10 Q1. (40 pts, 20 pts each) For a unity feedback system with a forward transfer function K G(s) = s(s + 20)(s + 40) (1) Use the root-locus method and an appropriate compensator to yield a closed- loop step response with 20% overshoot and settling time Ts < 0.4 seconds. Choose the compensator zero at -10. Design Compensator gain: Compensator pole: pen Compensated open-loop transfer function: Ge(s)G(s) = = S on Verification hoot Percent overshoot of the compensated system: tem: Settling time of the compensated system: (2) Use the root-locus method and an appropriate compensator to yield a closed- loop step response with 20% overshoot and steady-state error K, 100. Choose the compensator pole at -0.01. Design Compensator gain: Compensator zero: pensated open- -loop Compensated open-loop transfer function: Ge(s)G(s) = = Verification Percent overshoot of the compensated system: K, of the compensated system: