Impacts, bifurcations and chaos in DC/DC converters

Mario di Bernardo

DC/DC converters are one of the most widely used circuits in Power Electronics. They are basically used in all those situations where there is the need for adjusting a given DC voltage to an higher (boost converters) or lower (buck converter) value. These systems are typically represented by a piece-wise linear model and their behaviour is usually investigated by considering a uniform sampling of the system states (stroboscopic map).

Recently, it has been pointed out that DC/DC converters can exhibit several types of bifurcations and chaos. In particular, their route to chaos is characterised by a sudden "jump" to the chaotic region. This phenomenon was left unexplained in the existing literature.

This talk will address the analysis of PWM (pulse width modulated) feedback controlled buck converters, using a new kind of approach. Namely, the concept of "impact" will be first defined for this class of dynamical systems. Then, the analysis will be carried out by introducing an appropriate "impact map", obtained by a non-uniform sampling of the system states. These tools, which were successfully used to study the dynamical behaviour of the so-called mechanical impact oscillators, can provide a very useful framework to describe and explore the dynamics of DC/DC converters.

By using the "impact map", bifurcations and chaos in the buck converter will be studied. After studying the occurence of period-doubling bifurcations an explanation of their "strange" route to chaos will be offered, through he generalisation to these system of the "grazing" bifurcation.

Simulations will be presented which confirm the theoretical work described above.

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