A process with two inputs and two outputs has the following dynamics, [[8]-[C [G₁₁(s) G₁₂(S)] G₂1(s) with G₁₁(s)= 4e-5s 2s +1' G₁₂(s) = 2e-2s 4s +1' G₂ (S) U₂ (s)_ G₂1 (S) = -6s 3e 3s +1' G₂₂ (s) = 5e-3s 2s +1' b) Calculate the static gain matrix K, and RGA, A. Then, determine which manipulated variable should be used to control which output.

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A process with two inputs and two outputs has the following dynamics,
11
[P]-[C
[Y(s)] [G₁₁(s) G₁₂ (s)[U₁(s)
G₁(s)
[Y₂ (s)]
G₂ (s) U₂ (s)]
with G₁₁(s) =
-5s
4e-5
2s +1'
G₁₂(s)=
2e-2.s
4s +1'
G₂₁(s) =
3e-6s
3s +1'
G₂₂ (S) =
5e-3s
2s +1
b) Calculate the static gain matrix K, and RGA, A. Then, determine which manipulated
variable should be used to control which output.
Transcribed Image Text:A process with two inputs and two outputs has the following dynamics, 11 [P]-[C [Y(s)] [G₁₁(s) G₁₂ (s)[U₁(s) G₁(s) [Y₂ (s)] G₂ (s) U₂ (s)] with G₁₁(s) = -5s 4e-5 2s +1' G₁₂(s)= 2e-2.s 4s +1' G₂₁(s) = 3e-6s 3s +1' G₂₂ (S) = 5e-3s 2s +1 b) Calculate the static gain matrix K, and RGA, A. Then, determine which manipulated variable should be used to control which output.
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