s-Dynamics Designs for Uncertain Variable Structure Systems with Repetitive Controllers

This paper is concerned with uncertain systems subject to periodic disturbances with a known period, and the discrete-time variable structure repetitive control methodology is applied to address the control problem. The notion of quasisliding mode is reviewed in this paper. Switching-function dynamics obtained with the proposed repetitive strategies are desirable, which govern both reaching phase and sliding phase of the variable structure systems. The attractive layer bounds and quasi-sliding mode bandwidths are given for characterizing the switching-function dynamics. The repetitive control method ensures closed-loop robust stability, and achieves perfect tracking in the presence of periodic perturbations. Partial-period repetitive control is presented for improving transient performance, as more knowledge about the periodicity is available. Numerical simulation is carried out to verify the analytical results.