Question

Q1) Plot the root locus for the following systems where the given transfer function is located in a unit negative feedback system, i.e., the characteristic equation is 1+KG(s)=0. Where applicable, the plot should indicate the large gain asymptotes, the angle of departure from complex poles, the angle of arrival at complex zeros, and breakaway points. Verify your answer using MATLAB (“rlocus” command) and show the results obtained from MATLAB.

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)  G(s) = (s + 3) s 2 (s + 4)

f) G(s) = (s +1) s 2 (s + 2)

Answer 1