改进跟踪微分器设计

通过非线性和线性连续函数的恰当组合，使构造的奇次指数幂且连续的跟踪微分器函数的系统状态，无论在远离还是接近平衡点位置都能快速收敛。设计的跟踪微分器满足全局渐进稳定，仅收敛于一个平衡点。此外，由于未使用切换函数，也不存在抖振现象。计算机仿真表明，改进跟踪微分器跟踪效果优于经典的非线性跟踪微分器，且跟踪给定系统的状态变量与真实状态变量的响应高度吻合。

Design of a Modified Tracking Differentiator

A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified tracking differentiator by select a Lyapunov function. Through combining of the nonlinear and linear function properly, it can be sure that the state converges to the equilibrium point with high speed automatically no matter that the state was far away from the equilibrium point or near to it, and it can prevent the chattering. Simulation results show that the modified tracking differentiator tracking results is superior to the classical nonlinear tracking differentiator, and the responsing of state variables tracking differentiator estimated are almost coincide with the real state of the variables of the given system.