Feedback Design of a Canonical Multivariable System With Application to Shape Control in Sendzimir Mills

Abstract

The shape control problem, for a Sendzimir Cold Rolling Mill, is multivariable. The plant transfer function matrix, however, has the special form: G(s) = g(s)Gm , where g(s) is a scalar transfer function and Gm a square matrix of constant gains. The control philosophy presented exploits this structure by diagonalising the system using an eigenvector/eigenvalue decomposition resulting in a scalar frequency response design problem. An important consideration in shape control systems is the robustness of the design due to the wide range of materials rolled, reflected in changes in the elements of Gm . Therefore, a development is included which represents the robustness of the design, with respect to errors in Gm , in terms of a set of strict inequalities.