The analyzer of Example 15-5.1 is installed on the blending tank of Fig. 13-1.1a, in which both the outlet composition and flow must be controlled by manipulating the two inlet flows. Because of the slow sampling of the analyzer, both the analyzer and the flow reach steady state between samples, but there is no dead time in the flow transmitter, only on the analyzer. Thus the transfer functions of the tank are
where W is the product flow, X is the product weight % solute, and the gains are from Example 13-5.3, in %TO/%CO. Design a DMC control algorithm and determine the control gain vectors.