A transfer function G (s) has the pole-zero plot as shown

A transfer function G (s) has the pole-zero plot as shown in the given figure. Given that the steady state is 2, the transfer function G (s) will be given by—

Here, there are 2 pole and 1 zero. Let the transfer function G(s) of the type

G(s) =	K(s + 1)
	(s + 2 + j)(s + 2 – j)

G(s) =	K(s + 1)	=	K(s + 1)
	(s + 2)² – j²		s² + 4s + 5

Also given that steady state gain is 2. i.e.,

G(0) = 2 =	K(0 + 1)
	0² + 4·0 + 5

or
K = 10
Now, the

T.F. G(s) =	10(s + 1)
	0² + 4s + 5