A control system is depicted in Figure Q3. The reverse-acting proportional controller is implemented to control a simple process that has deadtime. G(s) Gc(s) S e(s) CO(s) 2e SP(s) Kc PV(s) 5s + 1 PV(s) Figure Q3: Simplified Block Diagram of Closed-Loop Process a) Show that the closed-loop characteristic equation is 5s +1+2K e-s = 0 [2 marks) b) Using the closed-loop characteristic equation from Part (a), replace e-s 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: 32 DS e D4 S+ 12 D2 S + 1 + S2