A Novel Second-Order Nonlinear Differentiator With Application to Active Disturbance Rejection Control

TL;DR

This paper introduces a new second-order nonlinear differentiator that combines linear and nonlinear elements, improving convergence speed and noise robustness, and demonstrates its effectiveness in active disturbance rejection control.

Contribution

A novel second-order nonlinear differentiator using hyperbolic tangent functions is proposed, offering enhanced performance and robustness over traditional differentiators.

Findings

Faster convergence due to high slope of tanh(.) near zero

Reduced chattering phenomenon in the differentiator

Improved noise robustness in disturbance rejection applications

Abstract

A Second-order Nonlinear Differentiator (SOND) is presented in this paper. By combining both linear and nonlinear terms, this tracking differentiator shows better dynamical performances than other conventional differentiators do. The hyperbolic tangent tanh(.) function is introduced due to two reasons; firstly, the high slope of the continuous tanh(.) function near the origin significantly accelerates the convergence of the proposed tracking differentiator and reduces the chattering phenomenon. Secondly, the saturation feature of the function due to its nonlinearity increases the robustness against the noise components in the signal. The stability of the suggested tracking differentiator is proven based on the Lyapunov analysis. In addition, a frequency-based analysis is applied to investigate the dynamical performances. The performance of the proposed tracking differentiator has been tested in active disturbance rejection control (ADRC) paradigm, which is a recent robust control technique. The numerical simulations emphasize the expected improvements.