The fractional-order state-space averaging modeling of the Buck Boost DC/DC converter in discontinuous conduction mode and the performance analysis

In this paper, the fractional-order state-space averaging model of the Buck Boost DC/DC converter in discontinuous conduction mode is presented based on the theory of fractional calculus. The order of the model can be considered as an extra parameter, and this extra parameter has a significantly influence on the performance of the model. The quiescent operation point of the fractional-order model is not only related to the switching time period, the duty ratio, and the inductance value, but also related to the inductor order. The amplitude of the output voltage, the inductor current, and the inductor current ripple increase with the decreasing of the inductor order. Subsequently, some low-frequency characteristics, such as the line-to-output transfer function and the control-to-output transfer function of the fractional-order model, are derived from alternating current components of the fractional-order state-space averaging model. And the results suggest that transfer functions are not only relative to the inductor order, but also have intimate correlation to the capacitor order. Fractional-order models can increase the flexibility and degrees of freedom by means of fractional parameters. Numerical and circuit simulations are presented to demonstrate the correctness of the fractional-order model and the efficiency of the proposed theoretical analysis. These simulation results indicate that the fractional-order model has a certain theoretical and practical significance for the design and performance analysis of DC/DC converter.