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 with the use of the describing function and the locus of a perturbed relay system approach. 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 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.