13.10 Summary

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 reduced; that is, one or more loops must be placed on manual control

• Switching rows on the process gain and relative gain matrices is equivalent to renumbering the outputs; switching columns on the process gain and relative gain matrices is equivalent to renumbering the inputs

• After selecting variable pairings, check the relative gain array for all subsystems to make certain that they are not sensitive to controller failure