Frequency-interval interaction measure for control configuration selection for multivariable processes

In many applications one is interested in control and analysis within a bounded frequency-interval. For such applications, the input-output interactions within the desired frequency-interval need to be quantified rather than the interactions within the whole frequency range. However, the interaction measures, which have been proposed so far, either quantify the input-output interactions for a single frequency or the whole frequency range. Motivated by this, a new interaction measure is proposed in this paper. The proposed interaction measure uses frequency-interval gramians and it can be used for control configuration selection of MIMO processes. Compared with other counterparts, the proposed gramian-based interaction measure can encode more information on the input-output interactions over a desired frequency-interval. This interaction measure in addition to decentralized control can be used to propose a richer sparse or block diagonal controller structure for distributed and partially decentralized control of multivariable systems. The method is illustrated with the help of a numerical example.