Sensitivity of Relative Gain Array for Processes with Uncertain Gains and Residence Times

The large scale industrial plants are often multivariable in nature. The preferred choice for the control of such plants is the decentralized multi-loop control system. The performance of a multi-loop control system depends strongly on the proper selection of control configuration. The most popular tool for control configuration selection is probably the steady-state "relative gain array (RGA)”. It has later been extended to consider the effect of process dynamics. A very few attempts have been made towards the sensitivity of RGA analysis to model uncertainty and is majorly limited to the steady-state systems only. The aim of this paper is to gain insights into how process dynamics can affect control configuration decision based on RGA analysis in the face of model uncertainty. For the study, parametric uncertainty in gain and residence time of the process has been considered. Analytical expressions for worst-case bounds of uncertainty in steady-state and dynamic RGA are derived for two-input, two-output (TITO) plant models. A simulation example which has been used in several prior studies is considered here to demonstrate the applicability of the proposed approach. The simulink based closed-loop response has also been obtained to show the accuracy of results. The obtained bounds of uncertainty in RGA provide valuable information pertaining to the necessity of robustness and accuracy in the model of decentralized multivariable systems.