What is the second loop when tuning controllers with relative gain array?

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gfd43tg
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Homework Statement


Hello, I want to control a system that looks like this
2x2 transfer function matrix: [y1(s); y2(s)] equals a matrix with entries -6e^(-0.75s)/(0.67s+1), 3e^(-s)/(2s+1), 12e^(-0.75s)/(0.67s+1), 35/(5s+1), multiplied by [u1(s); u2(s)].


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
Simulink block diagram of a 2x2 MIMO control system: two step inputs r1 and r2 with gains, two PID controllers, and four LTI System blocks Gp(1,1), Gp(2,1), Gp(1,2), Gp(2,2) feeding summing junctions Add and Add1 that drive scopes Y1 and Y2, with feedback paths.


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!
 

Discussion

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?