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(a) A control system is modelled by the transfer function G(s) +5 (1) Find its analytical expressions of both magnitude frequency response and phase frequency response. (li) Let Gz(s) = Ks where K is a positive gain. Using the results obtained in (). determine the analytical expressions of both the magnitude and phase frequency responses of G; ()G2(s). Then briefly discuss how the value of K affects the magnitude and phase frequency responses of G; (5)2(s). respectively. [8 marks) (b) The Bode plot of an open-loop transfer function of a unity feedback system is given in Figure 3.1. Estimate both the gain margin and phase margin. Then, determine the corresponding closed-loop system stability [4 marks) Bode plot of the open loop 20 Magnitude dB) $ -20 40 -60 -BO - 120 -150 -180 210 -240 -270 102 19 10 10 Frequency rad's) Figure 3.1