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Variable-, Fractional-Orders Closed-Loop Systems Description

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Języki publikacji
EN
Abstrakty
EN
In this paper we explore the linear difference equations with fractional orders, which are functions of time. A description of closed-loop dynamical systems described by such equations is proposed. In a numerical example a simple control strategy based on time-varying fractional orders is presented.
Rocznik
Strony
79--85
Opis fizyczny
Bibliogr. 18 poz., Wykr.
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autor
Bibliografia
  • 1. Carpinteri F., Mainardi A. [ed.] (1997) Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien and New York.
  • 2. Coimbra C. F. M. (2003), Mechanics with Variable Order Diferential Operators, Annalen der Physik, Vol. 12, no. 11-12, 692 – 703.
  • 3. Günther M. (1986), Zeitdiskrete Steuerungssysteme, VEB Verlag Technik, Berlin, Germany.
  • 4. Ifeachor E. C., Jervis B. W. (1993), Digital Signal processing, A Practical Approach, Addison Wesley Longman Limited, Edinburg Gate, England.
  • 5. Isermann R. (1998), Digitale Regelsysteme, Springer-Verlag, Berlin, Germany.
  • 6. Lorenzo C. F., Hartley T. T. (2002), Variable Order and Distributed Order Fractional Operators, Journal of Nonlinear Dynamics, Vol. 20, no. 1-4, 201-233.
  • 7. Lubich C. H. (1986), Discretized fractional calculus, SIAM Journal of Mathematica1 Analysis, Vol. 17, 704-719.
  • 8. Machado J. A. T. (2001), Discrete-time fractional-order controllers”, FCAA Journal, Vol. 1, 47-66.
  • 9. Miller K. S., Ross B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons Inc., New York, USA.
  • 10. Ogata K. (1987), Discrete-time Control Systems, PrenticeHall International Editions, Englewood-Cliffs, USA.
  • 11. Ostalczyk P. (2000), The non-integer difference of the discrete-time function and its application to the control system synthesis, International Journal of System Science, Vol. 31, no. 12, 1551-1561.
  • 12. Ostalczyk P. (2001), Discrete-Variable Functions, A Series of Monographs No 1018, Technical University of Łódź.
  • 13. Ostalczyk P. (2003), The linear fractional-order discrete-time system description,Proceedings of the 9th IEEE International Conference on Methods and Models in Automation and Robotics, MMAR 2002, Międzyzdroje, T.I, 429 – 434.
  • 14. Ostalczyk P. (2003), The time-varying fractional order difference equations, Proceedings of DETC’03, ASME 2003 Design Engineering Technical Conference & Computers and Information in Engineering Conference, Chicago, USA, 1-9.
  • 15. Ostalczyk P., Derkacz M. (2003), Minimal realisation of a linear fractional-order discrete-time system, Proceedings of the 9th IEEE International Conference on Methods and Models in Automation and Robotics, MMAR 2002, Międzyzdroje, T.I, 461 – 464.
  • 16. Oustaloup A. (1995), La dèrivation non entière, Éditions Hermès, Paris, France.
  • 17. Podlubny I. (1999), Fractional differential equations, Academic Press, San Diego, USA.
  • 18. Zhou K., Doyle J. C., Glover K. (1995), Robust and optimal control, Prentice Hall, New Jersey, USA.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0051-0023
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