Bifurcation behavior of a boost converter under voltage controlled pulse skipping modulation in the light of 1-D discontinuous map model

In our earlier work, we showed that the discrete-time model of a dc-dc converter governed by a pulse skipping modulation (PSM), could be modeled as a discontinuous map, comprising either 1-D functions only or a combination of 1-D and 2-D functions. In this paper, we show that the entire map can be restricted to one dimension for a wide range of parameters. As a parameter is varied, the periodicity of the output waveform may change either monotonically or non-monotonically depending on the character of the voltage mode control loop. Although the map in the right compartment is always stable, the slope of the left compartment may be greater than one for a range of control parameters, which may lead to chaos.