Discussion
Sketch the root locus for K ≥ 0 in the equation 1+ KL(s) = 0 and the listed choices for L(s). Clearly show your steps in order to receive credits. Also, analytically determine the value of K when the root locus cross the imaginary axis (if applicable) for each case. You should hand sketch the root locus but you may check your work with MATLAB.
a. L(s) = 1 / [s (s + 4) (s + 7)]
b. L(s) = 1 / [s (s2 +3s + 7)]
c. L(s) = (s + 3) / [s (s + 2) (s +6)]