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Stabilization of Inertial Plant with Time Delay Using Fractional Order Controller

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Języki publikacji
EN
Abstrakty
EN
The paper presents the problem of designing of a fractional order controller satisfying the conditions of gain and phase margins of the closed-loop system with time-delay inertial plant. The transfer function of the controller follows directly from the use of Bode's ideal transfer function as a reference transfer function for the open loop system. Using the classical D-partition method and the gain-phase margin tester, a simple computational method for determining stability regions in the controller parameters plane is given. An efficient analytical procedure to obtain controller parameter values for specified gain and phase margin requirements is also given. The considerations are illustrated by numerical examples computed in MATLAB/Simulink.
Słowa kluczowe
Rocznik
Strony
117--121
Opis fizyczny
Bibliogr. 23 poz., Wykr.
Twórcy
autor
autor
Bibliografia
  • 1. Barbosa R. S., Machado J. A., Ferreira I. M. (2004), Tuning of PID controllers based on Bode's ideal transfer function, Nonliner Dynamics, Vol. 38, 305-321.
  • 2. Boudjehem B., Boudjehem D., Tebbikh H. (2008), Simple analytical design method for fractional-order controller, Proc. 3-rd IFAC Workshop on Fractional Differentiation and its Applications, Ankara, Turkey, (CD-ROM).
  • 3. Busłowicz M. (2008), Frequency domain method for stability analysis of linear continuous-time fractional systems. In: Malinowski K. and Rutkowski L. (Eds.), Recent Advances in Control and Automation, Academic Publishing House EXIT, Warsaw, 83-92.
  • 4. Busłowicz M., Nartowicz T. (2009), Design of fractional order controller for a class of plants with delay, Measurement Automation and Robotics, No. 2, 398-405 (in Polish).
  • 5. Das. S . (2008), Functional Fractional Calculus for System Identification and Controls, Springer, Berlin.
  • 6. Gryazina E. N. (2004), The D-Decomposition Theory, Automation and Remote Control, Vol. 65, No. 12, 1872-1884.
  • 7. Hamamci S. E. (2007), An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using FractionalOrder PID Controllers, IEEE Trans. on Automatic Control, Vol. 52, 1964-1969.
  • 8. Kaczorek T. (2011), Selected Problems of Fractional Systems Theory, Springer, Berlin, (in print).
  • 9. Kilbas A. A., Srivastava H. M., Trujillo J. J. (2006), Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
  • 10. Monje C. A., Calderon A. J., Vinagre B. M., Chen Y., Feliu V. (2004), On fractional PI controllers: some tuning rules for robustness to plant uncertainties, Nonlinear Dynamics, Vol. 38, 369-381.
  • 11. Ostalczyk P. (2008), Epitome of the Fractional Calculus, Theory and its Applications in Automatics, Publishing Department of Technical University of Łódź, (in Polish).
  • 12. Oustaloup A. (1991), La commande CRONE, Editions Hermes, Paris.
  • 13. Oustaloup A. (1995), La derivation non entiere – theorie, syntheses at applications, Editions Hermes, Paris.
  • 14. Oustaloup A. (1999), La commande crone: du scalaire au multivariable, Editions Hermes, Paris.
  • 15. Podlubny I. (1999), Fractional Differential Equations, Academic Press, San Diego.
  • 16. Podlubny I. (1999), Fractional-order systems and PIDcontrollers, IEEE Trans. on Automatic Control, Vol. 44, No.1, 208-214.
  • 17. Skogestad, S. (2001), Probably the best simple PID tuning rules in the world, AIChE Annual Meeting, Reno, Nevada.
  • 18. Valerio D., da Costa J. S. (2006), Tuning of fractional PID controllers with Ziegler-Nichols type rules, Signal Processing, Vol. 86, 2771-2784.
  • 19. Valerio D. (2005), Fractional Robust Systems Control. PhD Dissertation, Technical University of Lisbona.
  • 20. Nartowicz T. (2010), Design of fractional order controller satisfying gain and phase margin of the closed loop system with time delay inertial plant with integral term, Measurement Automation and Robotics, No. 2, 443-452 (in Polish).
  • 21. O’Dwyer A. (2003), PI and PID Controller Tuning Rules, Imperial College Press/Word Scientific, London, 2003.
  • 22. Ruszewski A. (2008), Stability regions of closed loop system with time delay inertial plant of fractional order and fractional order PI controller, Bull. Pol. Ac.: Sci. Tech. Vol. 56, No. 4, 329–332.
  • 23. Ruszewski A. (2010), Stabilization of inertial processes with time delay using fractional order PI controller, Measurement Automation and Monitoring, No. 2, 160-162.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0051-0029
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