Rapid-convergent nonlinear differentiator

TL;DR

This paper introduces a rapid-convergent nonlinear differentiator that reduces chattering, improves dynamic performance, and enhances robustness without relying on system models, validated through simulations and experiments.

Contribution

It proposes a novel differentiator design combining singular perturbation, continuous power functions, and linear correction terms for improved performance and robustness.

Findings

Reduces chattering in derivative estimation

Enhances robustness against noise

Validated by simulations and experiments

Abstract

A nonlinear differentiator being fit for rapid convergence is presented, which is based on singular perturbation technique. The differentiator design can not only sufficiently reduce the chattering phenomenon of derivative estimation by introducing a continuous power function, but the dynamical performances are also improved by adding linear correction terms to the nonlinear ones. Moreover, strong robustness ability is obtained by integrating nonlinear items and the linear filter. The merits of the rapid-convergent differentiator include the excellent dynamical performances, restraining noises sufficiently, avoiding the chattering phenomenon and being not based on system model. The theoretical results are confirmed by computer simulations and an experiment.