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A novel fractional-order sliding mode control method based on a fractional-order extended state observer (FOSMC+FOESO) controller is developed to attenuate the matched and mismatched disturbances of a buck converter, i.e., load mutation and model errors. First, a novel fractional-order buck converter with matched and mismatched disturbances which can be derived from each other is proposed. The FOESO is designed to estimate and compensate for the mismatched disturbance and indirectly estimate the matched disturbance, which can reduce the sensitivity of the matched and mismatched disturbances. According to the proposed fractional-order model, the fractional-order sliding mode surface with the disturbance estimation term and exponential approach rate are introduced to improve the antidisturbance ability and voltage tracking performance of the system. The system stability is verified by a Lyapunov function with the Leibniz rule of fractional calculus. Finally, the comparison of several simulation and experimental results illustrates that the proposed FOSMC+FOESO controller has the superior voltage tracking performances than traditional sliding mode control (SMC), FOSMC, and SMC based on ESO methods.
Li et al. (Tue,) studied this question.