Tracking differentiator based on improved Gaussian distribution

Concerning the problems of the existing tracking differentiator, such as large computation, complex parameter tuning and output chattering, a nonlinear tracking differentiator (GTD) based on the improved Gaussian distribution was proposed. It is a simple calculating nonlinear tracking differentiator with easy parameters tuning and strong ability of noise restraint. Firstly, the amplitude gain and exponential factor are introduced to improve the Gaussian distribution, then the acceleration function is constructed by utilizing the improved Gaussian distribution. Secondly, the global asymptotic stability of the designed TD is proved by constructing Lyapunov function. And its singularity type and phase trajectory distribution are analyzed by the phase plane analysis method, and the qualitative law of parameter adjustment is also given. Finally, simulations are performed and results are compared with linear differentiator and anti-hyperbolic sinusoidal based TD. It concludes that the differential signal of the improved Gaussian-distribution-based nonlinear tracking differentiator does not have the high frequency flutter behavior in steady state. Moreover, the GTD not only has good dynamic response but also has strong filtering ability. (paper)