一类具有多重不匹配扰动的非同元次不确定系统的分数阶抗扰控制

Fractional anti-disturbance control for a class of incommensurate fractional-order uncertain systems with multiple mismatched disturbances

中文关键词  自抗扰控制  扰动观测器  滑模控制  非同元次分数阶系统

英文关键词  active disturbance rejection control  disturbance observer  sliding mode control  incommensurate fractional-order systems

中文摘要

      现有的自抗扰控制(ADRC)方法主要针对整数阶系统或同元次分数阶系统, 当应用于更一般的导数阶次互 不相同的非同元次分数阶系统时, 可能无法获得令人满意的性能. 针对具有多重外源干扰的非同元次分数阶不确定 系统的控制问题, 提出了一种改进的分数阶抗干扰控制方案(EFADC). 将非同元次分数阶特性当作模型不确定性, 采用分数阶自抗扰控制(FOADRC)进行补偿. 设计分数阶扰动观测器(FODO)来估计由外源模型描述的扰动. 在此 基础上, 设计一种基于不确定性和扰动补偿的分数阶滑模控制(FOSMC)方法, 使系统具有快速响应性能和鲁棒性. 通过理论分析和数值模拟验证了所提方法的有效性. 仿真结果表明, 所提方法有效改善了非同元次分数阶系统的 动态性能和对外部扰动的鲁棒性.

英文摘要

      The existing active disturbance rejection control (ADRC) approaches mainly aim at the integer-order systems or the commensurate fractional-order systems. When applied to more general incommensurate fractional-order systems, where the derivative orders are different from each other, the existing methods may not achieve satisfactory performance. To deal with the control problem of the incommensurate fractional-order uncertain systems with multiple exogenous disturbances, an enhanced fractional-order anti-disturbance control (EFADC) scheme is developed in this paper. The incommensurate-order dynamics are regarded as the model uncertainties and are compensated by a fractional-order ADRC (FOADRC) scheme. In addition, a fractional-order disturbance observer (FODO) is developed to estimate the disturbances described by exogenous models. Assisted by the commensurate model corrected by the FOADRC scheme, a novel fractional-order sliding mode control (FOSMC) scheme is developed to make the system achieve fast response and strong robustness to exogenous disturbances. Theoretical analysis and numerical simulations are presented to validate the effectiveness of the proposed EFADC scheme. Simulation results show that the proposed method effectively improves the dynamic performance of incommensurate fractional-order systems and enhances their robustness against exogenous disturbances.