Anti-Windup Schemes for Discrete-Time Super Twisting Algorithms*

Abstract

A discrete-time super twisting algorithm is extended such that the windup effect is avoided in the case of limitations in the amplitude of the actuating signal. This is achieved by proposing a so-called incremental version of the discrete-time super twisting algorithm. It is shown that this version of the algorithm coincides with the original formulation of the algorithm as long as the actuating signal is not limited. However, it is also shown in this paper that it can be easily extended for windup prevention if limitations in the actuating signal occur. The proposed incremental super twisting algorithm is further modified such that in case of actuator saturation not only boundedness of the state variable of the controller is ensured, also a consistency with regard to its input-output signals is achieved. This consideration results in the so-called error recalculation super twisting algorithm. Results obtained by applying the developed algorithms in simulations and an experimental case study are presented.