Steady-State and Stochastic Performance of a Modified Discrete-Time Prototype Repetitive Controller

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Abstract
Perfect regulation may be too stringent a condition in repetitive control. In this paper, the rigid stability requirement is relaxed by including an appropriately chosen filter in the repetitive signal generator. Lacking an internal model, perfect regulation is not assured in the modified system. The steady-state and stochastic performances of the resulting system are analyzed. These analyses reveal that under certain conditions the dual objectives of good steady-state and stochastic performances are conflicting. A high repetitive gain may give good steady-state performance, but the variance propagation of stochastic disturbances is large (extremely large for some choice of a parameter in the modified controller). The converse is true when the repetitive gain is small. The performance of the modified scheme is evaluated by applying it to a simulated disk-file actuator system.

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