Sliding mode controller design with fractional order differentiation: applications for unstable time delay systems

Abstract

This paper presents a design method for a sliding mode controller with the contribution of a fractional order differential operator. The conventional sliding mode controller has been widely studied in different control applications. This paper proposes that the fractional order differential operator enlarges the output span of the classical sliding mode controller to obtain a better-fitting control signal for enhanced control performance. The sliding surface and the equivalent control law are modified with the addition of a fractional differential operator and a conventional one. The proposed sliding mode controller with fractional order differentiation is applied to the unstable time delay systems successfully.Illustrative examples are presented to demonstrate the performance of the proposed design method.Key words: Sliding mode control, fractional order differentiation, unstable systems, time delay IntroductionFractional order systems and fractional order control structures are a promising research area in engineering problems. Recent research efforts have been focused on developing analysis and design procedures to extend classical control methods with fractional order integro-differential operators [1]. The first discussion of a fractional order derivative can be traced back to the 1690s, when L'Hospital wrote to Leibniz speculating about whether the order of a derivative could become a noninteger [2]. In the last several decades, with a better theoretical understanding of fractional calculus and subsequent developments in computing technologies, fractional calculus has begun to be widely utilized in various science and engineering areas [3]. The implementations of fractional order integro-differential operators have brought new horizons in control engineering. Consequently, fractional order integro-differential operators have been used in many control system applications in recent studies [4][5][6][7].

Analysis of Fractional Order Sliding Mode Control in a D-STATCOM Integrated Power Distribution System

“…The increase of fractional coefficient α reduces the effect of the (D α-1 (sig(e d ) γ )) integral term on the FOSMC sliding surface, and simultaneously increases the signal tracking error [65], and reduces the convergence time [69]. Similarly, due to the presence of model uncertainties and external disturbances, the fractional order sliding gains k d and k q are chosen to satisfy the reaching condition [79].…”

Image processing based object tracking application with fractional-order model reference controller

“…Kesir dereceli integro-diferansiyel ifadelerin sistemleri daha iyi modellediği, denetleyici ve sistem tasarımına yeni bir bakış açısı getirmiştir [14]. [15].…”

“…Bilgisayar ile hesaplama yöntemlerinin gelişmesiyle birlikte, uzun yıllar yabancı kalınan kesir dereceli türev ve integral uygulamaları; kimya, biyomedikal, kontrol teorisi, elektronik, sinyal işleme gibi mühendisliğin birçok alanında ilgi çeken konular arasına girmiştir. Kesir dereceli integro-diferansiyel ifadelerin sistemleri daha iyi modellediği, denetleyici ve sistem tasarımına yeni bir bakış açısı getirmiştir [14]. [16], [17].…”