For the unity feedback system shown in Figure P8.3, where

do the following:

a. Sketch the root locus.

b. Find the asymptotes.

c. Find the range of gain, K, that makes the system stable.

d. Find the breakaway points.

e. Find the value of K that yields a closed-loop step response with 25% overshoot.

f. Find the location of higher-order closed-loop poles when the system is operating with 25% overshoot.

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

h. Use MATLAB to obtain the closed-loop step response to validate or refute your second-order approximation.