This paper focuses on fast terminal sliding mode fault-tolerant control for a class of n-order nonlinear systems. Firstly, when the actuator fault occurs, the extended state observer (ESO) is used to estimate the lumped uncertainty and its derivative of the system, so that the fault boundary is not needed to know. The convergence of ESO is proved theoretically. Secondly, a new type of fast terminal sliding surface is designed to achieve global fast convergence, non-singular control law and chattering reduction, and the Lyapunov stability criterion is used to prove that the system states converge to the origin of the sliding mode surface in finite time, which ensures the stability of the closed-loop system. Finally, the effectiveness and superiority of the proposed algorithm are verified by two simulation experiments of different order systems.

本文重点研究一类n阶非线性系统的快速终端滑模容错控制。首先，当执行器故障发生时，使用扩展状态观测器（ESO）来估计系统的集总不确定性及其导数，从而不需要知道故障边界。理论上证明了 ESO 的收敛性。其次，设计了一种新型的快速终端滑面，实现全局快速收敛、非奇异控制律和减振，并利用Lyapunov稳定性判据证明系统状态收敛到滑模面原点有限时间，保证闭环系统的稳定性。最后通过两个不同阶次系统的仿真实验验证了所提算法的有效性和优越性。