An extension of generalized minimum variance control for multi-input multi-output systems using coprime factorization approach

This paper proposes a new generalized minimum-variance controller (GMVC) having new design parameters by using the coprime factorization approach for a multi-input multi-output (MIMO) case. The method is directly extended from a conventional GMVC and used to construct the controller; it needs to solve only one Diophantine equation as in the conventional method. In this paper, by using double-coprime factorization, a simple formula for the closed-loop system given by the parametrized controller is obtained; and using the formula, it is proved that the closed-loop characteristic from the reference signal to plant output is independent of the selection of the design parameters and the poles of the controller can be chosen by the design parameters without changing the closed-loop system.