High-order nonlinear differentiator and application to aircraft control

• High-order derivatives of a signal can be estimated, and the chattering phenomenon can be reduced sufficiently.
• Disturbance and phase shift can be restrained sufficiently.
• The parameters regulation is only required to be satisfied with Hurwitz condition.
• The theoretical results are applied successfully to quadrotor aircraft control.

In this paper, a high-order continuous nonlinear differentiator with lead compensation is presented based on finite-time stability. Not only the proposed high-order nonlinear differentiator can obtain the high-order derivatives of a signal, but also the chattering phenomenon can be reduced sufficiently. The parameters regulation is only required to be satisfied with Routh–Hurwitz Stability Criterion. The presented differentiator is a generalization of sliding mode differentiator and linear high-gain differentiator. The merits of the continuous differentiator include its simplicity, selecting parameters easily, restraining noises sufficiently, decreasing the phase shift and avoiding the chattering phenomenon. The theoretical results are confirmed by computer simulations and an experiment on a quadrotor aircraft: (i) the estimation of flying velocity and acceleration from the position measurement; (ii) a control law is designed based on the presented nonlinear differentiator to track a reference trajectory.