A Predictor Based on a Modified Full-Order Observer for Generalized Minimum Variance Control Equivalent to Polynomial Approach

This paper proposes a full-order based output predictor equivalent to a predictor designed by solving a Diophantine equation and based on polynomial approach. The predictor is used in the generalized minimum variance controller (GMVC). Hence, when the two predictors are shown to be equivalent, then two GMVC's based on the observer and on polynomial approach are equivalent. The observer based controller has a simple structure, that is, state-feedback plus state estimator observer and it is easy to design the closed-loop poles. Hence, the equivalence gives for the controller of polynomial approach to have the features of state-space based design. Although the controller using the reduce-order observer has the equivalence, the controller cannot be extended to Youla-Kucela generalized stabilizing controller. And the controller using the standard full-order observers has not the equivalence, but it has possibility to extend Yuola-Kucela controller. Hence, to have both of the equivalence and the ability of extension, in this paper, the predictor using full-order observer is modified and has the equivalence. The equivalence of the modified predictor is mathematically proved.