Sliding mode disturbance observer based control with arbitrary convergence time

Abstract

In this study, an arbitrary finite-time backstepping control method for a class of uncertain nonlinear systems in the presence of external disturbance is proposed based on disturbance observer. Motivated by the desire to attain external disturbance compensation, a sliding mode disturbance observer with arbitrary convergence time is presented to estimate the disturbance. This arbitrary prespecified time is independent of initial conditions and system parameters. The designed observer is very simple with only one tuning parameter used to tune the convergence rate. Only the upper bound of the first derivative of the disturbance is necessary. Then, based on the proposed disturbance observer, a backstepping control technique is developed in which the convergence time can be chosen arbitrarily. Utilizing the Lyapunov stability criterion, it is proven that the system states, as well as the disturbance observer error converge to the origin in arbitrarily chosen time. Finally, some numerical examples are presented to demonstrate the validity and applicability of the proposed disturbance observer-based controller.