Frequency analysis of a discrete-time fast nonlinear tracking differentiator algorithm based on isochronic region method

In fault detection, feedback control, and other fields, real-time differential estimation of a given signal in a complex noise environment is an important but challenging task. In this paper, a discrete-time fast nonlinear tracking differentiator (FNTD) based on hyperbolic tangent functions was proposed. To start, the differential signal acquisition problem was equated to the time-optimal control (TOC) law for constructing a double-integral system using a state feedback approach. Next, the FNTD algorithm based on the hyperbolic tangent function was presented by utilizing the isochronic region (IR) method in the discrete time domain. Then, the frequency-domain characteristics of the FNTD were analyzed and the rule for tuning the parameters was provided by the frequency scan test method. Finally, the simulation results demonstrated that the proposed FNTD had fast and accurate tracking performance, as well as excellent filtering and differential extraction capability compared with other differentiators.