Question: Water (F 1 ) is blended with a stream F 2 with 40% ethanol to make a whiskey product that is 30% ethanol. Assume F

Water (F₁) is blended with a stream F₂ with 40% ethanol to make a whiskey product that is 30% ethanol. Assume F₁ = 4 gal/min and F₂ = 4 gal/min.
(a) Develop a steady-state material balance model for the blending operation. Find the linearized gains for the 2 × 2 transfer function model using Example 18.3 as a guide. F₁ and F₂ are manipulated variables, and the controlled variables are the outlet composition z and the total ﬂow rate F.
(b) Derive the RGA in terms of F₁, F₂, and F.
(c) Determine the RGA and the preferred pairing for the controllers.

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