Question 2 (25 marks) Consider the feedback system shown in Figure 2.1. Here K(s) is the transfer function of a compensa

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Question 2 25 Marks Consider The Feedback System Shown In Figure 2 1 Here K S Is The Transfer Function Of A Compensa 1 (375.47 KiB) Viewed 36 times

Question 2 (25 marks) Consider the feedback system shown in Figure 2.1. Here K(s) is the transfer function of a compensator while G(s) is a stable transfer function with no finite zeros. An experiment is conducted that produces the frequency response shown in Figure 2.2. The low-frequency magnitude is observed to be approximately 5.7 dB, and the high-frequency phase lag is observed to be 270 degrees. The poles of this system are known to be repeated. i) iii) iv) v) magnitude punagો Use the frequency response (Figure 2.2) to sketch a Nyquist diagram of G(s) indicating the low- and high-frequency portions and the real-axis intercepts. Give an approximate value for the cross over point. [5 marks.] Determine, approximately, the transfer function of G(s). [5 marks.] State the Nyquist stability criterion. [3 marks.] Use the Nyquist stability criterion to determine the number of unstable closed- loop poles when 5.7JB- Phase a. K(s) = 1 [2 marks.] b. K(s) = 10 [2 marks.] Let K(s) = K₂ + Use your analytical skills and knowledge of Nyquist diagrams to explore the effects of K(s) on the performance and stability of the feedback loop. [8 marks.] 20 -40 180 10 -180 -270 -360 X (s) 16-2 + LOTI K(s) Figure 2.1 Frequency d/s) 11000 Frequency rad/s G(s) Figure 2.2 ID' Y(s)