A Novel Non-integer Indirect Adaptive Control for Non-integer Order Systems with Non-prior Knowledge

B. Bourouba, S. Ladaci

Abstract


In this study, a new non-integer indirect adaptive control method with reference model is suggested for the class of non-integer order systems. The objective of model reference control is to include the output of the given reference fractional model in tracking the output of a controlled plant by using the concept of on-line goal adaptation. The stability of the closed-loop system is analyzed via the Lyapunov method. Finally, Matlab simulation results are presented to illustrate the effectiveness of the proposed method of indirect fractional model reference adaptive control.


Keywords


non integer order system; fractional adaptive control; MRAC; control system; Lyapunov stability

Full Text:

PDF

References


F. A. Zaid, P. Ioannou, K. Gousman, R. Rooney, “Accommodation of failures in the f-16 aircraft using adaptive control”, IEEE Control Systems Magazine, Vol. 11, No. 1, pp. 73–78, 1991

B. Mirkin, P. O. Gutman, “Model reference adaptive control of state delayed system with actuator failures”, International Journal of Control, Vol. 78, No. 3, pp. 186–195, 2005

K. J. Astrom, B. Wittenmark, “On self-tuning regulators”, Automatica, Vol. 9, No. 2, pp. 185-199, 1973

P. Caines, S. Lafortune, “Adaptive control with recursive identification for stochastic linear systems”, IEEE Transactions on Automatic Control, Vol. 29, No. 4, pp. 312-321, 1984

G. Tao, Adaptive control design and analysis, John Wiley & Sons, 2003

P. A. Ioannou, J. Sun, Robust adaptive control, Prentice-Hall, 1996

I. D. Landau, R. Lozano, M. Saad, A. Karimi, Adaptive Control, Springer, 1998

M. Abedini, M. A. Nojoumian, H. Salarieh, A. Meghdari, “Model reference adaptive control in fractional order systems using discrete-time approximation methods”, Communications in Nonlinear Science and Numerical Simulation, Vol. 25, No. 1-3, pp. 27-40, 2015

B. Bourouba, S. Ladaci, “Comparative performance analysis of GA, PSO, CA and ABC algorithms for ractional PIλDµ controller tuning”, 8th IEEE International Conference on Modelling, Identification and Control, Algiers, Algeria, November 15–17, 2016

B. Bourouba, S. Ladaci, A. Chaabi, “Moth-Flame optimization algorithm based fractional order PIλDµ controller with MRAC tuning configuration”, International Journal of Systems, Control and Communications, Vol. 9, No. 2, pp. 148-171, 2018

S. Ladaci, A. Charef, “On fractional adaptive control”, Nonlinear Dynamics, Vol. 43, No. 4, pp. 365-378, 2006

I. Podlubny, Fractional differential equations, Academic Press, 1999

I. Podlubny, “Fractional-order systems and PIλDµ controllers”, IEEE Transactions on Automatic Control, Vol. 44, No. 1, pp. 208–214, 1999

R. Hilfer, Applications of fractional calculus in physic, World Scientific, 2000

B. Bourouba, S. Ladaci, A. Chaabi, “Reduced-order model approximation of fractional-order systems using differential evolution algorithm”, Journal of Control, Automation and Electrical Systems, Vol. 29, pp. 32–43, 2018

P. L. Butzer, U. Westphal, An introduction to fractional calculus, World Scientific, 2000

M. P. Aghababa, “Stabilization of a class of fractional-order chaotic systemsusing a non-smooth control methodology”, Nonlinear Dynamics, Vol. 89, No. 3, pp. 1357–1370, 2017

K. Khettab, S. Ladaci, Y. Bensafia, “Fuzzy adaptive control of a fractional order chaotic system with unknown control gain sign using a fractional order Nussbaum gain”, IEEE/CAA Journal of Automatica Sinica, Vol. 6, No. 3, pp. 816–823, 2019




eISSN: 1792-8036     pISSN: 2241-4487