Question: Q2. (40 pts, 20 pts each) For a unity feedback system with a forward transfer function K(s + 5) G(s) = (s + 2)(s

Q2. (40 pts, 20 pts each) For a unity feedback system with

Q2. (40 pts, 20 pts each) For a unity feedback system with a forward transfer function K(s + 5) G(s) = (s + 2)(s + 6)(s + 10) (1) Use the frequency-response method and a lead compensator to yield a closed- loop step response with 20% overshoot, settling time Ts < 0.5 seconds, and ess < 0.01. Design Compensator: Gc(s): = Compensated open-loop transfer function: Gc (s)G(s) = Verification poles: Percent overshoot of the compensated system: gain: Ts of the compensated system: S ess of the compensated system: (2) Use the frequency-response method and a lag compensator to yield a closed- loop step response with 20% overshoot and steady-state error ess < 0.01. Design Compensator: G(S) = Compensated open-loop transfer function: G(s)G(s): = Verification Percent overshoot of the compensated system: ess of the compensated system:

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