A water tank heating process shown in Fig. E16.4 controls the outlet temperature at a desired set point T_SPby manipulating the steam pressure P_Sof steam sent to the tank heat exchanger. The steam delivery pressure P_inis subject to variations that affect P_S. Disturbances in the inlet stream temperature T_iare the primary disturbance to the process. The transfer functions of the system in Fig. E16.4 are

(a) Assuming that a PI controller with Ï„_I = 0.2 min is used, find the range of K_c values for which the system is stable for a standard single control loop configuration.
(b) Suppose a cascade control strategy is implemented to handle variations in upstream steam pressure. How should the second loop be confgured? Draw the block diagram for the process using this strategy and label the process variables.
(c) For the flowrate measurement, G_m = 0.4, and an inner loop proportional controller, compare the cascade controller closed-loop response with that of the standard PI controller (K_c1 = 2 and τ_I1 = 5) for a unit step disturbance in steam pressure. For the cascade controller, use K_c1 = 2, τ_I1 = 5, and K _c2 = 2.

0.5 G, Process (5s + 1)(3s + 1) 4 G, s+1 Valve Temperature transmitter G, = 0.5 2 Inlet stream temperature Ga 2s +1 disturbance 0.4 Steam pressure disturbance 10s +1 Transmitter Controller , Tm TT TC I/P Thermocouple P in Steam Condensate ele