PROBLEM: Given a unity feedback system that has the forward-path transfer function
G(s)=\frac{K}{(s+2)(s+4)(s+6)}do the following:
a. Sketch the root locus.
b. Using a second-order approximation, design the value of K to yield 10% overshoot for a unit-step input.
c. Estimate the settling time, peak time, rise time, and steady-state error for the value of K designed in (b).
d. Determine the validity of your second-order approximation.