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Design of retarded fractional delay differential systems using the method of inequalities

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Abstract

Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian’s original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.

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Authors and Affiliations

  1. Control Systems Research Laboratory, Department of Electrical Engineering, Chulalongkorn University, Bangkok, 10330, Thailand

    Suchin Arunsawatwong & Quang Van Nguyen

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  1. Suchin Arunsawatwong
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  2. Quang Van Nguyen
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Correspondence to Suchin Arunsawatwong.

Additional information

This work was supported by the AUN/SEED-Net collaborative research program.

Suchin Arunsawatwong received the B.Eng. and M.Eng. degrees in electrical engineering from Chulalongkorn University, Thailand, in 1985 and 1988, respectively, and Ph.D. degree in control engineering from the Control Systems Centre, University of Manchester Institute of Science and Technology, UK, in 1995. He is currently an assistant professor at the Department of Electrical Engineering, Chulalongkorn University.

His research interests include delay differential systems, numerical solution of differential equations, and control systems design by the method of inequalities and the principle of matching.

Van Quang Nguyen received the B.Eng. degree in electrical engineering from Hanoi University of Technology, Vietnam, in 2006. He is currently conducting his graduate study at the Control Systems Research Laboratory, Department of Electrical Engineering, Chulalongkorn University, Thailand.

His research interests include delay systems, process control, and numerical methods in control system engineering.

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Arunsawatwong, S., Van Nguyen, Q. Design of retarded fractional delay differential systems using the method of inequalities. Int. J. Autom. Comput. 6, 22–28 (2009). https://doi.org/10.1007/s11633-009-0022-x

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  • DOI: https://doi.org/10.1007/s11633-009-0022-x

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