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山东大学学报(工学版) ›› 2014, Vol. 44 ›› Issue (6): 77-82.doi: 10.6040/j.issn.1672-3961.0.2014.172

• 控制科学与工程 • 上一篇    下一篇

一种高阶系统的分数阶IMC-IDμ控制器设计

王惠芳, 赵志诚, 张井岗   

  1. 太原科技大学电子信息工程学院, 山西 太原 030024
  • 收稿日期:2014-06-25 修回日期:2014-11-12 发布日期:2014-06-25
  • 通讯作者: 赵志诚(1970-),男,山西临猗人,教授,主要研究方向为先进控制及应用、计算机测控系统与装置.E-mail:zhzhich@126.com E-mail:zhzhich@126.com
  • 作者简介:王惠芳(1987-),女,河南平顶山人,硕士研究生,主要研究方向为先进控制及应用.E-mail:whf0326@163.com
  • 基金资助:
    山西省自然科学基金(2012011027-4);太原科技大学研究生创新项目(20130429)

Design of a fractional order IMC-IDμ controller for high order systems

WANG Huifang, ZHAO Zhicheng, ZHANG Jinggang   

  1. School of Electronic Information Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, Shanxi, China
  • Received:2014-06-25 Revised:2014-11-12 Published:2014-06-25

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摘要： 针对高阶系统提出了一种模型降阶以及分数阶内模IDμ控制器设计方法。首先基于积分平方误差(ISE)性能指标,利用微粒群优化(Particle Swarm Optimization, PSO)算法将高阶系统模型降阶为含有时滞环节的分数阶模型;然后根据内模控制(Internal Model Control, IMC)原理,并用一阶泰勒表达式逼近模型中的时滞环节,推导出了分数阶IMC-IDμ控制器,该控制器仅包含一个可调参数;最后根据系统的最大灵敏度指标,实现了控制器参数的鲁棒整定。仿真结果表明,本文方法可使系统同时具有较好的动态响应、干扰抑制性能以及克服参数摄动的鲁棒性。

关键词: 分数阶控制, 高阶系统, 微粒群优化算法, 内模控制, 最大灵敏度

Abstract: A method of model reduction and fractional order internal model IDμ controller design was presented for higher order systems. At first, based on the performance index of integral square error (ISE), particle swarm optimization (PSO) was used to reduce the higher order system model and a fractional order model with time-delay was obtained. Then, according to the principle of internal model control (IMC), a fractional order IMC-IDμ controller was derived by approximating the time-delay term of the model with the first-order Taylor series. The controller contained only one adjustable parameter. Finally, the robust tuning of the controller parameter was realized using the maximum sensitivity index of the system. The simulation results showed that the proposed method could make the system having a better dynamic response characteristic, disturbance suppression performance and robustness against the parameters perturbation of the system.

Key words: internal model control, particle swarm optimization, higher order systems, fractional order control, maximum sensitivity

中图分类号: 

  • TP273
[1] ASTROM K J, HAGGLUND T. PID controller:theory, design and tuning[M].[s.n.]:Instrument Society of America, 1995.
[2] ISAKSSON A J, GRAEBE S F. Analytical PID parameter expressions for higher order systems[J]. Automatica, 1999, 35(6):1121-1130.
[3] DAS S, SAHA S, DAS S, et al. On the selection of tuning methodology of FOPID controllers for the control of higher order processes[J]. ISA transactions, 2011, 50(3):376-388.
[4] KHADRAOUI S, NOUNOU H, NOUNOU M, et al. A model-free design of reduced-order controllers and application to a DC servomotor[J]. Automatica, 2014, 50(8):2297-2301.
[5] KUMAR E G, MITHUNCHAKRAVARTHI B, DHIVYA N. Enhancement of PID controller performance for a quadruple tank process with minimum and non-minimum phase behaviors[J]. Procedia Technology, 2014, 14(4):480-489.
[6] DWYER AO'. Handbook of PI and PID controller tuning rules[M]. London, UK:Imperial College Press, 2006.
[7] HEERDIA M C, PRIETO J S, BRIONGOS J V. Feedback PID-like fuzzy controller for pH regulatory control near the equivalence point[J]. Journal of Process Control, 2014, 24(7):1023-1037.
[8] BARDINI M E, NAGER A M. Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system[J]. ISA Transactions, 2014, 53(3), 732-743.
[9] CHEN Y Q, XUE D Y, BHASKARAN T. Practical tuning rule development for fractional order proportional and integral controller[J]. Journal of Computational and Nonlinear Dynamics, 2008, 3(2):21403-21408.
[10] TAVAKOLI K M, HAERI M. Fractional order model reduction approach based on retention of the dominant dynamics:Application in IMC based tuning of FOPI and FOPID controllers[J]. ISA transactions, 2011, 50(3):432-442.
[11] JIN C Y, RYU K H, SUNG S W, et al. PID auto-tuning using new model reduction method and explicit PID tuning rule for a fractional order plus time delay model[J]. Journal of Process Control, 2014, 24(1):113-128.
[12] MALWATKAR G M, SONAWANE S H, WAGHMARE L M. Tuning PID controllers for higher-order oscillatory systems with improved performance[J]. ISA Transactions, 2009, 48(3):347-353.
[13] PODLUBNY I. Fractional-order systems and PIλDμ controllers[J]. IEEE Trans on Automatic Control, 1999, 44(1):208-214.
[14] MONJE C A, RAMOS F, FELIU V, VINAGRE B M. Tip position control of a lightweight flexible manipulator using a fractional-order controller[J]. Control Theory and Applications, 2007, 1(5):1451-1460.
[15] MONJE C A, VINAGRE B M, FELIU V, et al. Tuning and auto tuning of fractional order controllers for industry applications[J]. Control Engineering Practice, 2008, 16(7):798-812.
[16] Tavazoei M S, Haeri M. Rational approximations in simulation and implementation of fractional order dynamics:a descriptor system approach[J]. Automatica, 2010, 46(1):94-100.
[17] BADRI V, TAVAZOEI M S. On tuning fractional order[proportional-derivative] controllers for a class of fractional order systems[J]. Automatica, 2013, 49(7):2297-2301.
[18] MESBAHI A, HAERI M. Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems[J]. Journal of Process Control, 2014, 24(9):1489-1494.
[19] ABADI M, RAHMANI M R, JALALI A. A fractional order PID controller tuning based on IMC[J]. International Journal of Information Technology, Control and Automation (IJITCA), 2012, 2(4):21-35.
[20] 李大字, 刘展, 曹娇. 基于IMC方法的分数阶系统控制器设计[J]. 仪器仪表学报, 2007, 28(8):362-365. LI D Z, LIN Z, CAO J. Design a controller for fractional system based on IMC[J]. Journal of instruments and meters, 2007, 28(8):362-365.
[21] LI D Z, FAN W G, JIN Q B. An IMC-PIλDμ controller design for fractional calculus system[C]//Proceedings of 29th Chinese Control Conference. Beijing, China: IEEE, 2010:3581-3585.
[22] VINOPRABA T, SIVAKUMARAN N, NARAYANAN S, et al. Design of internal model control based fractional order PID controller[J]. Journal of Control Theory and Applications, 2012, 10(3):297-302.
[23] BETTAYEB M, MANSOURI R. Fractional IMC-PID-filter controllers design for non-integer order systems[J]. Journal of Process Control, 2014, 24(4):261-271.
[24] ALI A, MAJHI S. PI/PID controller design based on IMC and percentage overshoot specification to controller set-point change[J]. ISA transactions, 2009, 48(1):10-15.
[25] OUSTALOUP A, SABATIER J, LANUSSE P. From fractal robustness to CRONE control[J]. Fractional Calculus & Applied Analysis, 1999, 2(1):1-30.
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