Variable structure control for uncertain sampled data systems

The discrete time sliding mode control theory is discussed from a robustness point of view. First, a twofold discrete time sliding mode control is proposed defining a boundary layer which divides the original state space into two regions. Inside the boundary layer, a modified equivalent control law is applied for disturbance rejection. The resulting controller eliminates the disturbance from the generalized control variable completely if its dynamics are known. If the disturbance dynamics are not available, a disturbance model is fitted using deviations from the manifold and this model is incorporated into the control law. Discrete time parameter identification of a continuous system is also discussed for the control problem in case of parametric uncertainties. Simulations on a truck-trailer system during a typical manoeuvre verify the robustness properties of the proposed discrete time sliding mode controller.