An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators. (May 2016)

• Record Type: Journal Article
• Authors: Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret; Atherton, Derek P.
• Is Part Of: ISA transactions. Volume 62(2016:May)
• Page Start: 154
• Page End: 163
• Publication Date: 2016-05
• Subjects: Fractional order operators -- Integer order approximation -- Fractional order control system -- Stability boundary locus; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2016.01.020
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications. Highlights: SBL analysis is widely used to obtain stability regions graphically. SBL fitting is used for integer order approximation of fractional order operators. This method is helpful for stability preservation problem in model approximation. The method provides straightforward solutions for integer order model approximation.