Control of Caustic Dilution Process. The tank of Fig below is used to mix a 50% solution of caustic with demineralized water to produce a dilute solution. The specified product composition is 30 mass % NaOH, and, at design conditions, the product flow is 40 klb/h. It is desired to control the product flow, wP (FC-3), and composition, xP (AC-3), by manipulating the set points on the flow con-trollers on the two inlet streams (FC-1 and FC-2). The tank is assumed perfectly mixed, and the total mass M of the solution in the tank is constant. Obtain the steady-state open-loop gains for the 2 × 2 system, and the relative gains at design conditions. Is the interaction positive or negative? Which pairing of the controlled and manipulated variables mini-mizes the effect of interaction? By how much does the gain of the product composition loop increase or decrease (specify which) when the product flow loop is closed?

 

FT Caustic SP FC 1 FT Water SP FC 2 SP AC 3 AT xp SP FC 3 FT Wp