A process is made up of two individual components with transfer functions H(s)=(2s+1)1 and F(s)=(3s+1)2 arranged as follows: Find the transfer function G(s) of the equivalent process. [3 Marks] (a) The process is controlled using a PID controller. Use the Direct Synthesis method to determine the controller settings for a time constant tc=2.5min. For a second-order-plus-time-delay model the controller settings are given by: Kc=K1(c+)1+2l=1+2D=1+212 (b) Explain why the process represented by G(s) is stable. (3 marks) ( 2 marks) (c) Suppose that the process gains of G(s) changes from 2 to (2+). 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+/S1+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. (f) Determine the values of for which the closed-loop system is stable