| Summary: | This work proposes a fractional-order mathematical model of a Buck-Boost converter performing in continuous conduction mode. To do so, we employ the average duty-cycle representation in state space, driven by the nonadimensionalize approach to avoid unit inconsistencies in the model. We also consider a Direct Current (DC) analysis through the fractional Riemann–Liouville (R-L) approach. Moreover, the fractional order Buck-Boost converter model is implemented in the Matlab/Simulink setting, which is also powered by the Fractional-order Modeling and Control (FOMCON) toolbox. When modifying the fractional model order, we identify significant variations in the dynamic converter response from this simulated scenario. Finally, we detail how to achieve a fast dynamic response without oscillations and an adequate overshoot, appropriately varying the fractional-order coefficient. The numerical results have allowed us to determine that with the decrease of the fractional order, the model presents minor oscillations, obtaining an output voltage response six times faster with a significant overshoot reduction of 67%, on average.
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