(202i) RGA Analysis of Systems With Uncertain Gain and Time Constants

The Relative gain array (RGA) analysis has been extensively used in the field of process control to identify control configuration with minimal interaction between controlled outputs and manipulated inputs. The study of effects of uncertainty in parameters of process models is still very recent. Much of the research that does exist in this field focuses predominantly on uncertainty in steady state gain only. The effect of uncertainty in time constant or uncertainty in time delay has remained largely unexplored. This paper is an attempt to bridge this gap in research by suggesting an approach for incorporating uncertainty in time constant for two-input, two-output (TITO) plant models and to show how pairing recommendations can turn out to be inaccurate if the uncertainty in time constant is not considered.

In the current paper, analytical expressions have been derived for incorporating uncertainty in time constant in the RGA analysis by two approaches - (i) considering uncertainty in single time constant only and (ii) considering uncertainty in all the time constants at the same time. The results thus obtained have been tabulated, analyzed and discussed. A comparative analysis is also presented, with the aim of aiding an understanding of how the variable pairing decision might change if the uncertainty in time constant is considered in contrast with the uncertainty in steady state gains only or considering uncertainty in steady state gains and the time constants together. To demonstrate the efficacy of results two 2 x 2 plant models which have been widely used in earlier studies have been worked out. The obtained uncertainty bounds validate the need to incorporate time constant uncertainty in RGA analysis to make the system more robust.