Pairing Relative Gain Array (RGA) and System Stability in Distillation Column

In this work the RGA of MIMO were obtained to pair the loops that give minimum interaction in a distillation column. Wood and Berry 2X2 and Ogunnaike and Ray 3X3 were taken as case studies: the procedure is to compute the RGA by firstly getting the matrix at s=0, this means the system is at its steady state. From the matrix obtained the inverse was calculated, from the inverse the transposed was made and the RGA was calculated by multiplying elements of transposed by elements of the matrix, from RGA the loops that gave minimum interaction were specified. The loops selected were subjected to stability analysis using Niederlinski index, the root locus analysis, bode and nyquist plots which were plotted using MATLAB software, they found to be unconditionally stable