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Complexity
Volume 2018, Article ID 5873230, 13 pages
https://doi.org/10.1155/2018/5873230
Research Article

No Chattering and Adaptive Sliding Mode Control of a Fractional-Order Phase Converter with Disturbances and Parameter Uncertainties

Center for Nonlinear Dynamics, Defence University, Ethiopia

Correspondence should be addressed to Karthikeyan Rajagopal; moc.liamg@nayekeihtrakr

Received 16 March 2018; Revised 27 July 2018; Accepted 31 July 2018; Published 22 October 2018

Academic Editor: Lucia Valentina Gambuzza

Copyright © 2018 Karthikeyan Rajagopal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Discussing the dynamical properties of various power system models is of significant importance in order to understand its complete behavior. Even though there are many literatures discussing about the chaotic behavior shown by phase converter circuits, none of them have reported the hazardous phenomenon of multistability. In this paper, we derive the fractional-order model of a phase converter circuit and investigate its dynamics. Bifurcation of the system with the parameters and fractional order are investigated. A forward and backward continuation scheme is adopted to display various coexisting attractors; the property of multistability is also discussed. Using forward and backward continuation, various coexisting attractors and the property of multistability are discussed. Two different sliding mode controllers for controlling chaotic oscillations with model disturbances and parameter uncertainties are derived, and the effectiveness of the controllers is discussed with numerical simulations.