On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design

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 improved tracking differentiator (INTD) has the required filtering features and can cope with the nonlinearities caused by the noise. Through simulations, the INTD is implemented as a signal's derivative generator for the closed-loop feedback control system with a nonlinear 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.