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This paper presents a new practical framework for multiloop controller design in which controllers are designed independently, i.e., a controller in one loop is designed without exploiting information of controllers used in other loops. The method is based on the (block) diagonal approximation of a system that is different from its (block) diagonal elements. The focus of this work is on unstable systems and the approximated systems are obtained by minimizing a scaled Linfin norm for the error systems. This extends the applicability of conventional mu-interaction measure to a more general scenario. The validity of the proposed approach is demonstrated through numerical simulation and application to an industrial boiler system.