Digital second order sliding mode control of SISO uncertain nonlinear systems

A digital variable structure control algorithm, directly derived from a continuous one, previously presented by the authors, is considered. The discretization effects of the control law on the system behaviour are analyzed for a class of uncertain SISO systems, and the sufficient conditions under which the considered digital VSC is able to perform a real second order sliding mode are derived. Furthermore the dimensions of the boundary layer of the sliding manifold are evaluated in the case the control amplitude is chosen according to an optimality criterion. The application of the considered digital VSC to a mechanical system with first order dynamics of the actuator is presented as an example