Question 3 (15 marks) A control system is depicted in Figure Q3. The reverse-acting proportional controller is implemented to control a simple process that has deadtime. Gls) Gc(s) e(s) CO(s) SP(s) Kc 2e 5s + 1 PV(s) PVIS) Figure Q3: Simplified Block Diagram of Closed-Loop Process a) Show that the closed-loop characteristic equation is 58 +1 +2K e-s = 0 [2 marks] b) Using the closed-loop characteristic equation from Part (a), replace es with a second- order Pad approximation and obtain a cubic equation [5 marks) C) Estimate the ultimate gain and ultimate frequency by utilising the direct substitution method. [8 marks) The second-order Pad approximation is: 1- 2 @s+ (3) + s +() 1+ 52