On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design

TL;DR

This paper introduces an improved nonlinear tracking differentiator with hyperbolic tangent function, enhancing signal differentiation accuracy and noise robustness, and integrates it into a nonlinear PID control system for better performance.

Contribution

The paper proposes a novel INTD with hyperbolic tangent, providing stability, high accuracy, and noise filtering, and demonstrates its effectiveness in nonlinear control systems.

Findings

Faster signal tracking and differentiation.

Reduced mean square error in control.

Effective noise filtering capabilities.

Abstract

This paper presents a new improved nonlinear tracking differentiator (INTD) with hyperbolic tangent function in the state space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error analysis, the proposed INTD can extract differentiation of any piecewise smooth nonlinear signal to reach a high accuracy. the INTD has the required filtering features and can cope with th nonlinearities caused by the niose. Through simulations, the INTD is implemented as signal derivative generator for the closed loop feedback control system with a nolinear PID controller for the nonlinear Mass Spring Damper system and showed that it could achieve the signal tracking and differentiation faster with a minimum mean square error.