二阶非线性不确定系统分段非奇异快速终端滑模控制

摘要

The sliding mode control for nonlinear uncertainty systems is studied.Aiming at nonsingular fast terminal slid-ing mode(NFTSM)'s problem of slow convergence near the equilibrium point,a piece-wise nonsingular fast termi-nal sliding mode(PWNFTSM)is proposed.The designed PWNFTSM introduces nonlinear terms to achieve system convergence in a limited time and continuous faster convergence in the local region near the equilibrium point and to avoid singularity by applying the nonlinear terms of classical fast terminal sliding mode(FTSM)structure.Fur-ther, a piece-wise nonsingular fast terminal sliding mode control algorithm based on the radial basis function (RBF)network disturbance observer(RBFNDO)for second-order nonlinear uncertainty systems is designed.The disturbance observer approach can estimate the system uncertainties and disturbances so as to improve the control precision and the robustness.The close-loop system stability can be demonstrated by using the Lyapunov method. Finally,the simulation results verify that the proposed approach can effectively increase the convergence rate,ac-quire higher control precision and achieve superior performance for second-order nonlinear uncertainty systems.%研究了非线性不确定系统的滑模控制.针对传统非奇异快速终端滑模(NFTSM)在平衡点附近收敛速度慢的问题,提出了一种分段非奇异快速终端滑模(PWN-FTSM),该滑模通过引入快速终端滑模非线性项,可实现系统有限时间收敛并在平衡点附近的局部区域保持快速收敛,避免了奇异现象,获得了比传统非奇异快速终端滑模更快的收敛速率.在此基础上,针对二阶非线性不确定系统,设计了一种基于径向基函数(RBF)神经网络干扰观测器(RBFNDO)的分段非奇异快速终端滑模控制算法.干扰观测器可准确估计系统不确定性和外界干扰,并对系统输入进行补偿,从而较大程度地提高了控制精度,改善了系统鲁棒性.运用Lyapunov方法证明了控制系统的闭环稳定性.仿真结果表明,该方法能大大加快系统的收敛速率,提高系统控制精度,改善系统的动态性能.