Semi-Implicit Euler Digital Implementation of Conditioned Super-Twisting Algorithm With Actuation Saturation

The standard super-twisting algorithm (STA) suffers from the windup problem when the actuator of the underlying controlled system is saturated. In the literature, an extension of the standard STA called conditioned STA was proposed to eliminate the windup effect through the feedback of the saturated control action. However, with the standard STA, the digital realizations of the conditioned STA with explicit Euler methods are prone to result in chattering and zigzag oscillations, which degenerate the control performance when the gains of STA are large or the sampling time-step increases. This article proposes a semi-implicit Euler realization for the conditioned STA to avoid these problems. The control accuracy and robustness of the proposed algorithm are analyzed in a discrete-time manner and it shows the proposed realization algorithm is consistent with the standard STA in terms of control accuracy. In addition, the proposed implementation method does not increase the magnitudes of numerical chattering when the gains of conditioned STA are overestimated and when the sampling time-step is large. The advantages of the proposed algorithm are demonstrated numerically with comparisons with other STA realization schemes through simulations and experiments with a platform of linear motor systems with saturated actuation.