On Fractional Adaptive Control
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Introducing fractional operators in the adaptive control loop, and especially in Model Reference Adaptive Control (MRAC), has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. The idea of introducing fractional operators in adaptation algorithms is very recent and needs to be more established, that is why many research teams are working on the subject. Previously, some authors have introduced a fractional model reference in the adaptation scheme, and then fractional integration has been used to deal directly with the control rule. Our original contribution in this paper is the use of a fractional derivative feedback of the plant output, showing that this scheme is equivalent to the fractional integration, one with a certain benefit action on the system dynamical behaviour and a good robustness effect. Numerical simulations are presented to show the effectiveness of the proposed fractional adaptive schemes.
- Van Der Ziel, A., ‘On the noise spectra of semiconductor noise and of flicker effects’, Physica 16, 1950, 359–372. CrossRef
- Duta, P. and Horn, P. M., ‘Low frequency fluctuations in solids: 1/f noise’, Review of Modern Physics 53(3), July 1981.
- El-Sayed, A. M. A. and Gaafar, F. M., ‘Fractional calculus and some intermediate physical processes’, Applied Mathematics and Computation 144, 2003, 117–126. CrossRef
- Loiseau, J. J. and Mounier, H., ‘Stabilisation de l'équation de la chaleur commandée en flux’, ESAIM: Proceedings 1998, 131–144.
- Oustaloup, A., La dérivation non entière, 1995, Hermès, Paris.
- Padovan, J. and Sawicki, J. T., ‘Nonlinear vibrations of fractionally damped systems’, Nonlinear Dynamics 16, 1998, 321–336. CrossRef
- Hartley, T. T. and Lorenzo, C. F., ‘Dynamics and control of initialized fractional order systems’, Nonlinear Dynamics 29, 2002, 201–233. CrossRef
- Podlubny, I., ‘Fractional-order systems and PIλDμ-controllers’, IEEE Transaction on Automatic Control 44(1), 1999, 208–214. CrossRef
- Sun, H. and Onara, B., ‘A unified approach to represent metal electrode interface’, IEEE Transactions on Biomedical Engineering 31, July 1984.
- Ladaci, S. and Charef, A., ‘MIT adaptive rule with fractional Integration’, in Proceedings of CESA'2003 IMACS Multiconference Computational Engineering in Systems Applications, Lille-France, July 9–11, 2003.
- Vinagre, B. M., Petras, I., Podlubny, I., and Chen, Y. Q., ‘Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control’, Nonlinear Dynamics 29, 2002, 269–279. CrossRef
- Sun, H. and Charef, A., ‘Fractal system – a time domain approach’, Annals of Biomedical Engineering 18, 1990, 597–621. CrossRef
- Brin, I. A., ‘On the stability of certain systems with distributed and lumped parameters’, Automatic Remote Control 23, 1962, 798–807.
- Charef, A., Djouambi, A., and Sun, H., ‘Fractional order feedback control systems’, in Proceedings of the 4th JIEEEC, Jordan, April 2001.
- Lorenzo, C. F. and Hartley, T. T., ‘Variable order and distributed order fractional operators’, Nonlinear Dynamics 29, 2002, 57–98. CrossRef
- Oldham, K. B. and Spanier, J., The Fractional Calculus, Academic Press, New York, 1974.
- Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
- Srivastava, H. M. and Saxena, R. K., ‘Operators of fractional integration and their applications’, Applied Mathematics and Computation 118, 2001, 1–52. CrossRef
- Chen, Y. Q. and Vinagre, B. M., ‘A new IIR-type digital fractional order differentiator’, Signal Processing 83, 2003, 2359–2365. CrossRef
- Diethelm, K., ‘An algorithm for the numerical solution of differential equations of fractional order’, Electronic Transactions on Numerical Analysis 5, 1997, 1–6.
- Edwards, J. T., Ford, N. J., and Simpson, A. C., ‘The numerical solution of linear multi-term fractional differential equations: Systems of equations’, Journal of Computational and Applied Mathematics 148, 2002, 401–418. CrossRef
- Ostalczyk, P., ‘Fundamental properties of the fractional-order discrete-time integrator’, Signal Processing 83, 2003, 2367–2376. CrossRef
- Podlubny, I., Petras, I., Vinagre, B. M., O'leary, P., and Dorcak, L., ‘Analogue realisations of fractional-order controllers’, Nonlinear Dynamics 29, 2002, 281–296. CrossRef
- Diethelm, K., Ford, N. J., and Freed A. D., ‘A predictor-corrector approach for numerical solution of fractional differential equations’, Nonlinear Dynamics 29, 2002, 3–22. CrossRef
- Vinagre, B. M., Chen, Y. Q., and Petras, I., ‘Two direct Tustin discretization methods for fractional-order differentiator/integrator’, Journal of the Franklin Institute 340, 2003, 349–362. CrossRef
- Charef, A., Sun, H. H., Tsao, Y. Y., and Onaral, B., ‘Fractal system as represented by singularity function’, IEEE Transactions on Automatic Control 37, 1992, 1465–1470. CrossRef
- Astrom, K. J. and Wittenmark, B., Adaptive Control, Addison-Wesley, MA, 1995.
- Landau, Y. D., Adaptive Control: The Model Reference Approach, Marcel Dekker, New York, 1979.
- Naceri, F., Lakhdari, N., and Sellami, S., Théorie de la Commande Adaptative, Batna University Press, Algeria, 1998.
- Mathieu, B., Melchior, P., Oustaloup, A., and Ceyral, Ch., ‘Fractional differentiation for edge detection’, Signal Processing 83, 2003, 2421–2432. CrossRef
- Sawicky, J. T. and Padovan, J., ‘Frequency driven phasic shifting and elastic-hysteretic partitioning properties of fractional mechanical system representation schemes’, Journal of the Franklin Institute 336, Pergamon, 1999, 423–433.
- On Fractional Adaptive Control
Volume 43, Issue 4 , pp 365-378
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- fractional derivative
- fractional integration
- fractional order system
- model reference adaptive control
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