A control scheme is to be developed for the evaporator shown hi Fig. E, The feed and product streams are mixtures of a solute and a solvent, while the vapor stream is pure solvent. The lquid level is tightly controlled by manipulating the feed flow rate, w_F. The product composition. x_p, and the feed flow rate, w_F, are to be controlled by manipulating the product flow, w_p, and the steam flow rate w_s. The evaporator ?economy? is approximately con5taflt because E kg of solvent are evaporated for each kg of steam. The flow rates have units of kg/min, while the compositions are expressed in weight fraction of solute.

Derive an expression for the relative gain array for this system.

Transcribed Image Text:

Vapor Steam ! Condensate FT AT Product Feed *p. Wp