The close-loop transfer function of a control system is

The close-loop transfer function of a control system is given by
C(s) = 1
R(s) 1 + s
For the input r (t) = sin t, the steady state value of C(t) is equal to—

Given

C(s)	=	1
R(s)	=	1 + s

r (t) = sin t
In order to calculate the C(t), we will calculate the magnitude and phase by the term 1/(1 + s)

Mag. of		1		=	1	=	1
		1 + s			√1 + 1		√2

Phase of		1		= - tan^-1		1		=	–π
		1 + s				1			4

so,

C(t) =	1	sin		t -	π
	√2				4

1	cos t
√2