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An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators |
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| Affiliation: | 1. Inonu University, Department of Electrical and Electronics Engineering, Turkey;2. School of Engineering and Informatics, Department of Engineering and Design, Sussex University, Brighton BN1 9QT, UK;1. Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta, Canada;1. Inonu University, Department of Electric-Electronics Engineering, Malatya, Turkey;2. Inonu University, Department of Physics, Malatya, Turkey;1. Institute of Automation, Beijing University of Chemical Technology, Beisanhuan East Road 15, Chaoyang District, Beijing 100029, PR China;2. Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Canada;1. Department of Chemical Engineering, Curtin University, 98009 Miri, Sarawak, Malaysia;2. Curtin Sarawak Research Institute, Curtin University, 98009 Miri, Sarawak, Malaysia;1. Department of Electrical and Electronic Engineering, Wenzhou University, Wenzhou, 325035, China;2. College of Information Engineering, Shenzhen University, Shenzhen, 518060, China |
| 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. |
| Keywords: | Fractional order operators Integer order approximation Fractional order control system Stability boundary locus |
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