luo Y, Zhang T, Lee B, Kang C, Chen Y Q. Fractional-order proportional derivative controller synthesis and implementation for hard-diskdrive servo system. IEEE Transactions on Control Systems Technology, 2014, 22(1):281-289 doi: 10.1109/TCST.2013.2239111
    Oustaloup A, Sabatier J, Lanusse P, Malti R, Melchior P, Moreau X, Moze M. An overview of the crone approach in system analysis, modeling and identification, observation and control. In:Proceedings of the 17th IFAC World Congress. COEX, Korea, South:IFAC, 2008. 14254-14265
    Mathieu B, Le Lay L, Oustaloup A. Identification of non integer order systems in the time-domain. In:CESA'96 IMACS Multiconference:Computational Engineering in Systems Applications. 1996. 843-847
    Trigeassou J C, Poinot T, Lin J, Oustaloup A, Levron F. Modeling and identification of a non integer order system. In:Proceedings of the 1999 European Control Conference (ECC). Karlsruhe:IEEE, 1999. 2453-2458
    Poinot T, Trigeassou J C. Identification of fractional systems using an output-error technique. Nonlinear Dynamics, 2004, 38(1-4):133-154 doi: 10.1007/s11071-004-3751-y
    Guevara E, Meneses H, Arrieta O, Vilanova R, Visioli A, Padula F. Fractional order model identification:computational optimization. In:Proceedings of the 20th IEEE Conference on Emerging Technologies and Factory Automation (ETFA). Luxembourg:IEEE, 2015. 1-4
    Hartley T T, Lorenzo C F. Fractional-order system identification based on continuous order-distributions. Signal Processing, 2003, 83(11):2287-2300 doi: 10.1016/S0165-1684(03)00182-8
    Jin C Y, Ryu K H, Sung S W, Lee J, Lee I B. PID auto-tuning using new model reduction method and explicit PID tuning rule for a fractional order plus time delay model. Journal of Process Control, 2014, 24(1):113-128 doi: 10.1016/j.jprocont.2013.11.010
    Narang A, Shah S L, Chen T. Continuous-time model identification of fractional-order models with time delays. IET Control Theory and Applications, 2011, 5(7):900-912 doi: 10.1049/iet-cta.2010.0718
    Luo Y, Chen Y Q, Wang C Y, Pi Y G. Tuning fractional order proportional integral controllers for fractional order systems. Journal of Process Control, 2010, 20(7):823-831 doi: 10.1016/j.jprocont.2010.04.011
    Wang Y G, Shao H H. PID autotuner based on gain- and phasemargin specifications. Industrial and Engineering Chemistry Research, 1999, 38(8):3007-3012 doi: 10.1021/ie9808007
    Ho W K, Lee T H, Gan O P. Tuning of multiloop proportional-integralderivative controllers based on gain and phase margin specifications. Industrial and Engineering Chemistry Research, 1997, 36(6):2231-2238 doi: 10.1021/ie960732t
    Li K Y. PID tuning for optimal closed-loop performance with specified gain and phase margins. IEEE Transactions on Control Systems Technology, 2013, 21(3):1024-1030 doi: 10.1109/TCST.2012.2198479
    Fung H W, Wang Q G, Lee T H. PI tuning in terms of gain and phase margins. Automatica, 1998, 34(9):1145-1149 doi: 10.1016/S0005-1098(98)80001-0
    Li M D, Li D H, Wang J, Zhao C Z. Active disturbance rejection control for fractional-order system. ISA Transactions, 2013, 52(3):365-374 doi: 10.1016/j.isatra.2013.01.001
    Lv Y, Wu M, Lei Q, Nie Z Y. Soft sensor based on a Pso-Bp neural network for a titanium billet furnace-temperature. Intelligent Automation and Soft Computing, 2011, 17(8):1207-1216 doi: 10.1080/10798587.2011.10643222


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(18)  / Tables(8)

    Article Metrics

    Article views (1221) PDF downloads(19) Cited by()


    DownLoad:  Full-Size Img  PowerPoint