In this paper, a new method for discrete-time repetitve control is presented. The control law is obtained using a technique of preview control based on LQ optimal control. As a similar method, preview-repetitive control (PRC), which is obtained using a technique of model predictive control, has been proposed. And the stability of the PRC system was studied, but explicit conditions for the stability were not derived because the relation between design parameters and the properties of the PRC system is not clear. Using optimal preview control instead of model predictive control, an explicit condition for the stability of the closed-loop system is derived. Furthermore, since the proposed feedback system has the properties of LQ optimal control, starightfoward and systematic design procedures can be given. It is shown that the tracking error between the output and the periodic reference command converges to zero as time tends to infinity by increasing preview steps. In addition, the relation between weighting matrices of the performance index and preview steps which guarantees the stability is studied. Furthermore, the asymptotic property of the system for weight selection is investigated. Numerical examples for motor position control illustrate the effectiveness of this method.
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