It is recognized today that active disturbance rejection control (ADRC) is an effective control strategy in the presence of uncertainties and disturbances and especially in the absence of a model. Its advantages and its power have been demonstrated practically on numerous engineering applications. This control technique has been widely developed in the case of integer-order systems. On the other hand, fractional-order systems are gaining more and more interest due to their use in modeling of many physical phenomena. Some works have been dedicated to the design of the ADRC for linear and nonlinear fractional-order systems. However, the sliding mode technique has not yet been used for the design of ADRC of fractional-order systems. The aim of this paper is to propose a sliding mode active disturbance rejection controller (SMADRC) for nonlinear fractional-order systems with uncertainties and external disturbances for stabilization and tracking purposes. First, a step by step sliding mode extended state observer (SMESO) for both state variables and total disturbance (uncertainties and external disturbances) estimation is proposed. The finite time convergence of the proposed extended state observer is established. Then, a sliding mode controller using the estimated states and total disturbance is presented to realize stabilization and desired references tracking with compensation of the total disturbance. The closed loop stability is analyzed. Simulation results of the proposed SMADRC applied to the control of fractional-order chaotic systems are compared to those of the conventional sliding mode control scheme.

如今公认的是，在存在不确定性和干扰的情况下，尤其是在没有模型的情况下，主动干扰抑制控制（ADRC）是一种有效的控制策略。它的优点和功能已在众多工程应用中得到了实际证明。在整数阶系统的情况下，已经广泛地开发了这种控制技术。另一方面，由于分数阶系统用于许多物理现象的建模，因此越来越受到关注。一些工作致力于线性和非线性分数阶系统的ADRC设计。但是，滑模技术尚未用于分数阶系统的ADRC设计。本文的目的是针对具有不确定性和外部干扰的非线性分数阶系统，提出一种用于稳定和跟踪目的的滑模主动干扰抑制控制器（SMADRC）。首先，针对状态变量和总扰动（不确定性和外部扰动）估计，提出了一种逐步滑模扩展状态观测器（SMESO）。建立了所提议的扩展状态观测器的有限时间收敛性。然后，提出了一种使用估计状态和总干扰的滑模控制器，以实现稳定和期望参考跟踪，并补偿总干扰。分析闭环稳定性。