A binary distillation column has three tray temperature measurements (17th, 24th, 30th trays) that can be used as possible controlled variables. Controlling temperature is equivalent to controlling composition. Step testing gives the following steadystate input- output relationships (uI = steam pressure in reboiler; u2 = reflux ratio):

All variables are deviation variables, Select the 2 ? 2 control system that has the most desirable interactions, as determined by the RGA (note that there are three possible 2 ? 2 control configurations). Explain why the combination of T₂₄ and T₃₀, is the least desirable controlled variable set, based on analyzing equations (2) and (3) and the resulting determinant,

Tin = 1.5t + 0.Suz (1) (2) T4 - 2.0u + 1.7uz Tio = 3.4us + 2.9u2 (3)