基于Riemann-Liouville分数阶模型的Buck变换器改进分数阶互补滑模控制

Improved fractional-order complementary sliding mode control for fractional-order Buck converter based on Riemann-Liouville derivative

主要研究分数阶Buck变换器的互补滑模控制(CSMC)方法.首先,基于电子元件实际非整数阶的特性与Riemann-Liouville(R-L)定义相比,Caputo定义更能准确描述Buck变换器模型的结论,建立基于R-L定义的分数阶Buck变换器数学模型.然后,将参数不确定性和外部扰动统一为匹配干扰和不匹配干扰,建立两个分数阶干扰观测器(FDOB)分别实现对干扰及其分数阶导数的跟踪.进而,设计新型分数阶互补滑模面,利用CSMC的高精度和分数阶微积分的记忆特性提升滑模运动的鲁棒性和稳态精度;设计新型趋近律,提升趋近速度的同时保证滑模面邻域内的鲁棒性.最后,基于Mittag-Leffler稳定性理论证明滑模控制器的稳定性.仿真结果验证了所提出FDOB的优越性,控制器相比传统滑模方法能够得到更好的动态性能和更低的稳态误差.

This paper focuses on the complementary sliding mode control(CSMC)of fractional-order Buck converters.Firstly,to establish a more accurate model for describing the characteristics of the Buck converter,a mathematical model based on the Riemann-Liouville definition is proposed,which is more precise in describing the characteristics of the Buck converter compared to the Caputo definition,considering the non-integer order characteristics of electronic components.Then,to deal with parameter uncertainties and external disturbances,which are lumped as matched and mismatched disturbances,two fractional-order disturbance observer(FDOB)are designed to track them and their fractional-order derivatives.Subsequently,a novel fractional-order CSMC surface is developed to improve the robustness and steady-state error of the sliding mode phase by taking advantage of the high accuracy of CSMC and the memory property of fractional calculus.A new reaching law is also introduced to increase the convergence rate while maintaining the robustness of the sliding mode.Finally,the stability of the sliding mode controller is demonstrated based on the Mittag-Leffler stability.The simulation results demonstrate the superiority of the FDOB.Compared with the traditional sliding mode strategy,the proposed controller achieves better dynamic performance and lower steady-state error.