Hybrid dynamic modeling and control of switched affine systems: Application to DC-DC converters

Abstract

Abstract-The paper deals with the problem of control of switched systems described by a set of affine differential equations. Among the potential applications, the DC-DC converters constitute an important class of systems, which concentrates the interest of the control community. The paper proposes a new formulation of the problem in the context of hybrid dynamic systems, which represents an adequate way for handling the requirements of DC-DC converters, while guaranteeing theoretically and practically all specifications in terms of stability and performance. In this sense, the proposed approach encompasses several methods considered in the literature. The method is illustrated for the cases of buck and boost converters. The developed results are preliminary but constitute an interesting direction for reducing the gap between theoretical results and their practical applications in power electronics.

Free-matrices min-projection control for high frequency DC-DC converters

“…This section aims at illustrating how Theorem 1 is applicable to the control of a classical boost converter, characterized by two functioning modes and a switching control working at high frequency. This system is governed by (1) where z := i L v C , where i L is the inductor current, and v C , the capacitor voltage. The matrices that define the modes are as follows…”

“…Last years, there have been remarkable efforts to analyze and control power converters by keeping their hybrid nature [4], [12], [23], often referring to the hybrid dynamical systems theory [7]. In this direction, one of the most popular approach consists in the introduction of minprojection control strategies [1], [5], [21]. These strategies consider aperiodic sampled-data control implementation.…”

Hybrid adaptive control of the boost converter

“…where the vertices of the polytope are given by β m ∈ {β m , β M }. Now, from [4], we assume next property of the boost converter.…”

“…This consideration captures the switching dynamics and achieves a new generation of converters that can operate in varying frequency. This is the case of the sliding-mode control [3] and hybrid dynamical control [4], [5], [6] for the boost converter.…”

“…In this work, we extend the hybrid dynamical controller proposed in [4], designing a hybrid adaptive control for the boost converter with unknown resistive load. This controller must regulate the voltage in a desired value.…”