Substantiations and Numerics of Continuous-Time Linear HTD (Han Tracking Differentiator) and Nonlinear or Unequal-Parameter ZTD (Zhang Time Derivativer) of Order 4

In this paper, continuous-time linear Han tracking differentiator (HTD), Zhang time derivativer (ZTD) introduced by Zhang neural dynamics (ZND) with initially nonlinear activation, and ZTD introduced by ZND with linear activation and unequal parameters are presented. Besides, the HTD and two types of ZTD are adopted and substantiated to obtain time-derivative signals from original signals in numerical experiments, and the corresponding numerical results are displayed and discussed in detail. Through three numerical experiments, the efficacy of HTD and ZTD is substantiated well. Moreover, the effects of different design parameters and activation functions on ZTD are illustrated. The results show that, to some extent, the larger the design parameters are, the better the performance of ZTD is. In addition, the nonlinear activation function does not greatly improve the performance of ZTD for some specific original signals.