Tracking variable periodic signals with fixed sampling rate

Research has, shown that the repetitive control is very efficient in tracking periodic signals. However, the existing repetitive control algorithms require an integer number of samples in each period. In some industry applications where the signal period varies but other requirements on the data acquisition system force a fixed sample rate, the number of samples per period may be a non-integer. To address this problem, the paper presents an adaptive repetitive control, consisting of two portions, the repetitive controller and the nominal controller. The repetitive controller uses a fictitious sampler operating at a variable sample rate maintained at multiple times of the signal frequency, while the nominal controller uses a fixed sampling rate. Interpolations are utilised to generate the fictitious samples required for the repetitive learning. The variation of the repetitive controller's sampling rate is limited to a small value, so that the system stability can be maintained without any changes on the controller parameters. The experimental results on the control of a servomotor demonstrate the effectiveness of the proposed schemes.