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Question 2 3 Fig 2 shows a mechanical system with an open-loop transfer function G(s) = 4s +1 The proportional controller of gain Kp is added to enable the speed of response of the system to be adjusted. a) State the time constant of the open-loop transfer function. b) Obtain the closed-loop transfer function of the system Y(s)/R(s). Ans: Y(s) 3Kp 4s + (1 + 3Kp) R(S) c) Hence, determine the set value of gain Kp to obtain a time constant of 0.5 for the closed-loop system. Ans: Kp == Ans: R(s) + E(s) d) (i) Obtain the error transfer function E(s)/R(s). (ii) Calculate the set value of gain Kp so that the steady-state error due to a unit step input is less than 0.2. 3 Kp U(s) Fig 2 = 3 4s +1 E(S) 4s + 1 R(S) 4s +1+3Kp Ans: Kp < Y(s)