Design of Direct Adaptive Fuzzy Controller for Nonlinear Fractional Order Systems with Compensation

Authors

1 Faculty of Electrical and Computer Engineering, University of Sistan and Balochistan, Zahedan, Iran

2 Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran

Abstract

Nowadays according to the rapid growth of the fractional order calculus, this field has converted to a beloved context for researchers. Also, there have been introduced various control algorithms with the fractional order approach. On the other hand, it has been proved that fuzzy systems are capable of controlling uncertain system with disturbance if they are well equipped with the expert knowledge. However, when there is not enough information to build fuzzy system or the expert knowledge cannot be properly transformed to the fuzzy inference part, a fuzzy system is not a universal approximation and cannot be applied. For these reasons, this paper proposes a direct adaptive fuzzy system with compensation to control a certain class of fractional order nonlinear systems with unknown nonlinearities. The stability criterion in fractional order definition is studied and based on a Lyapunov function candidate. Using the Lyapunov theorem ensures global Mittag-Leffler stability of the closed loop system. Free parameters are adjusted online and kept limited by the fractional order adaptation law, which is kept limited with a projection algorithm. In addition, according to the proposed method, the plant, which is little known, can be controlled effectively no matter whether the membership functions are suitable or not. Two numerical simulations show validity and effectiveness of the introduced control strategy for fractional order nonlinear models that perturbed by disturbance and uncertainty.

Keywords

TABRIZ JOURNAL OF ELECTRICAL ENGINEERING
Volume 47, Issue 3 - Serial Number 81
November 2017
Pages 917-929

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