Digital implementation of the supertwisting controller based on the deadbeat method

Abstract

The deadbeat method is developed in this paper to realize a chattering-free implementation of the supertwisting controller while keeping its important properties such as convergence rate, and robustness to uncertainties, disturbances, and measurement noise. The deadbeat implementation leads to a finite-time convergence of the discrete-time supertwisting algorithm without exceeding the control effort compared to the original supertwisting controller in the continuous-time domain. Several properties of the implemented supertwisting controller based on the proposed method are investigated analytically and validated based on numerical experiments including the chattering treatment, convergence rate, disturbance attenuation, and convergence in the presence of parametric uncertainty and measurement noise. The comparison of the developed method to the recently trending implicit discretization indicates a more straightforward realization without requiring to take into account the setvalued terms or solving generalized equations, which may not be possible for all sliding-mode algorithms.