Discrete implementation and adaptation of sliding mode control for robot manipulators

It is shown, by both theoretical argument and experimentation, that sliding control with a boundary layer does not outperform proportional-derivative (PD) control due to the fact that the gain in the boundary layer cannot exceed the PD gain due to noise and discretization. A combined switching and PD control is proposed with the level of switching selected so that the position error is reduced but is slightly higher than the noise level in order that chattering will not occur. The switching level can be further adaptively updated based on the position error level. Through extensive experimentation of a six-degrees-of-freedom (DOF) arm, it is shown that the proposed controllers avoid chattering and reduce the transient and steady state position errors of the PD control alone