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.