Fal函数的改进及3种新型非线性扩张状态观测器

Advanced fal function and three novel nonlinear extended state observers

首先分析现有fal函数和传统非线性扩张状态观测器中存在的6类问题,提出一种固定时间收敛的fal函数,其收敛速度快于传统fal函数,且收敛时间上界与初始误差无关;然后,分别设计基于新型fal函数的非线性扩张状态观测器、指数收敛非线性扩张状态观测器和全新结构的固定时间收敛非线性扩张状态观测器;最后,通过仿真验证这3种新型的非线性扩张状态观测器的估计总误差相对于传统非线性扩张状态观测器分别减少15.4%、16.9%和93.8%,对应的被控状态总误差分别减少13.6%、30.4%和78.3%.

Six disadvantages of fal functions and traditional nonlinear extended state observers are summarized firstly.To solve these problems,a fal function with fixed time convergence is proposed,which has better convergence ability compared to traditional fal functions,and the upper bound of convergence time is independent of the initial error.Then the nonlinear extended state observer based on the proposed fal function,the exponential convergent extended state observer and the fixed time convergent extended state observer are designed.Finally,the simulation results show that the estimation errors of the three novel nonlinear extended state observers are respectively reduced by 15.4%,16.9%and93.8%,compared to the traditional nonlinear extended state observer,and the steady-state errors of the controlled states are reduced by 13.6%,30.4%and 78.3%respectively.