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