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Process Control: Modeling, Design, and Simulation by B. Wayne Bequette

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13.5. Properties and Application of the RGA

Sum of Rows and Columns Property of the RGA

Notice that Equation (13.24) yields the following relationships

This property for 2 × 2 systems is general for n × n systems. That is, each row of the RGA sums to 1.0 and each column of the RGA sums to 1.0.

Then, for a 2 × 2 system, only one relative gain must be calculated to find the entire array,

Equation 13.25

For a 3 × 3 system, only four of the nine elements would need to be calculated. In practice, they are all calculated simultaneously using (13.23

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