An irreversible liquid phase reaction, A?B, takes place in a stirred-tank reactor, as shown in Fig. E.?The reaction is zero order, and thus (he rate of reaction does not depend on the concentrations of A or B. The rate of reaction, r (mols of A reacting/cu ft h), is given by where k₀ and E are constants. It has been suggested that feedforward control be used to control reactor temperature T by adjusting the inlet coolant temperature, T_c. The chief disturbance variable is the inlet temperature, T_i.

Using the information given below, do the following:

(a) Design a feedforward controller based on steady- state considerations.

(b) Do you recommend that dynamic compensation in the form of a lead?lag unit be added to this feed- forward controller? Briefly justify your answer.

Available Information

1. The volume of liquid V is held constant via an overflow line so that the volumetric flow rate q is the same for both inlet and outlet streams.

2. The variation in coolant temperature along the length of the cooling coil is negligible.

3. The rate of heat removal by the coolant can be expressed as Q = UA(T ? T_c) where U and A are constants.

4. The heat of reaction per mol of A reacted ??H_r is constant.

5. The reactor can be assumed to be perfectly mixed.

6, The density of each liquid stream is the same.

7. The sensor/electronic transmitter combination for the feed temperature has negligible dynamics and a steady-state gain, K_t.

8. The electronic control valve has negligible dynamics and a steady-state gain, K_v.

r = koe EIRT CAi CA CA T.