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What will be the closed loop transfer function of a unity feedback control system whose step response is given by C (t) = K [1 – 1.66e–8t sin (6t + 37º)]
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- 100K/s2 + 16s + 100
- 10/.s2 + 16s + 100
- K/s2 + 16s + 100
- 10K/s2 + 8s + 10
- 100K/s2 + 16s + 100
Correct Option: A
Given, C(t) = K [1 – 1·66e-8t sin (6t + 37°)] …(i)
The standard equation of C (t) is given as C (t) = 1 – sin 
ωn√1 -ξ2 
t + tan–1√1 - ξ2/ξ2 
√1 -ξ2
on comparing equation (i) with standard equation
tan–1√1 - ξ2/ξ = 37°
or
tan 37° = √1 - ξ2/ξ
or
.754 = √1 - ξ2/ξ2,/sup>
·568 ξ2 = 1 – ξ2
or
ξ = √1/1·568
or
ξ = ·798 ≈ ·8
and ωn = 8
or ωn = 8/ξ = 8/·8 = 10
Now, the required relation of transfer function = K R(s) s2 + 2ξ ωns + ω2n
or = R(s) s2 + 16s + 100
Hence alternative (A) is correct choice.
