This paper proposes a conformable fractional-order terminal sliding mode controller for a class of nonlinear systems subject to uncertainties. First, a novel conformable fractional terminal sliding surface is proposed and its finite-time stability to the equilibrium point is proven. Subsequently, a switching function with a time-varying gain is presented. The system’s stability is guaranteed by the fractional-order Lyapunov stability theorem. The reaching and convergence time are analytically calculated. The designed controller has simple calculations. The control scheme improves the convergence speed, chattering phenomena, and control effort in the presence of disturbance and uncertainty. The simulation results show the efficiency of the proposed controller.

本文针对一类受不确定性影响的非线性系统提出了一种适形分数阶终端滑模控制器。首先，提出了一种新型适形分数终端滑动面，并证明了其对平衡点的有限时间稳定性。随后，提出了具有时变增益的开关函数。系统的稳定性由分数阶李亚普诺夫稳定性定理保证。分析计算到达和收敛时间。设计的控制器计算简单。在存在干扰和不确定性的情况下，该控制方案提高了收敛速度、抖动现象和控制工作量。仿真结果显示了所提出的控制器的效率。