2D Model-Following Servo System

This paper gives, in view of the feature of practical 2D (2-dimensional) systems, a formulation of the 2D model-following servo problem for the case where one of the independent variables of the considered 2D systems is unbounded and the other one is bounded. That is, to determine a control input such that the outputs of a given 2D plant asymptotically track, with tracking error as small as possible, the (step) response of a given 2D model system as the unbounded variable approaches infinite. It is shown that this problem under a specified quadratic performance index can be transformed into a 1D LQR problem, and thus can be solved by the well-known 1D approaches. The relation between the solvability condition obtained for the equivalent 1D LQR problem and the practical stabilizability and detectability of the original 2D plant is clarified. Its application to the design of non-unit memory linear multipass processes is also shown. Finally, a numerical example for metal rolling process is given to verify the effectiveness.