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Question

# For the system governed by the set of equation: dx1dt=2x1+x2+u dx2dt=âˆ’2x1+u y=3x1 The transfer function Y(s)U(s) is given by

A
3(s+1)(s22s+2)
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B
3(2s+1)(s22s+1)
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C
(s+1)(s22s+1)
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D
3(2s+1)(s22s+2)
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Solution

## The correct option is A 3(s+1)(s2−2s+2)dx1dt=2x1+x2+u .....(i) dx2dt=−2x1+u ....(ii) On applying Laplace transform for equation (i), sX1=2X1+X2+U ...(iii) On applying Laplace transform for equation (ii), sX2=−2X1+U X2=(−2X1+Us) substitute X2 in equation (iii) sX1=2X1+(−2X1+Us)+U sX1−2X1+2X1s=Us+U X1(s−2+2s)=U(1+1s) X1U=(1+1/s)(s−2+2/s) ⇒YU=3X1U=3(1+1/s)(s−2+2/s) ⇒YU=3(s+1)(s2−2s+2)

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