Riemann-Liouville分数阶Buck变换器的自适应连续滑模控制

This paper investigates the adaptive continuous sliding mode control of the fraction-order Buck converter model. Initially, a refined mathematical model with both matched and mismatched disturbances is constructed through the application of the Riemann-Liouville definition to the fractional-order Buck converter system. This model is designed to mitigate the impact of multiple disturbances and the inherent non-integer order characteristics of electronic components. Subsequently, an adaptive algorithm is devised to circumvent the limitations of traditional sliding mode control algorithms, which necessitate prior knowledge of disturbance upper bounds. This adaptive approach enables estimation of unknown disturbance upper bounds. Utilizing the backstepping control method, a sliding mode controller is formulated, incorporating a fractional order sliding mode variable to improve robustness while achieving asymptotic convergence of the sliding mode. Moreover, in tackling the chattering phenomenon inherent in sliding mode control systems, a continuous sliding mode controller is engineered to alleviate chattering resulting from discontinuous control signal. This facilitates the approach of system state points towards the sliding mode surface within a finite time, with the maximum convergence time stipulated. Finally, the stability of the proposed control scheme is rigorously proved using the Mittag-Leffler stability theory. The efficacy of the proposed controller is validated through numerical simulations, affirming its ability to ensure system robustness, diminish chattering, and yield favorable dynamic performance with minimal steady-state error.