Question 6 Fig 6 shows a feedback control system, in which Kp is the controller gain and Ks the gain of the feedback sen

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Question 6 Fig 6 Shows A Feedback Control System In Which Kp Is The Controller Gain And Ks The Gain Of The Feedback Sen 1 (121.23 KiB) Viewed 30 times

Question 6 Fig 6 shows a feedback control system, in which Kp is the controller gain and Ks the gain of the feedback sensor. (a) Derive an expression for the closed-loop transfer function- C(s) Kp R(s) s² + as + KpKs (b) Show that the resulting closed-loop system has the general second-order form Ksson s² +250S+0nª (c) Determine Ks, K, and a such that the system will have a steady-state gain Kss of unity, a damping ratio = 0.6 and a natural frequency on = 5.0. Ans: Kp = 25, Ks = 1, a = 6 Fig 6 2 R(s) + (d) From the parameters determined in (c) plot the corresponding s-plane showing the pole locations. Ans: s = -3 + j4 Kp 2 (e) Assuming the values determined for a and Ks in (c), for what range of positive values of Kp will the resulting closed-loop response be non-oscillatory? Ans: 0 < Kp ≤ 9 C(s) R(s) Ks Ans: 1 s(s+ a) C(s)