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

Based on the frequency argument, a novel second order sliding mode differentiator with a variable exponent α is proposed in this article. The super twisting differentiator (α = 0, 5) is not sensible to perturbation but its accuracy is degraded when the signal is affected by the noise. The linear observer (α = 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 parameter α is made variable. In the absence of noise α 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 α fixed.