A total chattering-free sliding mode control for sampled-data systems

The discrete-time equivalent control, obtained from s/sub (k+1)/ = 0, is a chattering-free sliding mode control in theory. However, it involves two practical problems in implementation, they are the numerical accessibility problem and the physical admissibility problem. The numerical accessibility problem is due to the unknown external disturbances, which appears in the equivalent control. The physical admissibility problem arises in the reaching phase, in which the control law is to drive the current state to the sliding surface in one sampling period. In this paper, a one-step delay estimator for the disturbance is employed to approximate the equivalent control with an O(T/sup 2/) accuracy, where T is the sampling period. This leads to an O(T/sup 2/) boundary layer in the vicinity of the sliding surface. On the other hand, the control admissibility issue is solved by extending the reaching phase, leading to s/sub (k+1)/ = 0, with a positive on-line tuning parameter h.