Study of bifurcations in current-programmed DC/DC boost converters: from quasiperiodicity to period-doubling

Abstract

This paper studies the bifurcation paths exhibited by a simple second-order DC/DC boost converter under current-programmed control with and without voltage feedback. Previous work in this area has reported two distinct types of bifurcation paths, namely via regions of quasi-periodic orbits and period-doubling. This paper demonstrates that the two different types of bifurcation paths can, in fact, be viewed as part of another bifurcation in which the quasi-periodic sequence transmutes into the period-doubling sequence, and that such a bifurcation is observed regardless of the presence of the outer voltage feedback loop as long as a suitable set of bifurcation parameters is chosen. The describing iterative map is derived in closed form and is used to develop the main results via a series of computer experiments. The characteristic multipliers are calculated and the first onset of flip-bifurcation is predicted. Computer simulation based on an exact piecewise switched model confirms the predicted bifurcations. The exhibition of quasi-periodic orbits is confirmed by computation of the Lyapunov exponent. Finally, a series of return maps are generated to provide an alternative viewpoint to the reported bifurcations in terms of a transmutation from a tent-like map to a logistic-like map.