On phase deficit of the super-twisting second-order sliding mode control algorithm

The notion of phase deficit was introduced in [12], which allows one to determine if a nonlinear system can reveal finite-time or asymptotic convergence. Twisting and suboptimal second-order sliding mode control algorithms and a conventional relay feedback system were analyzed from the perspective of the phase deficit. However, phase deficit for the super-twisting algorithm was not determined at that time due to the complexity of the problem. Therefore, although it is known that the super-twisting algorithm reveals finite-time convergence (when no parasitic dynamics are present), it was not supported by the criterion based on the phase deficit. In the current article this problem has been solved through an open-loop interpretation of the phase deficit, which is proposed in the article. Another problem addressed in the article is the relationship between the frequency characteristics of the system and the type of convergence (finite-time or asymptotic). The mechanism of convergence is analyzed through considering time-varying frequency of self-excited oscillations and phase lag of the linear part of the system.