Design and Implementation of an Efficient Tracking Differentiator

Differential signals play significant roles in control practices, but they are prone to noise corruption. A noise-tolerant time-optimal system-based tracking differentiator (TD) was first proposed by Jingqing Han, which is constructed in the form of state feedback control for a discrete-time and double-integral system. However, its performances of signal-tracking filtering and differentiation extraction are sensitive to the sampling period. To relax the sensitivity on the sampling period, a time-criterion-based feedback control algorithm is proposed to construct the TD. The control algorithm is derived by comparing the time that the initial state is driven to the switching curve or the origin with any given sampling period. The impact of the algorithm parameter setting on filtering is analyzed in the frequency domain. Meanwhile, a compensation scheme is introduced to deal with the trade-off between the filtering ability and phase delay. The simulation results show that the proposed TD has smaller static errors in signal-tracking filtering, and better differentiation acquisition compared with others. The experiments conducted on STM32F405 reveal that the proposed TD uses the shortest execution time among others for processing the same input signals.