Design and frequency analysis of continuous finite-time-convergent differentiator

TL;DR

This paper introduces a continuous finite-time-convergent differentiator that reduces chattering and noise, providing smooth signal tracking and derivative estimation, with analysis comparing it to traditional sliding mode differentiators.

Contribution

It presents a novel continuous differentiator based on Lyapunov functions that improves noise suppression and eliminates chattering compared to existing sliding mode differentiators.

Findings

Reduces chattering significantly

Provides smoother signal and derivative outputs

Effective noise suppression demonstrated

Abstract

In this paper, a continuous finite-time-convergent differentiator is presented based on a strong Lyapunov function. The continuous differentiator can reduce chattering phenomenon sufficiently than normal sliding mode differentiator, and the outputs of signal tracking and derivative estimation are all smooth. Frequency analysis is applied to compare the continuous differentiator with sliding mode differentiator. The beauties of the continuous finite-time-convergent differentiator include its simplicity, restraining noises sufficiently, and avoiding the chattering phenomenon.