Design of second-order sliding mode tracking differentiator to reduce noise perturbation

The perturbation induced by signal frequency is one of the main problems for tracking differentiator design, and classical linear differentiators are usually sensitive to signal frequency. An improved second-order sliding mode nonlinear tracking differentiator is proposed in this paper using Lyapunov stability theory, considering the robustness of sliding mode control theory. This tracking differentiator can track and differentiate any signal. At the same time it has a simple form and is easy to be applied. A numerical simulation is presented for the linear tracking differentiator and the nonlinear tracking differentiator with different input signals, and results verified the effectiveness of the second order sliding mode tracking differentiator. A method to eliminate perturbation caused by noise is presented at the end of this paper.