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.
Similar content being viewed by others
References
Astrom, K. J. and Wittenmark, B., Adaptive Control, Addison-Wesley, Reading, MA, 1995.
Debnath, L., Integral Transforms and Their Applications, CRC Press, Boca Raton, FL, 1995.
Landau, Y. D., Adaptive Control: The Model Reference Approach, Marcel Dekker, New York, 1979.
Miller, K. S. and Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
Oldham, K. B. and Spanier, J., The Fractional Calculus, Academic Press, New York, 1974.
Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
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].
Hang, C. C. and Parks, P. C., 'Comparative studies in model reference adaptive control systems', IEEE Transactions on Automatic Control 18, 1973, 419–428.
Lurie, B. J., 'Three-parameter integral and its application to control systems', US Patent US5371670.
Manabe, S., 'The non-integer integral and its application to control systems', Japanese Institute of Electrical Engineers Journal 80(860), 1960, 589–597.
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.
Petras, I., 'The fractional-order controllers: Methods for their synthesis and application', Journal of Electrical Engineering 50(9–10), 1999, 284–288.
Podlubny, I., 'Fractional-order systems and PIλDμ-controllers', IEEE Transactions on Automatic Control 44(1), 1999, 208–214.
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.
Oustaloup, A., Sabatier, J., and Lanusse, P., 'From fractal robustness to CRONE control', Fractional Calculus & Applied Analysis 2(1), 1999, 1–30.
Raynaud, H. F. and Zergalnoh, A., 'State-space representation for fractional order controllers', Automatica 36, 2000, 1017–1021.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1023/A:1016504620249