Dynamical modeling and border collision bifurcation in pulse train controlled discontinuous conduction mode buck converter

Abstract

According to the charge variation of output capacitor in a switching cycle, the output voltage variation in a switching cycle can be obtained, from which an approximate discrete-time model of pulse train (PT) controlled buck converter operating in discontinuous conduction mode (DCM) is established. Based on the model, the border-collision bifurcations of the PT controlled DCM buck converter with the variations of the load resistance and the input voltage are studied. By constructing the corresponding iterative map curves, the stabilities of the fixed points, formed by the orbits of period-1, period-2, period-3 and so on, are analyzed, and the mechanisms of border-collision bifurcations of the converter under different operation states are revealed. The analysis results indicate that with the variation of parameters, the PT controlled DCM buck converter always operates in different periodic states, in which the change of the operation mode with periodic state is caused by the border-collision bifurcation and the lyapunov exponent is always less than zero. By using PSIM circuit simulation software, the time domain waveforms and phase portraits under different load resistances are obtained. Experimental results are provided to verify the correctnesses of theoretical analyses and circuit simulations and the feasibility of dynamical modelling.