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(1) Please answer the following questions: (a) Root loci are usually plotted for variations in the gain. Sometimes we are interested in the variation of the closed-loop poles as other parameters are changed. Consider a unity feedback system with the following forward transfer function ds +8) 1015t Stadt G(s)=- 10(s+a) s(s+1)(s+8) SASNE
(f) A unity feedback system has open-loop transfer function G(s). Bode plot of Gjo) is shown below. The feedback system has: positive or negative phase margin (PM). positive or negative gain margin (GM) - please circle the correct answer (4 points) 19 -180 (g) A unity feedback system has open-loop transfer function G(s). Polar plot of Gje) is shown below. Find thee gain margin (GM) and the phase margin (PM) of the system. PM= (6 points) GM- 0.3 (h) The Nyquist plot of the following loop transfer function is given below for some gain K. Assume T, >0, i=1, 2, 3, 4, 5. K(s+T) (8 points) G(s) (s+T,Xs+T,Xs+T,Xs+T) OC