Consider proportional-only control of the stirred-tank heater control system in Fig. The temperature transmitter has a span of 50?F and a zero of 55?F. The nominal design conditions are T? = 80?F and T? _i = 65?F. The controller has a gain of 5, while the gains for the control valve and current-to-pressure transducer are K _v = 1.2 (dimensionless) and K _ip = 0.75 psi/mA, respectively. The time constant for the tank is T = 5 min. The control valve and transmitter dynamics are negligible. After the set point is changed from 80 to 85?F, the tank temperature eventually reaches a new steady-state value of 84.14?F, which was measured with a highly accurate thermometer.

(a) What is the offset?

(b) What is the process gain K ₂ ?

(c) What is the pressure signal pt to the control valve at the final steady-state?

Tils) [F] Km , E(s) [[mA] [mA P'(8) [mA] [mA] Kip P'ls) [psi] Km T'(s) [f] P'ls) T'(8) [psi 8+1 | [F]