A unity feedback control system has a forward path transfer

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A unity feedback control system has a forward path transfer function equal to 42·25/s(s + 6·5) The unit step response of this system starting from rest, will have its maximum value at a time equal to—

1. 0 sec
2. 0.56 sec
3. 5.6 sec
4. infinity

Correct Option: D

Given	C(s)	=	42·25
	R(s)		s(s + 6·5)

If r(t) = u(t)
then
R(s) = 1/s
and

C(s) = R(s)·	42·25
	s(s + 6·25)

C(s) =	1	×	42·25
	s²		s(s + 6·25)

C(s) =	A	+	B	+	C
	s		s²		s + 0·6s

C(s) =	– 1	+	6·5	+	1
	s		s²		(s + 6·5)

(by using partial fractions) By taking inverse Laplace transform
C(t) = – u(t) + tu(t) + e^–6·5t
response at steady state means C(t) as t → ∞
i.e., C(t) = ∞
Hence alternative (D) is the correct choice.