1. in an oil refinery, a furnace is used to continuously preheat crude oil for a fractionator. the feed to the furnace exhibits larges fluctuations in its flow rate F [kg/min] and temperature Ti [C]. despite, we wish to maintain the temperature of the output crude oil, T [C], at a set point Tsp 390 [C] via a feedback control system. a linear, direct-acting temperature sensor/transmitter (TT) measures T and transmits it to the temperature controller (TC) as an electrical signal T [mA]. the range of the temperature sensor is 200 C-500 C. the temperature controller (TC) is a P-controller. the controller then outputs an electrical signal p [mA] to a linear, direct-acting current-to-pressure transducer (I/P). finally, this transducer outputs a pneumatic signal p [psig] to a linear, air-to-open control valve that manipulates the flow rate of fuel to the furnace. electric and pneumatic signals obey industrial standard ranges of 4-20 mA and 3-15 psig. crude oil F Kg/min Ti C furnace Stack gases 7 MA TC -Tsp PMA P psig /P air Fuel (a) (2 points) calculate the internal set point, Tsp [mA]. C heated crude oil = Tsp when the (b) (2 points) at steady-state conditions, we experimentally observe that T pneumatic signal to the control valve p = 10 psig. calculate the bias [mA] of the TC. (c) (4 points) we wish for the control valve to be fully open when T = 320 C ( < Tsp). calculate the value of the TC gain K that achieves this. (d) (1 point) finally, using your numbers for Kc, Tsp, and , write the P-control law that specifies the output of the TC, p, given its input from the TT, T. (e) (1 point) considering safety, is employing an air-to-close control valve a better choice? [yes/no?]