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Recent research has shown that the repetitive control is very efficient in tracking periodic signals, where it is required that an integer number of samples in each period. However, in some industrial applications where the signal period varies but other requirements force a fixed sample rate, the number of samples per period may be a non-integer. To address this problem, this paper presents a new adaptive repetitive control, which deals with the non-integer samples per period due to the fixed sampling rate. The proposed adaptive repetitive control consists of two portions, the repetitive controller and nominal controller, where the former uses a fictitious sampler operating at a variable sample rate maintained at multiple times of the signal frequency, while the latter uses a fixed sampling rate. Interpolations are utilized to generate the fictitious samples required for the repetitive learning. The nearly perfect tracking was achieved for non-integer samples per period, when a simple linear interpolation is used. The error due to the interpolation is quantified, which is negligible to the residual tracking error. The comparison of the proposed and the existing schemes shows the significant improvement on the tracking performance. The experimental results on the control of a servomotor demonstrate the effectiveness of the proposed schemes.