Complex Interaction Between Tori and Onset of Three-Frequency Quasi-Periodicity in a Current Mode Controlled Boost Converter

It is known that power electronic circuits like dc-dc converters are highly nonlinear systems, and that period doubling and Neimark-Sacker bifurcations are common sources of instability in such systems. It has also been shown that these two types of bifurcation may interact, giving rise to interesting dynamical phenomena. In this paper we show that in a current mode controlled dc-dc converter, periodic, quasi-periodic, and saturation behavior can coexist for the same parameter value, and there can be complex interactions between them. Furthermore, abrupt exit to saturation mode can be triggered by a torus-torus collision. Finally, we report the first observation of three-frequency quasi-periodicity in a power electronic system.