A discrete‐time preview repetitive control (PRC) scheme was proposed for linear discrete‐time periodic systems that were subjected to previewable reference signals. First, the state augmentation technique was used to derive an augmented system that included future information on previewable signals. Second, a two‐dimensional (2D) model was developed for the augmented system so that the control and leaning actions can be adjusted preferentially by using control gains. Sufficient conditions that guarantee the closed‐loop stability of the augmented 2D systems were derived, and the design of a periodic controller with preview action and repetitive control was proposed using the linear matrix inequality approach. Finally, the effectiveness of the proposed PRC was established by using two numerical simulation examples.
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Li et al. (2021) studied this question.
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