Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications

详细信息    查看全文

• 作者：Farshad Merrikh-Bayat (1)
  Nafiseh Mirebrahimi (1)
  Mohammad Reza Khalili (1)
  
• 关键词：ARMA ; ARMAX ; discrete ; time controller ; fractional ; order PID ; long memory ; tuning
• 刊名：International Journal of Control, Automation and Systems
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：13
• 期：1
• 页码：81-90
• 全文大小：928 KB
• 参考文献：1. K. J. Astrom and T. Hagglund, / Advanced PID Control, ISA-The Instrumentation, Systems, and Automation Society, 2006.
  2. A. Visioli, / Practical PID Control, Springer-Verlag, London, 2006.
  3. K. Ogata, / Discrete-Time Control Systems, 2nd ed., Prentice Hall, Englewood Cliffs, New Jersey, 1995.
  4. W.-D. Chang, R.-C. Hwang, and J.-G. Hsieh, 鈥淎 self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach,鈥? / Journal of Process Control, vol. 12, no. 2, pp. 233鈥?42, February 2002. CrossRef
  5. K. J. Astrom and T. Hagglund, 鈥淩evisiting the Ziegler-Nichols step response method for PID control,鈥? / Journal of Process Control, vol. 14, no. 6, pp. 635鈥?50, September 2004. CrossRef
  6. A. Madady, 鈥淎n extended PID type iterative learning control,鈥? / International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 470鈥?81, June 2013. CrossRef
  7. M. Farahani and S. Ganjefar, 鈥淚ntelligent control of static synchronous series compensator via an adaptive self-tuning PID controller for suppression of torsional oscillations,鈥? / International Journal of Control, Automation and Systems, vol. 10, no. 4, pp. 744鈥?52, August 2012. CrossRef
  8. V. Feliu-Batlle, R. Rivas-Perez, and F. J. Castillo-Garc铆a, 鈥淪imple fractional order controller combined with a smith predictor for temperature control in a steel slab reheating furnace,鈥? / International Journal of Control, Automation and Systems, vol. 11, no. 3, pp. 533鈥?44, June 2013. CrossRef
  9. F. Merrikh-Bayat, 鈥淕eneral rules for optimal tuning the PI^位D^渭 controllers with application to first-order plus time delay processes,鈥? / Canadian Journal of Chemical Engineering, vol. 90, no. 6, pp. 1400鈥?410, December 2012. CrossRef
  10. I. Podlubny, 鈥淔ractional-order systems and / PI ^位 / D ^渭-controllers,鈥? / IEEE Trans. on Automatic Control, vol. 44, no. 1, pp. 208鈥?14, 1999. CrossRef
  11. I. Podlubny, / Fractional Differential Equations, Academic Press, San Diego, 1999.
  12. J. A. T. Machado, 鈥淒iscrete-time fractional-order controllers,鈥? / Journal of Fractional Calculus and Applied Analysis, vol. 4, no. 1, pp. 47鈥?6, 2001.
  13. Y.-Q. Chen and K. L. Moore, 鈥淒iscretization schemes for fractional-order differentiators and integrators,鈥? / IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 3, pp. 363鈥?67, 2002. CrossRef
  14. A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, / Signals and Systems, 2nd ed., Prentice Hall, 1996.
  15. A. V. Oppenheim and R. W. Schaffer, / Discrete-Time Signal Processing, 3rd ed., Prentice Hall, NJ, 2010.
  16. C. A. Monje, B. M. Vinagre, V. Feliu, and Y.-Q. Chen, 鈥淭uning and auto-tuning of fractional order controllers for industry applications,鈥? / Control Engineering Practice, vol. 16, no. 7, pp. 798鈥?12, July 2008. CrossRef
  17. R. W. Hornbeck, / Numerical Methods, Quantum Publishers, New York, 1975.
  18. I. R. Khan and R. Ohba, 鈥淐losed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series,鈥? / Journal of Computational and Applied Mathematics, vol. 107, no. 2, pp. 179鈥?93, July 1999. CrossRef
  19. B.-S. Chen and T.-Y. Yang, 鈥淩obust optimal model matching control design for flexible manipulators,鈥? / Journal of Dynamic Systems, Measurement, and Control, vol. 115, no. 1, pp. 173鈥?78, March 1993. CrossRef
  
• 作者单位：Farshad Merrikh-Bayat (1)
  Nafiseh Mirebrahimi (1)
  Mohammad Reza Khalili (1)
  
  1. Faculty of Electrical and Computer Engineering, University of Zanjan, Zanjan, Iran
  
• 刊物类别：Engineering
• 刊物主题：Control Engineering
  
• 出版者：The Institute of Control, Robotics and Systems Engineers and The Korean Institute of Electrical Engi
• ISSN：2005-4092

文摘

In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID (FOPID). Commonly, after tuning the parameters of FOPID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discrete-time version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems.