Dynamic Analysis and Fractional-Order Terminal Sliding Mode Control of a Fractional-Order Buck Converter Operating in Discontinuous Conduction Mode

Abstract

Fractional calculus provides a new tool for designing the control scheme of a PWM converter. However, in most studies of fractional-order converters, one has used the fractional orders of the converters to construct the controllers. Essentially, this controller does not add any additional fractional-order parameters, which will affect its flexibility. Taking the fractional-order Buck converter operating under discontinuous conduction mode (DCM) as well as the chaotic state as an example, this study proposes a novel fractional-order terminal sliding mode control strategy utilizing additional fractional orders. In order to analyze the nonlinear behaviors attributed to load changes, the discrete iterated mapping model of the voltage-controlled fractional-order Buck converter is proposed and built. According to the discrete iterated map, the bifurcation diagrams and Lyapunov exponent spectrums following different fractional orders are generated, indicating a process attributable to chaos. To suppress the undesirable nonlinear behaviors, a novel fractional-order terminal sliding surface is formed, and the corresponding controller is established. Moreover, the hyperbolic tangent function is introduced to solve the chattering problem. The proposed controller provides greater flexibilities to further improve the control capability. Furthermore, to verify the robustness of the proposed control method, the Mittag–Leffler stability condition of fractional-order systems is adopted. The effects of fractional orders on control performance are also discussed. Finally, circuit simulations with the approximate fractal structures of fractional-order components are implemented and compared so as to further verify the feasibility of the proposed controller.