Design and Analysis of a Novel Generalized Continuous Tracking Differentiator

Abstract

In this work, an n-th order Generalized Tracking Differentiator (GTD) is proposed based on sigmoid function with a continuous structure, including both linear and nonlinear parts, thus increasing the estimation accuracy of the input signal and its derivatives, and overcoming the inherent issues related to the classical Tracking Differentiators (TDs). Then, a 2nd-order version of the proposed GTD is derived and optimized with further improvements which are reflected in the excellent behavior in the time and frequency domains. Moreover, stability analysis using the method of Lyapunov analysis is also investigated and the performance of the GTD is proven in the time and frequency domains and revealed that the proposed GTD considerably reduces the “peaking phenomenon” and “noise” and eliminates the “chattering phenomenon” from the signal derivatives. The excellent results of the proposed GTD are demonstrated through simulations on noise-free and noisy signals and compared with the Robust Exact Uniformly Convergent Arbitrary Order Differentiator (REUCAOD).

Keywords

• Tracking differentiator
• Sigmoid function
• Peaking phenomenon
• Noise
• Chattering phenomenon
• Signal derivative