A Comparison Study of Tracking Differentiator and Robust Exact Differentiator

This paper presents a comparison study of two commonly-used differentiators, namely tracking differentiator (TD) and robust exact differentiator (RED) in both the frequency and the time domains. Specifically, we compare their performances in filtering and differentiation estimation for a large number of inputs with different levels of noises. Meanwhile, the parameter adaptability regarding different inputs for the two differentiators is tested. Furthermore, the efficiency of the two algorithms are evaluated respectively by the hardware. The results show that TD outperforms RED in quickness, smoothness, and noise-tolerance with no overshoots, while RED has advantageous exactness and robustness in the filtering and algorithm's simplicity. Also, TD has a better parameter adaptability and tolerance to signal frequency's variations whereas the performance of RED is heavily dependent on parameter setting. To overcome the overshoot problem in RED, an enhancement by adoption of the transition function is proposed. These results shall provide useful tips for selecting appropriate differentiators in real-life engineering, and designing new differentiators as well.