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 Poincaré 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.

This paper presents a methodology to study the local stability of periodic orbits (orbital stability) in switched discontinuous piecewise affine (DPWA) periodically driven multiple-input multipleoutput (MIMO) systems. The switched system of interest has a bilinear state space representation where the controller inputs are binary signals taking values in the set {0,1}. These systems are characterized by a set of affine differential equations together with switching rules to commute between them. These switching rules are described by switching functions that are periodic in time and linear in state. The methodology is based on obtaining a discrete time model (Poincaré map), its steady state operation points, and its Jacobian matrix. This provides a powerful tool for studying their stability and to predict some kind of instability phenomena that the system can undergo like subharmonic oscillations. The proposed approach is applied to a power electronic circuit which toggles among six different system equations with five switching boundaries within a switching cycle.

No abstract

No abstract

No abstract