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Design of non-rational MIMO feedback systems with inputs and outputs satisfying certain bounding conditions by using rational approximants

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Abstract

When a feedback system has components described by non-rational transfer functions, a standard practice in designing such a system is to replace the non-rational functions with rational approximants and then carry out the design with the approximants by means of a method that copes with rational systems. In order to ensure that the design carried out with the approximants still provides satisfactory results for the original system, a criterion of approximation should be explicitly taken into account in the design formulation. This paper derives such a criterion for multi-input multi-output (MIMO) feedback systems whose design objective is to ensure that the absolute values of every error and every controller output components always stay within prescribed bounds whenever the inputs satisfy certain bounding conditions. The obtained criterion generalizes a known result which was derived for single-input single-output (SISO) systems; furthermore, for a given rational approximant matrix, it is expressed as a set of inequalities that can be solved in practice. Finally, a controller for a binary distillation column is designed by using the criterion in conjunction with the method of inequalities. The numerical results clearly demonstrate that the usefulness of the criterion in obtaining a design solution for the original system.

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Acknowledgments

T. Chuman gratefully acknowledges the financial support from the honour program of the Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University.

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Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, 10330, Thailand

    Suchin Arunsawatwong & Tadchanon Chuman

Authors
  1. Suchin Arunsawatwong
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  2. Tadchanon Chuman
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Correspondence to Suchin Arunsawatwong.

Additional information

Recommended by Associate Editor James Whidborne

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 control systems design by the method of inequalities and the principle of matching, delay differential systems, fractional-order control systems, numerical solution of differential equations and power systems control.

ORCID iD: 0000-0002-7467-9429

Tadchanon Chuman received the B.Eng. and M.Eng. degrees in electrical engineering from Chulalongkorn University, Thailand in 2012 and 2014, respectively. He is currently a Ph. D. degree candidate at Control Systems Research Laboratory, the Department of Electrical Engineering, Chulalongkorn University.

His research interests include control systems design using the method of inequalities and the principle of matching, control systems with saturation, and load frequency control.

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Arunsawatwong, S., Chuman, T. Design of non-rational MIMO feedback systems with inputs and outputs satisfying certain bounding conditions by using rational approximants. Int. J. Autom. Comput. 14, 360–370 (2017). https://doi.org/10.1007/s11633-016-0991-5

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  • DOI: https://doi.org/10.1007/s11633-016-0991-5

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