Analysis of steady state behavior of second order sliding mode algorithms

An analysis of a second order sliding mode algorithm, which is known as the super-twisting algorithm, is carried out in the frequency domain with the use of the describing function method. It is shown that in the presence of an actuator, the transient process converges to a periodic motion. Parameters of this periodic motion are analyzed. A comparison between 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.