A process has the following transfer function: G(s)=(10s+1)(5i+1)2et a) Determine the steady state gain K of the process. [ 2 marks] b) Using the Direct Synthesis method find the controller tuning parameters for this process model given that the tuning relations for a PID controller are given by Kc=1(1+2),1=1+2,2=(1+2)r1T2. [ 3 marks] c) Determine the response Y(s) of the process as a result of a unit step change in the input to the process. [4 marks] d) Determine the response Y(s) of the process as a result of an impulse input to the process. [4 marks] e) Assume that the transfer function has no time delay i.e., G(s)=(10s+1)(5s+1)2 and that a controller with a proportional gain Kc is used to control the process. Draw a block diagram to represent the control system. Assume the transfer functions of the control valve and the transmitter are Gy=(0.1s+1)5 and Gm=1, respectively. [2 marks] f) Determine the transfer function of the control system. [4 marks] g) Find the characteristic equation. [ 2 marks] h) Find the values for which the control system is stable. [4 marks] [Total 25 marks]