Relative gain array estimation based on non-parametric frequency domain system identification

Since the introduction of the Relative Gain Array (RGA) by Bristol in 1966, it has received a high level of attention as a practical tool for solving the input-output pairing problem in decentralized control. Moreover, many extensions have been proposed like e.g. for the dynamic case and non-square system matrices. Recently, extensions that provide tools for uncertain parametric process models were suggested. In order to remove the dependency of these tools on a parametric description and accurate knowledge of a nominal model this paper proposes a method to calculate the RGA directly from a non-parametric frequency response matrix (FRM), derived from frequency domain system identification approach. The proposed method reduces the influence of model uncertainties on the calculation of the RGA and derives the RGA at frequencies of interest. Using Monte-Carlo principles, the variance of the estimated RGA is derived and compared with recently proposed methods. The results are exemplified on 2×2, 2×3 and 3×3 systems. It concluded that the proposed methods performs well and robust, while simplifying the estimation of the RGA.