Hopf and Homoclinic Loop Bifurcations on a DC-DC Boost Converter under a SMC Strategy

TL;DR

This paper analyzes bifurcations in a DC-DC boost converter with sliding mode control, revealing how Hopf and homoclinic bifurcations occur on the switching manifold, affecting system stability.

Contribution

It models the boost converter as a Filippov system and identifies the occurrence of subcritical Hopf and homoclinic bifurcations within this framework.

Findings

Subcritical Hopf bifurcation creates an unstable limit cycle.

Limit cycle confined to the switching manifold disappears at a two-fold point.

Homoclinic loop forms when the limit cycle touches the two-fold point.

Abstract

In this paper, a dc-dc boost converter with sliding mode control and washout filter is analysed. This device is modelled as a three-dimensional Filippov system, characterized by the existence of sliding movement and restricted to the switching manifold. The operating point of the boost converter is a pseudo-equilibrium, and it, undergoes a subcritical Hopf bifurcation. Such a bifurcation occurs in the sliding vector field and creates, in this field, an unstable limit cycle. The limit cycle is confined to the switching manifold and disappears when it touches the visible-invisible two-fold point, resulting in a homoclinic loop which itself closes in this two-fold point.