If the open-loop transfer function of the system is G(s)

If the open-loop transfer function of the system is
G(s) H(s) = K(s + 10)
s(s + 8) (s + 16) (s + 72)

then a closed loop pole will be located at s = –14, when the value of K is—

Here the value of K can be obtained by

\|K\| =		All the poles of G(s) H(s)	⎪_{at s = – 14}
		All the zeros of G(s) H(s)

\|K\| =		s(s + 8) (s + 16) (s + 72)
		(s + 10)

\|K\| =		– 14 (– 14 + 8) (– 14 + 16) (– 14 + 72)
		(– 14 + 10)

\|K\| =		– 14 × – 6 × 2 × 58
		– 4

or
K = |– 2436| = 2436