A novel differentiator: A compromise between super twisting and linear algorithms

Malek Ghanes 1 Jean-Pierre Barbot 2, 3 Leonid Fridman 4 Arie Levant 5
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 Departamento de Ingenieria de Control y Robotica
Departamento de Ingenieria de Control y Robotica
Abstract : Based on the frequency argument, a novel second order sliding mode differentiator with a variable exponent is proposed in this article. The super twisting differentiator (exponent = 0, 5) is not sensible to perturbation but its accuracy is degraded when the signal is affected by the noise. The linear observer (exponent= 1) has better property in the presence of noise but is less robust to perturbations. The goal of this paper is to propose a trade-off between the exact differentiator and linear observer. To reach this objective, the exponent parameter is made variable. In the absence of noise exponent goes to 0; 5 and tends to 1 when the noise increases. In free-noise case and with or without perturbation, the novel differentiator behaves as a super twisting differentiator (exact differentiation). When the signal is affected by noise, only a practical stability of the differentiator is ensured. Finally simulation results are given to show that the novel differentiator has better performances compared to differentiators having exponent fixed.
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Conference papers
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Contributor : Malek Ghanes <>
Submitted on : Friday, September 15, 2017 - 10:13:54 PM
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  • HAL Id : hal-01588632, version 1


Malek Ghanes, Jean-Pierre Barbot, Leonid Fridman, Arie Levant. A novel differentiator: A compromise between super twisting and linear algorithms. IEEE CDC, Dec 2017, Melbourne, Australia. ⟨hal-01588632⟩



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