A schematic diagram for a pH neutralization process is shown in Fig. E. The transfer function matrix and relative gain array are also shown.

(a) Suppose that a multiloop control system consisting of four PID controllers is to be designed. Recommend a pairing of controlled and manipulated variables. Briefly justify your recommendation based on steady-state, dynamic, and physical considerations.

(b) Suppose that only pH₂ and h₂ are to be controlled using Q₄ and Q₆ as the manipulated variables (Q₁ and Q₃ are held constant).

(i) What is the RGA for this 2 ? 2 control problem?

(ii) What pairing of controlled and manipulated variables do you recommend? (Justify your answer.)

94 LT 42 Tank i Tank 2 pHe-PHT 78 () 0.22 ea5 4.42 s+1 D43 e 4.32s +1 -0.33 e-la 0.32 e 0s -0.20 e 0.20 e 2.56s +1 2.58 a +1 0.22L 5.52 +1 -0.22 e1 0.221 -0.32 eda 0.32 et 0.43 nt. 0.23 e1 3.10s +1 3.24 : + 1 3.30 a +1 2.82 +1 0.23 0.41 edis 0.42 e 4 4.49+1 3.32s+1 2.07 1+1 pita 2.03 a+ 1 2.36a + 1 324s+1 2.65 +1 0.64 0.72 -0.20-0.20 085 -0.35-0.35 O87 RGA 0.70 0.88 -0.18 -0.21 -0.36 0.37 0.20 0.85