Study of chaos in DC/DC switching converters

This thesis studies chaos in DC/DC switching converters. Five specific phases of studies are described. The first phase reviews the existing tools for analysis and synthesis of nonlinear systems. It is shown that a clear understanding of nonlinear dynamics theory leads to better analysis and synthesis techniques for DC/DC converters. Specifically, the methods are employed to explore the chaotic behaviour of the current-programmed Ćuk converter. The second phase focuses on the analysis of “general bifurcations” of current-programmed DC/DC converters. Investigation has been performed to identify the various routes leading to chaotic motion. In particular, a “universal” path through which the systems go to chaos is conjectured. The third phase rigorously analyzes the stability criterion of current-programmed DC/DC converters from a more general viewpoint. A theorem is developed to give the condition for stabilization of current-programmed converters using a general compensating function. Based on this theorem, a control method is proposed to stabilize the system by applying a variable compensating ramp function which dynamically adjusts its slope to suppress chaos and at the same time permits fast transient response of the system. The fourth phase establishes the conditions under which switching power converters operating in discontinuous mode can be chaotic. An important theorem has been established, which provides important insights into the condition for a class of power converters to exhibit the well known period-doubling route to chaos. The last phase discusses some possible future applications of chaos in power converters.