Non-smooth Dynamics in Ramp-Controlled and Sine-Controlled Buck Converters

The DC-DC Buck converter is a power converter system that transforms high DC voltages to low DC voltages and is widely used in several applications. However, a plethora of non-smooth dynamics have been found especially in the ramp-controlled buck converter configuration that lead the system to undesired behaviors, mainly due to the non-smooth nature of the ramp signal. As a consequence, we propose to change the ramp signal by a sine waveform as a smooth alternative to the non-smoothness of the ramp waveform, and thus try to avoid the non-smooth behaviors of the buck converter system without resorting to advanced control strategies. Nevertheless, we found that non-smooth dynamics remain present in the system even by using a smooth sine waveform instead of a non-smooth ramp waveform. In fact, a new variety of non-smooth bifurcations were found, cascade of border collision bifurcations and different non-smooth transitions from nT-periodic orbits to another nT-periodic orbits and chaotic bands, behaviors only observed in power inverter systems controlled by ramp signals. Finally, the simulation results are validated by computing the Lyapunov exponents.