Given the unity feedback system of Figure P9.1, with

do the following:

a. Sketch the root locus.

b. Find the coordinates of the dominant poles for which ζ = 0.8.

c. Find the gain for which ζ = 0.8.

d. If the system is to be cascade-compensated so that T_s = 1 second and ζ = 0.8, find the compensator pole if the compensator zero is at -4.5.

e. Discuss the validity of your second-order approximation.

f. Use MATLAB or any other computer program to simulate the compensated and uncompensated systems and compare the results to
those expected.

K(s + 6) G(s) (s +3(s +4)(s+ 7)(s +9)