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Question

For the system governed by the set of equation:
dx1dt=2x1+x2+u
dx2dt=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)(s22s+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

sX12X1+2X1s=Us+U

X1(s2+2s)=U(1+1s)

X1U=(1+1/s)(s2+2/s)

YU=3X1U=3(1+1/s)(s2+2/s)

YU=3(s+1)(s22s+2)

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