A sub-optimal second order sliding mode controller for systems with saturating actuators

In this technical note, the problem of the possible saturation of the continuous control variable in the sub-optimal second order sliding mode controller, applied to systems with saturating actuators, is addressed. It is proved that during the sliding phase, if basic assumptions are made, the continuous control variable never saturates. On the contrary, during the reaching phase, the presence of saturating actuators can make the steering of the sliding variable to zero in a finite time not always guaranteed. In the present technical note, the original algorithm is modified in order to solve this problem: a new strategy is proposed, which proves to be able to steer the sliding variable to zero in a finite time in spite of the presence of saturating actuators.