Frequency characteristics based on describing function method for differentiators

TL;DR

This paper employs the describing function method to analyze and optimize differentiators, highlighting the advantages of hybrid nonlinear-linear designs in terms of simplicity, convergence speed, and noise suppression.

Contribution

It introduces a novel analysis approach for differentiators using the describing function method and proposes a hybrid differentiator that combines linear and nonlinear features.

Findings

Hybrid differentiator effectively combines advantages of linear and nonlinear types.

The method provides clear parameter selection guidelines.

Examples confirm improved performance and noise resilience.

Abstract

In this paper, describing function method is used to analyze the characteristics and parameters selection of differentiators. Nonlinear differentiator is an effective compensation to linear differentiator, and hybrid differentiator consisting of linear and nonlinear parts is the combination of both advantages of linear and nonlinear differentiators. The merits of the hybrid differentiator include its simplicity, rapid convergence at all times, and restraining noises effectively. The methods are confirmed by some examples.