A process has the following transfer function: H(s)=(1s+1)(4s+1)1 It is controlled using a PID controller. a) Use the Direct Synthesis Method to determine the controller settings for a time constant c=5min. For a second-order-plus-time-delay model the controller settings are given by: Kc=K1(c+)1+2,ls=1+2,D=1+212 [5 marks] b) Explain why the process represented by Eq. (1) is stable. [2 marks] c) Suppose that the process gain changes from 1 to 1+ in Eq. (1). Draw a block diagram of the feedback control system assuming that in the close-loop system there are only the transfer function of the controller and the transfer function of the process [i.e. Gv (control valve) =1,Gm (transmitter) =1]. The transfer function of a PID controller is given by Gc=Kc(1+1s1+Ds) [5 marks ] d) Write the characteristic equation of the feedback control system [5 marks] e) State the necessary stability condition that must be fulfilled by the characteristic equation. [ 3 marks] f) Determine the values of for which the closed-loop system is stable. [5 marks]