Variable Structure Discrete Time Position Control

A robust, nonlinear controller is proposed for point to point positioning of a single degree of freedom system. This controller is developed for discrete time implementation and is based upon the discrete time input to state relations of a second order positioning system with bounded parametric uncertainties. The controller´s robustness properties are derived from a variable structure control law that is adapted from continuous time sliding mode control to discrete time. The sliding surface is chosen to be parabolic in order to produce fast convergence to the desired position and to minimise the effect of stiction with a high velocity approach to the position setpoint. To establish the effectiveness of the proposed control scheme, it is implemented on a single axis direct drive robot. Simulations are also conducted for comparison purposes.