Design of super-twisting control gains: A describing function based methodology.

The Describing Function approach is used to adjust the parameters of fast-oscillations (chattering) caused by the presence of fast-actuators in Super-Twisting control loops. Estimated parameters, amplitude and frequency of self-excited oscillations, allow to compute the average power needed to maintain the trajectories of the system into real sliding-modes. Through the parametrization of the actuator dynamics by a critically damped second-order system or by a constant delay, sets of STA gains are provided to minimize the amplitude of oscillations or the average power. The results are confirmed by simulations.