A Novel Discrete Second-order Tracking Differentiator with Dynamic Boundary Characteristics

The input of the traditional second-order tracking differentiator system is characterized by perturbation, and the output state experiences disturbance and hysteresis. To solve these problems, we propose a novel discrete second-order tracking differentiator with dynamic boundary characteristics (DBC-TD). We use a state backstepping method to determine the boundary equation for optimal time control, then dynamically adjust the boundary by observing the absolute value of the first-order state or its statistical function, and re-program the optimal-time control function in the phase plane. We found the convergence speed and anti-interference ability of the proposed method to be better than those of traditional systems, and the complexity is reduced. On the simulation platform, we applied the proposed method to verify its track and filter performances and compared them with those of traditional tracking differntiators. The results confirm its good performance with respect to convergence speed, immunity, and algorithm complexity. On the experimental platform, we applied the proposed method to grid voltage signal processing and the results confirm the feasibility of the proposed method.