Question 2 The temperature in a water tank is to be maintained at 110C. The water tank is heated by a low pressure steam coil flowing at a rate of 20kg/min. The water tank temperature rises to 120C as a result of a step change in the LP steam flow of 5kg/min. (a) Calculate the process steady state gain K. (5 marks) (b) The time-domain temperature response of the tank follows a first order behaviour and is given by H(t)=20(1e10t) i. Give a definition of the time constant. ii. Estimate the time-constant pf, the vessel level. iii. After how many time constants can we expect a first order system to have reached a new steady state? (5 marks) (c) Determine the process model transfer function (s)(s) ( 3 marks) (d) A feedback proportional control system is used to control the vessel level by manipulating the feed flowrate using a control valve. Draw a block diagram to represent the control system assuming that in the close-loop system you only have the transfer function of the controller and the transfer function of the process i.e., G. ( control valve )=1,Gm( transmitter )=1. ( 5 marks) (e) Investigate the stability of the system if a proportional controller with a gain Kc is used. ( 5 marks) (f) What is the main drawback of proportional control and how can this drawback be addressed