Quasi-Periodicity, Chaos and Coexistence in the Time Delay Controlled Two-Cell DC–DC Buck Converter

Abstract

In addition to border collision bifurcation, the time delay controlled two-cell DC/DC buck converter is shown to exhibit a chaotic behavior as well. The time delay controller adds new design parameters to the system and therefore the variation of a parameter may lead to different types of bifurcation. In this work, we present a thorough analysis of different scenarios leading to bifurcation and chaos. We show that the time delay controlled two-cell DC/DC buck converter may also exhibit a Neimark–Sacker bifurcation which for some parameter set may lead to a 2D torus that may then break yielding a chaotic behavior. Besides, the saturation of the controller can also lead to the coexistence of a stable focus and a chaotic attractor. The results are presented using numerical simulation of a discrete map of the two-cell DC/DC buck converter obtained by expressing successive crossings of Poincaré section in terms of each other.