5-19 from the textbook (Smith and Corripio): a controller receives a signal from a temperature transmitter with a range of 100 to 150 C. Assume the controller is proportional-integral (PI) with a gain of 3 %CO/%TO and an integral time of 5 min.

a. Write the transfer function of the controller relating the output M(s) to the error signal E(s); assume both signals are in percent of range. Show the numerical values of the controller parameters.

b. Calculate the gain of the transmitter and write its transfer function assuming that it can be represented by a first-order lag time with a time constant of 0.1 min.