Variable-structure repetitive control: a discrete-time strategy

This paper addresses the problem of periodic disturbance rejection arising from rotational plants following periodic trajectories. Repetitive control is a method usually employed in solving such a problem. The reported analysis results give sufficient conditions for stability of the controlled systems in the frequency domain. In this paper, discrete-time variable-structure repetitive control (VSRC) is proposed, where the periodicity features are taken into account and no disturbance estimate is involved explicitly. The presented VSRC control scheme ensures robust stability of the resultant quasi-sliding-mode dynamics to parameter variations and exogenous disturbances. The complete rejection of periodic disturbances and the perfect tracking of periodic trajectories are achieved. Time-domain sufficient conditions for the robust stability are presented by which the controller parameters can be chosen. A numerical simulation is conducted to illustrate the validity of the developed method.