A liquid-phase reversible reaction, A ‡„ B, takes place isothermally in the continuous stirred-tank reactor shown in Fig. E15.8. The inlet stream does not contain any B. An over-flow line maintains constant holdup in the reactor. The reaction rate for the disappearance of A is given by

The control objective is to control exit concentration c_B by manipulating volumetric flow rate, q. The chief disturbance variable is feed concentration c_Ai. It can be measured on-line, but the exit stream composition cannot. The control valve and sensor-transmitter have negligible dynamics and positive steady-state gains

(a) Design a feedforward controller based on a dynamic model.
(b) If the exit concentration c_B could be measured and used  or feedback control, should this feedback controller be reverse- or direct-acting?

(c) Is dynamic compensation necessary?

moles of A reacting (time) (volume) -ra = k,cA k,Cg, A [=] CAi CA > CB Figure E15.8