Direct discretization of second order sliding mode control for uncertain nonlinear systems

In this paper the digital implementation of a second order sliding mode controller, previously proposed in continuous time, is presented. The adopted point of view is that of considering the discretization period as an intentional nonideality whose effect on the continuous plant must be evaluated in order to assure that the motion results to be confined in a o(δ³) boundary layer of the ideal continuous time sliding manifold, where δ is the sampling period. Since the resulting control can be viewed as a piecewise continuous approximation of the equivalent control, also the chattering phenomenon is avoided