Optimal Repetitive Control Based on Two-Dimensional Hybrid Model

Abstract

This paper proposes a new method of doing that for a repetitive control system containing a class of linear plants based on hybrid continuous-discrete two-dimensional (2D) model. First, by analysing of the control and learning processes independently, a hybrid continuous-discrete 2D model for the repetitive control system is established and the repetitive controller design problem is then converted to a stabilization problem for the continuous-discrete 2D systems. Next, under some performance index function, a forward-feedback controller for the continuous-discrete 2D systems is obtained by using LQR optimal control theory. Based on this, the optimal control law is transformed into the optimal repetitive control law. Unlike previous methods, the control and learning processes can be adjusted independently by the parameters in the performance index function and the relations between parameters and the performance of the repetitive controller are more intuitive than previous. Finally, the validity of the method is verified by a numerical example.