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Question 1 (a) Figure 1 shows a block diagram of a unity feedback system. RU) EG) C(₂) K (3²+38+30) (5+5) Figure 1: A block diagram of a unity leedback system i Il the system has 1/6000 error for an input of 10 ku(t), determine the value of K and n to meet the specification. (4 marks, C3) ā. With the value of K and in obtained in Question (a)i, determine the value of K, K, and (3 marks, C3) R. Obtain the steady state error for the input of Su(t), 15tu(t) and 25fu(t). (3 marks, C3) Figure 2 shows a block diagram of a unity feedback system. Find the number of closed- loop poles located in the right hall-plane, lelt hall-plane, and on the jo-axis by using Routh-Hurwitz criterion. Conclude the system stability. (10 marks, C4) 4 R(S) C(s) 3x² +6x²-5x 10+14 Figure 2: A block diagram of a unity feedback system.

Question 2 (a) Consider a unity feedback system as shown in Figure 3. 315 R(s) K sis+ 4s +8s +100) C(s) Figure 3: A unity feedback system Plot the asymptotic Bode plot for the system it X 500. From the plot, determine the gain margin (GM), phase margin (M), gain cross over frequency (w), phase cross over Irequency (w), and hence state and justify the stability of the system. (10 marks, C4) An open loop transfer function of a unity feedback system is given by GOK s-65 +115+6 i. Sketch the Nyquist diagram for (0<<x) for = 1 ii. Determine the range of K for stability. Determine the frequency of oscillation for marginally stable (b) iii. (7 marks, C4) (2 mark (1 man

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