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# pset_3 - Fall 2004 ICE Topics Process Control by Design...

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Fall 2004 ICE Topics: Process Control by Design 10.492 Problem Set 3: Calculating RGA and DC For this problem set, I will accept submissions with one or two names. (1) Beginning with linearized material and energy balances for the shower, expressed in physical terms, F = F h + F c T F hr + T F T F hr + T F hr hr cr cr F T = cr cr + T hr ( F + F ) ( F F hr ) + F hr ( T T hr ) hr + F F hr + F 2 h F hr + F h cr cr hr cr cr T T F hr + T F + cr hr cr cr cr ( F + F ) ( F F ) + F ( T T ) F hr + F 2 c cr F hr + F c cr cr hr cr cr derive an expression for each individual element λ ij of the RGA from the definition x the of gain mj with loop y open loops other i λ ij x the of gain mj with loop y perfect loops other i y i x mj x mj constant x mk = y i x mj y k y i constant (please use the nomenclature of the Lecture Notes) (2) Beginning with linearized material and energy balances for the shower, expressed in scaled deviation terms, F *' F h F h *' + F c F *' = c

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