An improved repetitive controller with fractional time-delay for discrete-time linear systems: Synthesis and comparison study

This paper develops a discrete-time repetitive control (RC) system with a fractional-delay internal model. Unlike the conventional RC, the time delay for constructing the internal model is not necessarily an integer, implying that the time delay is allowed to be fractional. In this work, a fractional delay-based repetitive control system is presented. Firstly, the fractional time delay is calculated based on the information of the reference or disturbance along with the associated sampling period. Secondly, the fractional time delay is divided into two parts, i.e., the large integer and small fractional delays. Finally, the fractional part is realized by a stable and causal infinite impulse response (IIR) filter, whose coefficients are calculated using the Thiran formula. The controller structure and stability analysis are developed for three different RCs, namely a fractional-delay general RC (FD-GRC), a fractional delay-odd harmonics RC (FD-OHRC), and a fractional delay-(6l±1) RC (FD-(6l±1)RC). Experiments and comparison studies of the integer delay-based RCs are conducted to verify the effectiveness and improved tracking accuracy of the proposed method.