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It is shown that four input-four output transfer functions with identical RGA entries in zero frequency exist and such transfer functions can be parameterized. Four input-four output transfer function entries are parameterized with respect to entries of RGA. This parameterization is useful for independent loops design, where the compensator is designed such that RGA has desired value. Finally a numerical criterion for being close to triangularity for compensated transfer function matrix is proposed.
In this paper, a new approach towards input-output pairing for an unstable system has been proposed. First, it is demonstrated that the previous method of input-output pairing for unstable plants cannot find appropriate pairs as it only checks necessary conditions for stability and integrity. Then, a new approach using relative error matrix and genetic algorithm for finding appropriate pairs in unstable systems is proposed. As it is shown, this approach takes into consideration both static and dynamic information of plant in measuring interaction. Finally, the accuracy of proposed method is demonstrated by an example and closed loop simulation.
In the paper problems with dynamic decoupling of the left-invertible multi-input multi-output dynamic (MIMO) linear time invariant plants using a squaring down technique are considered. The procedure of squaring down the plant model and grouping of plant inputs and outputs are discussed. The final part of the paper includes a few examples of different strategies of synthesis of a decoupled system along with conclusions and final remarks.
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