A novel sliding mode repetitive control scheme is proposed for discrete‐time systems. It aims to address aperiodic disturbances, and simultaneously address a set of disturbances of known frequencies that can be unrelated. The sliding mode handles the former, and a repetitive control algorithm deals with the latter, creating a low‐order sliding model repetitive control law. The approach addresses each disturbance frequency individually. In contrast to the usual repetitive control approach, this allows one to address multiple unrelated frequencies without difficultly. Even when the addressed frequencies are harmonically related, but a relatively small number have significant error, this approach offers both substantial computation benefit, and benefit facilitating improved control of aperiodic disturbances. When both multiperiodic and aperiodic disturbances are present, the system trajectories can converge to a smaller switching band and keep moving within it. When there is only multiperiodic disturbance, the system trajectories will cross the switching surface within every specific steps when in the switching zone, and will converge to zero eventually. Simulation results demonstrate obvious advantages compared with the traditional method.

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This work was supported by the National Natural Science Foundation of China under grants 62103298 and the Natural Science Foundation of Tianjin under grants 18JCYBJC87700; and the Training plan for young and middle-adged backbone innovative talents in colleges and universities in Tianjin.

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