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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.

Design of rapid exponential integral nonlinear tracking differentiator