This article provides a comparative study of four different second-order sliding-mode (SOSM) differentiators proposed in the literature, namely, standard higher-order sliding-mode (HOSM) differentiator, non-homogeneous HOSM differentiator, uniform robust exact differentiator and hybrid fixed-time differentiator. Based on sliding-mode principles, these differentiators can provide robust exact differentiation with finite/fixed-time convergence. First, a comprehensive summary of the different methods is provided. Then, the differentiators are applied experimentally to estimate the states of a Van der Pol oscillator. Through experiments, it is shown that the different differentiators outperformed a Kalman-like observer, high-gain differentiator and extended Kalman filter. Finally, some suggestions are provided on the selection of SOSM differentiators for various applications.
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