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.
Highlights
Nowadays, power converters application is attracting attention in academy due to the global energy demand growth and the search for new types of renewable energy
This control methodology is applied on a DC-DC buck converter while taking a parametric variation, such as load resistance variation and voltage reference setpoint variation into account; the proposed methodology uses the Chebyshev sphere theorem as constraints of the optimization problem to compute the robust controller gains aiming to guarantee the performance and stability of the system
The remaining of this paper is organized, as follows: Section 2 describes the mathematical model of the DC-DC buck converter as well as the operating conditions; Section 3 discuss the digital robust control based on convex optimization constrained to a Chebyshev sphere design as well as presents a robust control methodology based on Kharitonov rectangle; Section 4 performs the proposed methodology, shows the board system developed, besides that presents a brief description of the tests performed; Section 5 discusses results performed by the performed tests; and Section 6 concludes this study
Summary
Power converters application is attracting attention in academy due to the global energy demand growth and the search for new types of renewable energy. This article proposes a direct form to design the digital RST robust control (i.e., name given because of the R, S, and T polynomials computed) when considering the set of parametric interval uncertainties, i.e., the family of uncertainties is a hyper box representation to work with the LPV model of the DC-DC buck converter This control methodology is applied on a DC-DC buck converter while taking a parametric variation, such as load resistance variation and voltage reference setpoint variation into account; the proposed methodology uses the Chebyshev sphere theorem as constraints of the optimization problem to compute the robust controller gains aiming to guarantee the performance and stability of the system. The remaining of this paper is organized, as follows: Section 2 describes the mathematical model of the DC-DC buck converter as well as the operating conditions; Section 3 discuss the digital robust control based on convex optimization constrained to a Chebyshev sphere design as well as presents a robust control methodology based on Kharitonov rectangle; Section 4 performs the proposed methodology, shows the board system developed, besides that presents a brief description of the tests performed; Section 5 discusses results performed by the performed tests; and Section 6 concludes this study
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