Direct Form Digital Robust RST Control Based on Chebyshev Sphere Optimization Applied in a DC-DC Power Converter

Cleonor C. das Neves, Walter B. Junior, Renan L. P. de Medeiros, Florindo A. C. Ayres Junior, Iury V. Bessa, Isaías V. Bessa, Gabriela de M. Veroneze, Luiz E. S. e Silva and Nei J. S. Farias
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Cleonor C. das Neves: Institute of Technology, Faculty of Electrical Engineering, Federal University of Pará—UFPA, Pará, Belém City 66075-110, Brazil
Walter B. Junior: Institute of Technology, Faculty of Electrical Engineering, Federal University of Pará—UFPA, Pará, Belém City 66075-110, Brazil
Renan L. P. de Medeiros: Faculty of Technology, Department of Electricity, Federal University of Amazonas—UFAM, Manaus City 69067-005, Amazonas, Brazil
Florindo A. C. Ayres Junior: Faculty of Technology, Department of Electricity, Federal University of Amazonas—UFAM, Manaus City 69067-005, Amazonas, Brazil
Iury V. Bessa: Faculty of Technology, Department of Electricity, Federal University of Amazonas—UFAM, Manaus City 69067-005, Amazonas, Brazil
Isaías V. Bessa: Faculty of Technology, Department of Electricity, Federal University of Amazonas—UFAM, Manaus City 69067-005, Amazonas, Brazil
Gabriela de M. Veroneze: Faculty of Technology, Department of Electricity, Federal University of Amazonas—UFAM, Manaus City 69067-005, Amazonas, Brazil
Luiz E. S. e Silva: Faculty of Technology, Department of Electricity, Federal University of Amazonas—UFAM, Manaus City 69067-005, Amazonas, Brazil
Nei J. S. Farias: Faculty of Technology, Department of Electricity, Federal University of Amazonas—UFAM, Manaus City 69067-005, Amazonas, Brazil

Energies, 2020, vol. 13, issue 15, 1-22

Abstract: This paper presents a novel direct form to design a digital robust control using RST structure (i.e., name given because of the R, S and T polynomials computed) based on convex optimization such as Chebyshev sphere; this approach was applied to a DC-DC Buck converter. This methodology takes into account parametric uncertainties and a Chebyshev sphere constraint in order to ensure robust performance and stability of the system in the discrete domain. For this purpose, a mathematical model for the DC-DC Buck converter is presented when considering uncertainties in electrical variables, such as load resistance, inductance, capacitance, and source voltage variation, also to obtain the discrete model of the system by using the bilinear transformation. The proposed methodology is compared with two other approaches designed in a discrete domain: the classical pole placement and the robust methodology based on the Kharitonov theorem. Wide-ranging experiments are performed in order to evaluate the behavior of the control methodologies when the system is subject to parametric variations of the load resistance and voltage setpoint variation. The results show that the proposed methodology outperforms the other approaches in 90% of the tests and ensures robust stability and robust performance when the system is subjected to a parametric uncertainties family.

Keywords: digital robust RST controller; Chebyshev sphere constraint; DC-DC power converter; parametric uncertainties (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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