Optimizing Control with Relative Gain Array in Simulink

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SUMMARY

The discussion focuses on optimizing control systems using the Relative Gain Array (RGA) in Simulink. The specific RGA provided is Λ = [[0.8537, 0.1463], [0.1463, 0.8537]], indicating that the first input should be paired with the first output and the second input with the second output. The user seeks clarification on whether to eliminate the second controller when the condition 0 < λij < 1 is met, and what the "Second Loop" refers to in this context. The solution involved creating separate controllers for each pathway and tuning them individually before integrating them into the Simulink model.

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  • Understanding of Relative Gain Array (RGA) concepts
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Homework Statement


Hello, I want to control a system that looks like this
upload_2015-12-16_14-12-16.png


Homework Equations

The Attempt at a Solution


So my relative gain array is

$$ \Lambda = \begin{bmatrix} 0.8537 & 0.1463 \\ 0.1463 & 0.8537 \end{bmatrix} $$
So I know I should pair ##u_{1}## with ##y_1## and ##u_2## with ##y_2##

Here is my simulink block
upload_2015-12-16_14-14-4.png


I know when ##0 < \lambda_{ij} < 1##, then I should tune the controller with the second loop closed. However, does that mean I should delete the second controller and work with only one controller initially? What is the "Second Loop"? I don't know which pathway that corresponds to!
 
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I was able to solve it by just creating a separate controller and tuning each ##g_{c1}## for ##g_{11}## and ##g_{c2}## for ##g_{22}##, then putting those controllers into my simulink model in the OP. However, I'm wondering in general what steps should be done?
 

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