Question 1 In a cascade control of a furnace, the exit temperature, T is controlled by manipulating the flow rate of fuel Ffed to a furnace. Both the outer and inner loops are proportional-only controllers. The main disturbance is the pressure of the fuel P being fed to the furnace. The transfer functions for the system are as follows: Ffu (5) V'(s) 1/(4s+1); Fd (5) Pl(s) 0.5/(4s+1); T'(s) F (S) 2/(12s+1)(4+1) where; - Fru denotes as the change in flow rate due to V" (change in output from controller) in the inner loop F'ra denotes as the change in flow rate due to P' (change in disturbance) in the inner loop. Transfer function for sensor/transmitter is assumed to be 1 a) Draw a complete block diagram for this system including the cascade control system. (6 marks) b) Derive the closed loop transfer functions for the master loop T'(s)/Tsp(s) (9 marks) c) Tune the master control loop of T'(s)/T*sp(s) (identifying Kci) so that the offset is less than 0.25 with a unit step change in set point. Given that kc2 is 0.5. (use final value theorem at 120)