This paper presents a new fractional-order sliding mode controller (FOSMC) for disturbance rejection and stabilization of a class of fractional-order systems with mismatched disturbances. To design this control strategy, firstly, a fractional-order extended disturbance observer (FOEDO) is proposed to estimate the matched and mismatched disturbances and their derivatives. Then, according to the design procedure of the sliding mode controller and based on the designed FOEDO, a proper sliding mode surface is proposed. Subsequently, the proposed FOSMC is designed to guarantee that the system states reach the sliding surface and stay on it forever. The stability of the controlled fractional-order systems is proved via fractional-order Lyapunov stability theory. The numerical examples are used to illustrate the effectiveness of the proposed fractional-order controller. The simulation results of the proposed FOSMC are compared with the results of some other researchers’ works to show the superiority of the proposed control method. The new approach displays some attractive features such as fast response, the chattering reduction, robust stability, less disturbance estimation error, the mismatched disturbance, noise rejection, and better control performance.

中文翻译：

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通过分数阶滑模控制器控制一类具有失配扰动的分数阶系统

本文提出了一种新的分数阶滑模控制器 (FOSMC)，用于抑制一类具有失配干扰的分数阶系统的干扰和稳定。为了设计这种控制策略，首先，提出了一个分数阶扩展扰动观测器（FOEDO）来估计匹配和不匹配的扰动及其导数。然后，根据滑模控制器的设计过程，并基于设计的FOEDO，提出了合适的滑模面。随后，提议的 FOSMC 旨在保证系统状态到达滑动表面并永远停留在滑动表面上。通过分数阶Lyapunov稳定性理论证明了受控分数阶系统的稳定性。数值例子被用来说明所提出的分数阶控制器的有效性。将所提出的 FOSMC 的仿真结果与其他一些研究人员的工作结果进行比较，以表明所提出的控制方法的优越性。新方法显示出一些吸引人的特性，例如快速响应、减少抖动、鲁棒稳定性、更少的干扰估计误差、不匹配的干扰、噪声抑制和更好的控制性能。