Two-dimensional bifurcation diagrams.: Background pattern of fundamental DC-DC converters with PWM control

One of the usual ways to build up mathematical models corresponding to a wide class of DC-DC converters is by means of piecewise linear differential equations. These models belong to a class of dynamical systems called Variable Structure Systems (VSS). From a classical design point of view, it is of interest to know the dynamical behavior of the system when some parameters are varied. Usually, Pulse Width Modulation (PWM) is adopted to control a DC-DC converter. When this kind of control is used, the resulting mathematical model is nonautonomous and periodic. In this case, the global Poincare map (stroboscopic map) gives all the information about the system. The classical design in these electronic circuits is based on a stable periodic orbit which has some desired characteristics. In this paper, the main bifurcations which may undergo this orbit, when the parameters of the circuit change, are described. Moreover, it will be shown that in the three basic power electronic converters Buck, Boost and Buck-Boost, very similar scenarios are obtained. Also, some kinds of secondary bifurcations which are of interest for the global dynamical behavior are presented. From a dynamical systems point of view, VSS analyzed in this work present some kinds of bifurcations which are typical in nonsmooth systems and it is impossible to find them in smooth systems.