Disturbance observer-based fractional-order nonlinear sliding mode control for a class of fractional-order systems with
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Disturbance observer-based fractional-order nonlinear sliding mode control for a class of fractional-order systems with matched and mismatched disturbances Amir Razzaghian1
· Reihaneh Kardehi Moghaddam1
· Naser Pariz2
Received: 26 June 2020 / Revised: 29 August 2020 / Accepted: 12 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study presents a novel fractional-order nonlinear sliding mode controller (FONSMC) based on an extended nonlinear disturbance observer (ENDOB) for a class of fractional order systems with matched and mismatched disturbances. Firstly, an ENDOB is introduced to estimate both the matched and mismatched disturbances. Then, the fractional-order nonlinear sliding surface is designed to satisfy the sliding condition in finite time. Accordingly, the corresponding FONSMC is proposed using the Lyapunov stability theorem. The proposed method shows an impressive disturbances rejection and also guarantees finitetime stability of closed-loop systems. Finally, the effectiveness of the proposed FONSMC-ENDOB structure is illustrated via numerical simulation. The simulation results exhibit the superiority of the proposed controlling method. Keywords Fractional-order systems · Nonlinear sliding mode control · Disturbance observer · Matched and mismatched disturbances · Finite-time stability
1 Introduction Fractional calculus is a field of mathematics which applies non-integer and complex orders in derivative and integral definitions which are called the fractional-order derivative and fractional-order integral, respectively [1]. Fractional-order operators are widely-used in both pure and applied mathematics. Recently, novel fractional-order derivatives were introduced in [2, 3], and the authors present some new properties and applications for general fractional-order derivatives and fractional-order integrals in [4–7]. During recent decades, fractional-order systems and controllers, as an interesting issue, has been considered by many researchers. Because of the capability of describing dynamic
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Amir Razzaghian [email protected] Reihaneh Kardehi Moghaddam [email protected] Naser Pariz [email protected]
1
Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2
Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
behaviors more accurately, fractional-order derivatives are vastly appeared in modeling of many practical processes and dynamical systems. Increasing degrees of freedom in modeling and including more adjustment parameters, provides more accuracy in control systems design [8]. In [9–13], fractional-order model is derived for electrical circuit elements and then fractional RCL circuits are investigated. [14], develops a fractional-order model of lithium ion batteries for electric vehicle, and in [15], fractional-order single-link lightweight flexible manipulator system is investigated. In [16, 17], fractional-order model for the transmission line with and withou
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