ABSTRACT This paper presents a sliding mode control (SMC) based framework to design a stabilizing controller for uncertain fractional order time-delay systems (FOTDS) using the Lambert W function technique. This technique is exploited to design the fractional order (FO) sliding manifold which provides a constructive method to design an FO sliding manifold as compared to the other methods. A stabilizing switching controller is derived, that ensures the finite time reachability of the system trajectories to the sliding manifold for all subsequent time. Moreover, the conventional SMC technique can be readily applied to a particular class of FOTDS with delay free sliding mode dynamics obtained through a specific transformation. A Duffing oscillator is considered here to illustrate the proficiency of the proposed approach. Simulation results demonstrate the efficiency of the proposed method in the presence of time delay and uncertainty.

中文翻译：

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带延迟的不确定分数阶系统的滑模控制

摘要 本文提出了一种基于滑模控制 (SMC) 的框架，用于使用 Lambert W 函数技术为不确定分数阶时延系统 (FOTDS) 设计稳定控制器。该技术用于设计分数阶 (FO) 滑动流形，与其他方法相比，它提供了一种构造方法来设计 FO 滑动流形。一个稳定的切换控制器被推导出来，它确保系统轨迹在所有后续时间到滑动流形的有限时间可达性。此外，传统的 SMC 技术可以很容易地应用于特定类别的 FOTDS，具有通过特定转换获得的无延迟滑模动力学。此处考虑使用 Duffing 振荡器来说明所提出方法的熟练程度。