Design of rapid exponential integral nonlinear tracking differentiator

In this paper, a tracking differentiator with novel acceleration function is proposed. An exponential integral function with adjustable slope near the equilibrium point is designed as an acceleration function to construct the tracking differentiator. By adding the linear function and the terminal attractor function to the tracking differentiator, the tracking performance and response speed are improved compared with the existing acceleration function. The frequency domain characteristics are analyzed based on the least squares sweep test and the stability is proved by Lyapunov method. Numerical simulations show that the rapid exponential integral nonlinear tracking differentiator can effectively suppress the high-frequency noise and make the tracking input signal more accurate.

Automated summary

This paper proposes a novel tracking differentiator with an acceleration function, utilizing an exponential integral function with adjustable slope in combination with linear and terminal attractor functions to improve tracking performance and response speed. Frequency domain characteristics are analyzed using the least squares sweep test, stability is proved with the Lyapunov method, and numerical simulations demonstrate effective suppression of high-frequency noise and increased accuracy in tracking input signals.