a) A proportional-integral (PI) controller with a gain of 2.3 %C0/%TO and an integral time of 5 min is used to control the temperature of the process fluid outlet stream of a heat exchanger by manipulating the inlet steam flowrate. The controller receives a signal from a temperature transmitter (TT) measuring the temperature of the process fluid coming out of the heat exchanger. The TT is of zeroth order with a gain of 2.8 %TO/C, and the control valve is an air-to-close valve with a gain of 3 (kg/h)/%CO and negligible time constant and time delay. The process fluid temperature coming out of the heat exchanger increased by 20C when operators made a step change of 5C to the temperature of the process fluid in the inlet stream of the heat exchanger. The process has a damping ratio of 0.29, oscillation period of 5 min, and negligible deadtime. Develop transfer functions for the controller and the process. Then, construct a block diagram for the overall feedback control system. (8 marks)