Q1) Plot the root locus for the following systems where thegiven transfer function is located in a unit negative feedbacksystem, i.e., the characteristic equation is 1+KG(s)=0. Whereapplicable, the plot should indicate the large gain asymptotes, theangle of departure from complex poles, the angle of arrival atcomplex zeros, and breakaway points. Verify your answer usingMATLAB (“rlocus” command) and show the results obtained fromMATLAB.
a) G(s) = (s + 4) (s + 2) 2 (s +1+ j4)(s +1? j4)
b) G(s) = 1 s(s + 2)(s 2 + 2s + 2)
c) G(s) = (s 2 + 25) s(s +1)(s + 2)
d) G(s) = 1 s(s 2 + 4s + 3)
e)Ă‚Â Ă‚Â G(s) = (s + 3) s 2 (s + 4)
f) G(s) = (s +1) s 2 (s + 2)
