Switching Differentiator

TL;DR

This paper introduces a simple switching differentiator that accurately estimates derivatives without chattering or peaking, demonstrating superior performance over existing methods through simulations.

Contribution

It proposes a novel, simple switching differentiator capable of estimating derivatives with asymptotic convergence and no chattering, applicable to higher orders.

Findings

Estimation errors converge asymptotically to zero.

No chattering or peaking observed in estimates.

Outperforms existing differentiators in simulations.

Abstract

A novel switching differentiator that has considerably simple form is proposed. Under the assumption that time-derivatives of the signal are norm-bounded, it is shown that estimation errors are convergent to the zeros asymptotically. The estimated derivatives shows neithor chattering nor peaking pheonomenon. A 1st-order diffentiator is firstly proposed and, by connecting this differentiator in series, higher-order derivatives are also available. Simulation results show that the proposed differentiator show extreme performance compared to the widly used previous differntiators such as high-gain observer or hige-order sliding mode differentiator.