Design of Nonlinear-Linear Tracking Differentiator with High Stability and High Speed

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Design of Nonlinear-Linear Tracking Differentiator with High Stability and High Speed

更新时间：2025-07-09

- Design of Nonlinear-Linear Tracking Differentiator with High Stability and High Speed
- Vol. 45, Issue 8, Pages: 43-48(2011)
- 作者机构：
  
  第二炮兵工程学院602教研室,西安,710025
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP273
- Online First：10 August 2011，
  
  Published：2011
- 稿件说明：
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Design of Nonlinear-Linear Tracking Differentiator with High Stability and High Speed[J]. 2011, 45(8): 43-48.
DOI：

Design of Nonlinear-Linear Tracking Differentiator with High Stability and High Speed[J]. 2011, 45(8): 43-48. DOI：

摘要

针对典型跟踪微分器函数形式复杂、稳定性差和输出振颤明显的问题

设计了一种改进的高稳定性快速收敛非线性-线性跟踪微分器(MTD). 首先通过引入非线性奇指数函数环节和线性函数环节构造MTD的跟踪函数

然后利用李雅普诺夫直接法和系统等价性证明MTD的全局渐近稳定性

最后通过对参数物理意义和参数变化对跟踪输出精度影响的分析得到MTD参数整定规则. 跟踪过程中

当状态与平衡点距离较远时

MTD以非线性环节为跟踪函数主体驱动状态向平衡点快速收敛

以提高系统输出的跟踪速度; 当状态与平衡点接近时

MTD以线性环节为跟踪函数主体驱动状态平稳逼近平衡点

以抑制系统输出振颤. 仿真表明

MTD参数容易整定

与典型跟踪微分器相比

MTD在系统稳定性、收敛速度和输出平稳性方面具有优势

且具有滤波功能.

Abstract

A modified nonlinear-linear tracking differentiator(MTD)with high stability and high speed is proposed to improve the performance of tracking differentiator(TD)with complicated function

poor stability and obvious chatter. A combination of a nonlinear odd exponent function and a linear function are introduced into the MTD as a tracking function

and then the global asymptotic stability of MTD is proved using Lyapunov's direct method and the equivalence of systems. The principle of parameter tuning is deduced through analyzing the physical meaning and effects of parameters on accuracy of system outputs. In the signal tracking process

the fast convergence to equilibrium point is mainly achieved by the nonlinear exponent function when the state is far away from the equilibrium point

and the linear function works as a main portion in the convergence to generate the output without chattering when the state is near the equilibrium point. Simulation results show that tuning of MTD parameters are simple

and that the performance of MTD is better than the classical TD in stability

tracking speed

smoothness of outputs and filtering.

关键词

Keywords

references

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