Bifurcation Analysis of DC-DC Converters using Discrete Time Model

Abstract

DC-DC Converters have been reported as exhibiting a wide range of bifurcations and chaos under certain conditions [2]. This paper analyses the bifurcations in current controlled SEPIC and boost topologies operating in the continuous conduction mode by means of a discrete time model. Stroboscopic mapping is used to investigate possible bifurcation phenomena that periodic-1 orbits can undergo bifurcation in the SEPIC and boost converters when the reference current is taken as bifurcation parameter [8]. The characteristic multipliers locate the onset of the flip bifurcation [7]. Such a jump from stable operation to chaos has been verified by the computation of Lyapunov exponent. The periodic-1 orbit loses its stability via flip bifurcation and the resulting attractor is a periodic-2 orbit. This later bifurcates to chaos via border collision bifurcation. A computer simulation using MATLAB SIMULINK confirms the predicted bifurcations. It has been inferred that margin of system stability decreases with decrease in input voltage as well as increase in reference current and the load.