Synthesis of run-to-run repetitive control methods using finite impulse response models

This paper presents linear quadratic (LQ) repetitive control (RC) methods for processes represented by a conventional FIR model and a circulant FIR model. The latter, which represents a FIR system under the assumption of a cyclic steady state, is named as such as its input–output map is represented by a circulant matrix. Using the complete frequency resolving property of a circulant matrix, a special tuning method for the LQ weights is proposed. Performance of the proposed method is investigated through numerical examples.