P7.13 A unity feedback system has the loop transfer function

(a) Find the breakaway point on the real axis and the gain for this point.

(b) Find the gain to provide two complex roots nearest the jω-axis with a damping ratio

ζ = 0.6.

(c) Are the two roots of part

(b) dominant?

(d) Determine the settling time (with a 2% criterion)

of the system when the gain of part

(b) is used.

K L(s) = Ge(s)G(s) = s(s+1)(s+3s+12)