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Question

The Closed loop transfer function of a control system is given by C(s)R(s)=1s+1. For the input r(t) = sin t, the steady response c(t)______.

A
12cost
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B
12sin(t+π4)
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C
1
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D
12sin(tπ4)
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Solution

The correct option is D 12sin(tπ4)
Transfer function=1s+1=G(s)

G(jω)=1jω+1=1ω2+1tan1ω

Input=1Asin((1ω)t+0oϕ1)

Output=B sin(ωt+ϕ2)

where
B=A|G(jω)|=1×11+1=12

and ϕ2=ϕ1+G(jω)=tan11
=45o

Steady state o/p
=12sin(tπ4)

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