Cai Zhongze, Zeng Qingshuang
School of Astronautics, Harbin Institute of Technology, Harbin 150006, China.
Entropy (Basel). 2023 Apr 21;25(4):700. doi: 10.3390/e25040700.
This study proposes a continuous adaptive finite-time fractional-order sliding mode control method for fractional-order Buck converters. In order to establish a more accurate model, a fractional-order model based on the Riemann-Liouville (R-L) definition of the Buck converter is developed, which takes into account the non-integer order characteristics of electronic components. The R-L definition is found to be more effective in describing the Buck converter than the Caputo definition. To deal with parameter uncertainties and external disturbances, the proposed approach combines these factors as lumped matched disturbances and mismatched disturbances. Unlike previous literature that assumes a known upper bound of disturbances, adaptive algorithms are developed to estimate and compensate for unknown bounded disturbances in this paper. A continuous finite-time sliding mode controller is then developed using a backstepping method to achieve a chattering-free response and ensure a finite-time convergence. The convergence time for the sliding mode reaching phase and sliding mode phase is estimated, and the fractional-order Lyapunov theory is utilized to prove the finite-time stability of the system. Finally, simulation results demonstrate the robustness and effectiveness of the proposed controller.
本研究针对分数阶Buck变换器提出了一种连续自适应有限时间分数阶滑模控制方法。为了建立更精确的模型，基于Riemann-Liouville（R-L）定义开发了Buck变换器的分数阶模型，该模型考虑了电子元件的非整数阶特性。结果发现，R-L定义在描述Buck变换器方面比Caputo定义更有效。为了处理参数不确定性和外部干扰，该方法将这些因素组合为集总匹配干扰和失配干扰。与以往假设干扰有已知上界的文献不同，本文开发了自适应算法来估计和补偿未知有界干扰。然后采用反步方法设计了一种连续有限时间滑模控制器，以实现无抖振响应并确保有限时间收敛。估计了滑模到达阶段和滑模阶段的收敛时间，并利用分数阶Lyapunov理论证明了系统的有限时间稳定性。最后，仿真结果验证了所提控制器的鲁棒性和有效性。
