Question $1$

The measurements and manipulated variables are shown in the Figure; you may not alter them and need not to use them all. The following information will help in the design of the control strategies.

The goal is to tightly control the exit temperature $T_5$ at the outlet of the last tank. The major disturbance is the temperature of one of the feed streams, $T_2.$

The flow$-$rates to the stirred tanks cannot be changed by your control strategy and are essentially constant; $F_1=F_2=5\frac{m^3}{m}in.$

The volume of each tank is constant, $10m^3.$

The sensor$,$ valve and heating coil dynamics are negligible and the heat losses are small but not negligible.

a$)$ Decide whether a single$-$loop feedback control strategy is possible. Explain your answer. If yes, draw the single$-$loop feedback control system on the process figure. $[1+1+2$ marks$]$

b$)$ Decide whether a cascade control strategy is possible. Explain your answer. If yes, draw the best cascade control system on the process figure. $[1+1+3$ marks$]$

$1$

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c$)$ Decide whether feedforward$/$feedback control strategy is possible. Yes, or no$.$ Explain your answer. If yes, draw the best feedforward$/$feedback control system on the process figure. $[1+1+3$ marks$]$

d$)$ Rank the strategies in $($a$)$ through $($c$)$ according to their control performance and draw the block diagram for the control strategy identified as the best in terms of performance. $[1+5$ marks$]$