Analysis and Control of the Chaotic Behavior in a Multi-Cell DC/DC Buck Converter

Multi-cell power converters have been widely used in real applications since they circumvent shortcomings of ordinary switching devices due to their ability to support high-voltages. In this book, we deal with the case of an N-cell DC/DC buck converter, and we present a systematic method to control the voltage across the flying capacitors and the current through the load that can be generalized from a two-cell converter to an N-cell converter. The system was described by a discrete-time model through some simplifying assumptions to derive easily the general model in the form of a recurrence equation, which is useful in the design of control laws and exhibits chaotic behavior, bifurcations and strange phenomena when applying feedback control methods. In addition, the problem of the windup phenomenon, which is caused by the effect of switching, was discussed along with an anti-windup approach that was developed and successfully applied to the controlled DC/DC buck converter. A generalization of the various control laws adopted and a comparison between the results obtained with these methods were given, including the performance of the controlled system and the types of bifurcations encountered. Throughout this work, it has been shown that as the number of cells in the converter increases, the complexity of the uncontrolled system model and the closed loop system also increases.