A Reduced-Order Small-Signal Model for Four-Switch Buck–Boost Under Soft-Switching Current Shaping Control Strategy

The four-switch buck–boost (FSBB) converter, which possesses both step-up and step-down capabilities, is highly suitable for applications where input and output voltages have overlapping ranges. Correspondingly, the current shaping control (CSC) strategy is investigated for the FSBB converter, which shapes a quadrilateral inductor current waveform featuring the minimum RMS value to improve efficiency and power density. However, the small-signal model for the CSC algorithm has not yet been established, and the traditional and common modeling method requires considering multiple duty cycles and phase shifts of the FSBB converter, whose calculation is complex and inconvenient to use. For the special case of the CSC strategy using cycle-by-cycle current detection, an additional constraint of the averaged volt-second on the inductor can be regarded as zero, making the inductor current no longer a variable of the state-space, which eliminates the pole generated by the inductor and reduces the order of the small-signal model. Thus, this paper greatly simplifies the computation and design of the compensator by using the constraint condition mentioned above. This one-pole first-order model is simplified, maintains enough accuracy in the low-frequency domain, and can be corrected using only a simple PI controller. Finally, a prototype of the 300 W FSBB converter under the digital CSC algorithm was built to validate the precision and dynamic performance of the proposed first-order small-signal model.