Analysis of second-order sliding-mode algorithms in the frequency domain

A frequency domain analysis of the second-order sliding-mode algorithms, particularly of the twisting algorithm is carried out in the frequency domain with the use of the describing function method and Tsypkin´s approach. It is shown that in the presence of an actuator, the transient process may converge to a periodic motion. Parameters of this periodic motion are analyzed. A comparison of the periodic solutions in the systems with higher order sliding-mode controllers and the oscillations that occur in classical sliding-mode systems with actuators is done.