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

The shape control problem, for a Sendzimir Cold Rolling Mill, is multivariable. The plant transfer function matrix, 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. Gm, however, is not invertible, but the system is diagonalised 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. To this end, 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.