RGA & Selection of control loops

In last blog we learned about how we can get Relative Gain Array by two stages.

If you haven't gone through yet, click below link:

Multi-variable System

In this blog, we will analyze different conditions for Relative Gain Array.

RGA provides a quantitative criterion for for selection of control loops that would lead to minimum interaction among the process.

Direct & Indirect Effects of control loop interaction

• Let us open the loops and detach the controllers from the process. Let us keep u2 constant and introduce step input in u1. That would yield a static gain and indicate 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 u1 while maintaining y2 at its desired setpoint through the loop 2 controller. That would yield another open loop gain and indicate direct as well as indirect effect of u1 on output y1.

Let's analyze the following conditions for RGA:

Decoupling of control loops:

The relative gain array indicates how the inputs should be paired with the outputs. However, if the interaction between the loops is beyond acceptable limit, then a control designer ought to seek a solution whereby he/she can implement some technique that would decouple the loops from one another and make several non-interacting loops in result. For the present 2 x 2 system, it is evident that u2 does affect y1 however it is possible to negate the effect by manipulating u1. 

Added Decoupler D1 & D2

Now the manipulated inputs of the new loops are:

 

Rearrange the equation and putting previous value of u1 & u2 in above equation;

Above equation are completely decoupled from each other and there are no interaction in between any variables.It should be noted that decouplers are essentially feed-forward control elements. These elements are very much sensitive to operating conditions of the process.

Thanks & Keep Learning.