Second-Order Sliding-Mode Differentiators: An Experimental Comparative Analysis Using Van der Pol oscillator

Hafiz Ahmed, Héctor Ríos, Beshah Ayalew, Yongqiang Wang

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9 Citations (Scopus)
189 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)2100-2112
Number of pages13
JournalInternational Journal of Control
Issue number9
Early online date16 Feb 2018
Publication statusPublished - 2018

Bibliographical note

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Control on 16th February 2018, available online:


  • Sliding-mode differentiation
  • Van der Pol oscillator
  • real-time estimation


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