Design of a tracking differentiator based on Gaussian error function

In order to solve problems of output chattering, difficulty in tuning and poor noise suppression ability of tracking differentiators (TDs), a TD based on the Gaussian error function (ERFTD) is designed. The ERFTD has a simple form and applies the Gaussian error function to construct the acceleration function, and introduces a terminal attractor function. The application of Gaussian error function reduces chattering caused by high-frequency signals of TD, and the terminal attractor function enhances noise suppression capability of the TD. The stability of ERFTD is proved by theoretical derivation. The parameter tuning rules were summarized through frequency sweep testing. Numerical simulations show that ERFTD has good tracking capability for signals contaminated by noise, with fast response speed and high tracking accuracy; The differential ability of ERFTD is strong, which effectively suppresses the noise. The tracking differentiator based on the Gaussian error function has excellent performance.