Discrete-time variable structure repetitive control

This paper addresses the control problem of periodic disturbance rejection arisen from rotational machinery which follows a periodic reference input. Discrete-time variable structure repetitive control (VSRC) is formulated based on a repetitive reaching condition given in this paper. Sufficient conditions for asymptotic convergence of the resultant closed-loop system are presented by which the controller parameters can be chosen. Complete rejection of periodic disturbance as well as asymptotic tracking of periodic reference input are achieved. The developed VSRC method also ensures robust stability of the quasi-sliding mode dynamics to parameter variations and exogenous disturbances. Numerical simulation is conducted to illustrate the effectiveness of the proposed method in repeatable runout compensation of hard disk drives.