Coexistence of solutions in a DC-DC Buck converter controlled by sine wave

Low power systems are widely used in robotics and industrial areas; therefore, modeling and systems analysis provide reliable and best designs of such systems. In that way, a Buck converter controlled by PWM is investigated using a new design, replacing the T periodic ramp signal by a T periodic sine wave for two reasons: the sine wave is easier to generate and analyze, and in order to get rid of non-linear qualities of the ramp signal. Then, bifurcation diagrams are obtained varying the parameters ascending and descending in the new Buck converter design to find coexisting attractors, which are normally an undesired behavior in nonlinear systems or useful for some applications. Although it is demonstrated that these bifurcation diagrams are not the sufficient remedy to find coexistence of solutions, it is also shown that they are a good tool. Once bifurcation diagrams show the range where coexistence of solutions appear, we proceed to study in that range the shape of the basins and the system solutions, with the aim of determining the specific regions in which the system presents different behaviors. This is because many practical applications today need not only periodic solutions but also more complex ones. Finally, basins of attraction are obtained and studied for some parameters of the system. Bounded and fractal regions are observed; moreover, the evolution of the attractors in the time domain for each parameter value are shown.