LMI Approach for Sliding Mode Control and Analysis of DC-DC Converters

TL;DR

This paper applies a linear matrix inequality-based LMI approach to analyze the steady-state behavior of DC/DC converters, specifically the Cuk converter, in sliding mode control regimes.

Contribution

It introduces a novel LMI-based method for stability analysis of DC/DC converters in sliding mode, incorporating nonlinear sector bounds.

Findings

Validated the approach with simulation results for different switching surfaces.

Provided stability conditions using LMIs for the converter's dynamic system.

Established limits for applying ripple approximation in converter analysis.

Abstract

Circuits' and in particular DC/DC converters' switching behavior is analyzed in this paper using the equivalent control modeling of the dynamic systems' sliding mode regime. As a representative example and also being one of the most complex circuits among DC/DC converters, the \'Cuk converter is chosen. It is shown how the converter's behavior in the steady state regime can be studied and analyzed by the linear matrix inequalities based stability conditions for linear dynamic systems with nonlinear sector bounded perturbations. The maximization of the nonlinear sector bound provides a limit for applying the linear ripple approximation in the converter operation analysis. Furthermore, our approach is validated by providing simulation results for two different switching surfaces of practical interest.