Augmented nonlinear differentiator design

This paper presents a sigmoid function based augmented nonlinear differentiator (AND) for calculating the noise-less time derivative from a noisy measurement. The prominent advantages of the present differentiation technique are: (i) compared to the existing tracking differentiators, better noise suppression ability can be achieved without appreciable delay; (ii) the enhanced noise-filtering mechanism not only can be applied to the designed differentiator, but also can be extended for improving noise-tolerance capability of the available differentiators. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, applications on autopilot design and displacement following for nonlinear mass spring mechanical system are given to demonstrate the effectiveness and applicability of the proposed AND technique.