Integral-Square-Error Based Normalized Relative Gain Array for the Input-Output Pairing and Equivalent Transfer Function Design of MIMO Processes

Abstract

Input-output pairing effectively minimizes the loop interaction in MIMO processes and avoids integral instability. In this article, a modified Relative Normalized Gain Array is proposed for the Input-Output Pairing and design of the First-order and Second-order Equivalent Transfer function. The proposed modified Relative Gain Array (mRNGA) matrix is derived by Normalizing the Relative Gain Array matrix with a normalization factor, which is calculated by minimizing the Integral Square Error of the given MIMO process. After that, the first order and second order Equivalent Transfer function is design by the derived mRNGA matrix, which offers an improved estimation of the Effective open-loop transfer function of the given MIMO process. The proposed method is corroborated with the help of the Input-Output pairing examples up to the 5 × 5 MIMO processes and three ETF design example.