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Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control

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Abstract

This paper investigates the use of Fractional Order Calculus (FOC) inconventional Model Reference Adaptive Control (MRAC) systems. Twomodifications to the conventional MRAC are presented, i.e., the use offractional order parameter adjustment rule and the employment offractional order reference model. Through examples, benefits from theuse of FOC are illustrated together with some remarks for furtherresearch.

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References

  1. Astrom, K. J. and Wittenmark, B., Adaptive Control, Addison-Wesley, Reading, MA, 1995.

    Google Scholar 

  2. Debnath, L., Integral Transforms and Their Applications, CRC Press, Boca Raton, FL, 1995.

    Google Scholar 

  3. Landau, Y. D., Adaptive Control: The Model Reference Approach, Marcel Dekker, New York, 1979.

    Google Scholar 

  4. Miller, K. S. and Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.

    Google Scholar 

  5. Oldham, K. B. and Spanier, J., The Fractional Calculus, Academic Press, New York, 1974.

    Google Scholar 

  6. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, CA, 1999.

    Google Scholar 

  7. Samko, S. G., Kilbas, A. A., and Maritchev, O. I., Integrals and Derivatives of the Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk, 1987 [in Russian].

    Google Scholar 

  8. Hang, C. C. and Parks, P. C., 'Comparative studies in model reference adaptive control systems', IEEE Transactions on Automatic Control 18, 1973, 419–428.

    Google Scholar 

  9. Lurie, B. J., 'Three-parameter integral and its application to control systems', US Patent US5371670.

  10. Manabe, S., 'The non-integer integral and its application to control systems', Japanese Institute of Electrical Engineers Journal 80(860), 1960, 589–597.

    Google Scholar 

  11. Osburn, P. V., Whitaker, H. P., and Kezer, A., 'Comparative studies of model reference adaptive control systems', Institute of Aeronautical Sciences, Paper No. 61–39, 1961.

  12. Petras, I., 'The fractional-order controllers: Methods for their synthesis and application', Journal of Electrical Engineering 50(9–10), 1999, 284–288.

    Google Scholar 

  13. Podlubny, I., 'Fractional-order systems and PIλDμ-controllers', IEEE Transactions on Automatic Control 44(1), 1999, 208–214.

    Google Scholar 

  14. Oustaloup, A., Mathieu, B., and Lanusse, P., 'The CRONE control of resonant plants: application to a flexible transmission', European Journal of Control 1(2), 1995, 113–121.

    Google Scholar 

  15. Oustaloup, A., Sabatier, J., and Lanusse, P., 'From fractal robustness to CRONE control', Fractional Calculus & Applied Analysis 2(1), 1999, 1–30.

    Google Scholar 

  16. Raynaud, H. F. and Zergalnoh, A., 'State-space representation for fractional order controllers', Automatica 36, 2000, 1017–1021.

    Google Scholar 

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Vinagre, B.M., Petráš, I., Podlubny, I. et al. Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control. Nonlinear Dynamics 29, 269–279 (2002). https://doi.org/10.1023/A:1016504620249

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  • DOI: https://doi.org/10.1023/A:1016504620249

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