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(a) A control system is modelled by the transfer function G(S) 5 +5 (0) Find its analytical expressions of both magnitude frequency response and phase frequency response. (1) Let G (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;(s)G(s). Then, briefly discuss how the value of K affects the magnitude and phase frequency responses of G, (),(s), respectively [8 marks] (b) The Bode piot 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 doop 20 Magnitude 108 -20 10 -50 -80 -120 (oplo 150 .180 -210 -240 270 100 10+ 10 10 Frequency rad's) Figure 3.1