The purpose of this chapter was to develop a technique (the RGA) to assist us with the decision of how to pair input and output variables to form multiple SISO control loops. The relative gain between output i and input j is defined as
and the RGA is a matrix of relative gains. Some of the important things that we learned about the RGA are summarized below.
The rows and columns of the RGA sum to 1
Do not pair on a negative or zero relative gain
Try to pair on relative gains close to 1
If you cannot pair on positive relative gains, or if the relative gains are high (>25), then the number of closed-loop control loops must generally be ...