Sampled-data modeling and dynamical effect of output-capacitor time-constant for valley voltage-mode controlled ewline buck-boost converter

By analyzing the output voltage ripple of a buck-boost converter with large equivalent series resistance (ESR) of output capacitor, one valley voltage-mode controller for buck-boost converter is proposed. Considering the fact that the increasing and decreasing slopes of the inductor current are assumed to be constant during each switching cycle, an especial sampled-data model of valley voltage-mode controlled buck-boost converter is established. Based on this model, the dynamical effect of an output-capacitor time-constant on the valley voltage-mode controlled buck-boost converter is revealed and analyzed via the bifurcation diagrams, the movements of eigenvalues, the Lyapunov exponent spectra, the boundary equations, and the operating-state regions. It is found that with gradual reduction of output-capacitor time-constant, the buck-boost converter in continuous conduction mode (CCM) shows the evolutive dynamic behavior from period-1 to period-2, period-4, period-8, chaos, and invalid state. The stability boundary and the invalidated boundary are derived theoretically by stability analysis, where the stable state of valley voltage-mode controlled buck-boost converter can enter into an unstable state, and the converter can shift from the operation region to a forbidden region. These results verified by time-domain waveforms and phase portraits of both simulation and experiment indicate that the sampled-data model is correct and the time constant of the output capacitor is a critical factor for valley voltage-mode controlled buck-boost converter, which has a significant effect on the dynamics as well as control stability.