A feedforward only controller system is to be designed for the stirred-tank heating system shown in Fig E. Exit temperature T will be controlled by adjusting coolant flow rate, q_c. The chief disturbance variable is the inlet temperature T_i which can be measured on-line. Design a feedforward-only control system based on a dynamic model of this process and the following assumptions:

1. The rate of heat transfer, Q, between the coolant and the liquid in the tank can be approximated by,

Q = U(1 + q_c)A(T ? T_c)

where U, A, and the coolant temperature T_c are constant.

2, The tank is well mixed and the physical properties of the liquid remain constant.

3, Heal losses to the ambient air can be approximated by the expression,

Q_L U_LA_L(T ? T_a)

where T is the ambient temperature.

4. The control valve on the coolant line and the T sensor/transmitter (not shown in Fig.) exhibit linear behavior. The dynamics of both devices can be neglected, but there is a time delay ? associated with the T_i measurement due to the sensor location.

r = koe EIRT CAi CA CA T.