Design of a modified repetitive-control system based on a continuous–discrete 2D model

This paper concerns the problem of designing a modified repetitive-control system for a class of strictly proper plants. Repetitive control involves two types of actions: control and learning; but the insertion of a low-pass filter in a modified repetitive controller, which is employed to guarantee the stability of the system, mixes the two actions together. In this paper, a continuous–discrete two-dimensional model is first constructed. Next, the continuity of repetitive control and Lyapunov stability theory are applied to the model to establish two linear-matrix-inequality (LMI) based sufficient stability conditions, one for the design of the cutoff angular frequency and one for the design of the feedback gains. The features of these conditions are exploited to develop an iterative algorithm that searches for the best combination of the maximum cutoff angular frequency of the low-pass filter and the feedback gains. A numerical example illustrates the design procedure and demonstrates the validity of the method.