Fractional-Order Adaptive Sliding Mode Control for Fractional-Order Buck-Boost Converters

In previous studies, the combination of fractional calculus (FC) and sliding-mode control (SMC) has been gaining more and more interest due to fusion characteristics of SMC and FC. But most study integer-order buck converters, and few study control strategies of fractional-order converters. In this paper, the sliding mode controller and fractional adaptive sliding mode controller for fractional-order buck-boost converters are proposed. An affine nonlinear system model of the fractional-order buck-boost converter is built. Based on the differential geometry theory, the exact feedback linearization is performed on the affine nonlinear model of the fractional-order buck-boost converter. On this basis, a fractional adaptive sliding mode controller is designed by selecting a linear sliding surface and adaptive control law. The stability of the fractional controller is proved by the Mittag–Leffler stability theorem. The simulation results show that the fractional adaptive sliding mode control has good dynamic response performance and small steady-stage error regulating characteristics. Compared with traditional sliding mode control and PIλ control, the control method demonstrates stronger robustness under various disturbances.