Improving the Rapidity of Nonlinear Tracking Differentiator via Feedforward

Differential of a signal is required for high-performance motion control and many other fields. Nonlinear tracking differentiator (NTD) is a feasible solution; however, it is limited in achieving better practical effect because of the problem of phase lags. This paper proposes a new idea of design with feedforward. By the feedforward of an input signal in solving the equations of the differentiator, differential estimate is more accurate. The proposal is simple; however, it provides an additional freedom in the design of a differentiator. This idea extends the theoretical structure of NTD. Moreover, it improves the practical effect of the differentiator. The application experiments are implemented in a servo system. Compared to the traditional NTD, the L2 norm of the servo error is reduced by 88% in a fast motion when the proposal is used. The validity is confirmed.