Question 3 The following block diagram represents a cascade control system for a temperature furnace The block diagram transfer functions have the following values: Hy=1,Gp=(10s+1)1,Hp=(s+4)1,T1=1,T2=1,Hc=1 a) What is the main advantage in using cascade control? Describe the function of each loop in a typical cascade system. [ 5 marks] b) Calculate the transfer function Ysp2Y2 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 YspY1 [5 marks] d) Using a proportional and integral controller in the primary loop Gc=Kc(1+s1) find the characteristic equation of the cascade system. [5 marks] e) Find the values of Kc for which the cascade system is stable. [5 marks]