VI.4 Relative Gain Array and selection of control loops

The RGA provides a quantitative criterion for selection of control loops that would lead to minimum interaction among the loops. Consider the following two experimentations (or simulations):

•  Let us open the loops and detach the controllers from the process. Let us keep constant and introduce a step input in . That would yield a static gain that would indicate the direct effect of input on output .

•  Let us now close only the loop 2 and attach the corresponding controller with the process. Let us now introduce a step input in while maintaining at its desired setpoint through the loop 2 controller. That would yield another open loop gain that would indicate the direct as well as indirect effect of input on output .

The ratio of above two open loop gains is defined as the relative gain

(VI.8)