Riemann-Liouville分数阶Buck变换器的自适应连续滑模控制

Adaptive continuous sliding mode control for fractional-order Buck converter with Riemann-Liouville derivative

中文关键词  分数阶微积分  Riemann-Liouville  Buck变换器  自适应律  连续滑模控制  Mittag-Leffler稳定

英文关键词  fractional calculus  Riemann-Liouville  Buck converter  adaptive law  continuous sliding mode control  Mittag-Leffler stability

中文摘要

      本文主要研究了分数阶Buck变换器的自适应连续滑模控制问题. 首先, 针对Buck变换器中存在多重干扰和电子元件具有非整数阶特性的情况, 建立了存在匹配和不匹配干扰的Riemann-Liouville分数阶Buck变换器数学模型. 然后, 针对传统滑模控制算法要求预知干扰上界的问题, 设计了自适应算法以估计干扰的未知上界, 基于反步控制方法建立了滑模控制器, 引入分数阶滑模面, 提升系统鲁棒性的同时, 实现滑动模态的渐近收敛. 进而, 针对滑模控制系统中的抖振问题, 设计了连续滑模控制信号, 减小了不连续控制带来的抖振, 使系统状态能够在有限时间内收敛至滑模面上, 并给出了最大收敛时间. 最后, 基于Mittag-Leffler稳定性理论, 证明了所提出总体控制方案的稳定性. 数值仿真验证了所提出控制器的有效性, 保证了系统鲁棒性的同时, 减小了抖振, 得到了良好的动态性能和较小的稳态误差.

英文摘要

      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.