Question 1 At steady state the level in a vessel is controlled at 2m. The steady state inlet flowrate is 10m3/min. The outlet stream Qo flows through a valve with resistance R=h/Q0 where h is the liquid height in the vessel. The area of the vessel is 2m2. a) Find the following: i. the transfer function of the process, [5 marks] ii. the order of this process, [2 marks] iii. the steady state gain and the time constant of the process. [2 marks] b) Give a definition of the time constant. [1 mark] c) After how many time constants can we expect this system to have reached a new steady state? [ 2 marks] d) A feedback control system is used to control the water level in the vessel by using a control valve installed on the inlet stream. Draw a block diagram to represent the control system. [ 3 marks] e) The transfer function of the control valve is: Gy=(0.1s+1)5 and the transfer function of the transmitter is Gm=1. A proportional controller with a gain Kc is used to control the level of the process. Determine the transfer function of the process. [4 marks] f) Find the characteristic equation of the process. [2 marks] g) Investigate the stability of the system if a proportional controller with a gain Kc is used. Find the values of Kc for which the system is stable. [4 marks]