Design and analysis of continuous hybrid differentiator

TL;DR

This paper introduces a continuous hybrid differentiator that reduces chattering, improves dynamic performance, and enhances robustness by combining nonlinear, linear, and sliding mode elements, validated through frequency analysis.

Contribution

It presents a novel continuous hybrid differentiator design that integrates multiple techniques to improve derivative estimation performance and robustness.

Findings

Reduces chattering in derivative estimation

Enhances robustness with sliding mode and filtering

Shows improved dynamic performance through frequency analysis

Abstract

In this paper, a continuous hybrid differentiator is presented based on a strong Lyapunov function. The differentiator design can not only reduce sufficiently chattering phenomenon of derivative estimation by introducing a perturbation parameter, but also the dynamical performances are improved by adding linear correction terms to the nonlinear ones. Moreover, strong robustness ability is obtained by integrating sliding mode items and the linear filter. Frequency analysis is applied to compare the hybrid continuous differentiator with sliding mode differentiator. The merits of the continuous hybrid differentiator include the excellent dynamical performances, restraining noises sufficiently, and avoiding the chattering phenomenon.