基于改进sigmoid函数的非线性跟踪微分器

Nonlinear tracking differentiator based on improved sigmoid function

本文受神经网络中常用的sigmoid激励函数特性的启发,提出了一种形式简单、调参相对容易的非线性跟踪微分器(STD).首先,在sigmoid函数的基础上引入指数和幅度因子,利用改进后的sigmoid函数构造加速度函数,接着,借助Lyapunov直接法证明了所设计的跟踪微分器的非摄动形式具有全局渐近稳定性,随后利用系统等价性给出了跟踪微分器的具体形式并通过扫频测试分析了其频域特性;最后,与线性微分器(LD)、全程快速跟踪微分器(HSTD)以及改进的跟踪微分器(ITD)、反正切形式的跟踪微分器(ATD)分别进行对比仿真分析.结果表明,基于sigmoid函数设计的跟踪微分器可以兼顾响应的快速性以及平稳性、全程无抖振,对信号的广义导数具有良好的逼近能力和滤波效果.

Inspired by the characteristic of common activation function of neutral network, which is known as sigmoid function, we propose a nonlinear tracking differentiator （STD） with simple form and fewer tuning parameters. Firstly, exponential and scale factors are introduced to improve the sigmoid function, then the acceleration function is constructed by utilizing the improved sigmoid function. Secondly, the global uniformly asymptotical stability of the tracking differentiator （TD） in nonerturbation form is proved by using Lyapunov direct method. Moreover, the concrete form of TD is presented by the principle of system equivalence, and its frequency-domain characteristic is analyzed by utilizing the frequency-sweep test. Finally, simulations are performed and results are compared with those of linear differentiator, high-speed nonlinear tracking differentiator and improved nonlinear tracking differentiator, arctangent-based TD. It concludes that the sigmoid function-based nonlinear tracking differentiator not only guarantees the response with high speed and smoothness but also presents the behavior with no chattering in the whole course and exhibits excellent performance in approximating and filtering the generalized derivative of the signal.