Abstract: For a class of fourth-order underactuated mechaincal systems,a Decoupled Time-Varying Fast Terminal Sliding Mode Control based on Non-linear Disturbance Observer (NDODTVFTSMC) strategy was proposed.The fourth-order system was decomposed into two second-order subsystems,and a non-linear function about the system state was used to design the exponential parameters of the time-varying sliding mode surface of each subsystem.The sliding mode surface of the second subsystem was used to construct the intermediate variable,which was introduced into the sliding surface of the first subsystem to construct the overall sliding surface of the fourth-order system.The improved non-singular time-varying fast terminal sliding mode control law was used to make the states of the two subsystems converge to the equilibrium point in a finite time.At the same time,to weaken the influence of external disturbance on the system control effect,a non-linear disturbance observer based on hyperbolic tangent tracking differentiator was designed to estimate the external disturbance and system uncertainty,and the estimated value was compensated to the controller.Lyapunov stability principle was used to prove the asymptotic stability of the sliding surface of the system.The proposed method was applied to the stability control of the inverted pendulum and compared with the existing decoupled sliding mode control algorithm to verify its effectiveness and superiority.

Key words: underactuated mechanical system, time-varying fast terminal sliding mode, decoupled control, non-linear disturbance observer, asymptotic stability

摘要： 针对一类四阶欠驱动系统,提出一种基于非线性干扰观测器的解耦时变快速终端滑模控制策略。将四阶系统分解为两个二阶子系统,分别用一个关于系统状态的非线性函数设计各子系统时变滑模面的指数项参数,用第2个子系统的滑模面构造中间变量,将其引入第1个子系统的滑模面中,构造出整个四阶系统的整体滑模面。采用改进的非奇异时变快速终端滑模控制律使两个子系统的状态分别在有限时间内收敛到平衡点;同时为削弱外部扰动对系统控制效果的影响,设计了一个基于双曲正切跟踪微分器的非线性干扰观测器估计外部干扰和系统的不确定性,并将估计值补偿给控制器。利用Lyapunov稳定性原理证明了系统滑模面的渐近稳定性。将该方法应用于小车倒立摆系统的稳定控制,并与现有的解耦滑模控制算法相比,验证了其有效性及优越性。

关键词: 欠驱动系统, 时变快速终端滑模, 解耦控制, 非线性干扰观测器, 渐进稳定性