Question 2 The following block diagram represents a cascade system for controlling the temperature of a heating oil in a fumace. The block diagram transfer functions have the following values: Hv=(s+1)5,Gp=(4s+1)(2s+1)4,Hp=1,T1=1,T2=1,Hc=1 a) What is the main advantage in using cascade control? [2 marks] b) Calculate the transfer function Ysp2Y2, the steady state gain and the time constant of the inner loop. What can you say about the stability of this inner loop? [ 5 marks] c) Redraw the block diagram by replacing the inner loop by its transfer function and find the transfer function of the outer loop Ysp1r1. [ 5 marks] d) Find an expression for the transfer function Di.Y1 e) Using a proportional controller in the primary loop (Gc=Kc) find the characteristic equation of the cascade system. [4 marks] f) Find the values of Kc for which the cascade system is stable. [6 marks] [Total 25 marks]