Bifurcations in DC-DC switching converters:: Review of methods and applications

This paper presents, in a tutorial manner, nonlinear phenomena such as bifurcations and chaotic behavior in DC-DC switching converters. Our purpose is to present the different modeling approaches, the main results found in the last years and some possible practical applications. A comparison of the different models is given and their accuracy in predicting nonlinear behavior is discussed. A general Poincare map is considered to model any multiple configuration of DC-DC switching converters and its Jacobian matrix is derived for stability analysis. More emphasis is done in the discrete-time approach as it gives more accurate prediction of bifurcations. The results are reproduced for different examples of DC-DC switching converters studied in the literature. Some methods of controlling bifurcations are applied to stabilize Unstable Periodic Orbits (UPOs) embedded in the dynamics of the system. Statistical analysis of these systems working in the chaotic regime is discussed. An extensive list of references is included.