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Given a system represented by equations
x = - 
0 1 
x + 0 u and y = [1 0]x -2 -3 1
The equivalent transfer function representation G(s) of the system is—
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G(s) = 1 s2 + 5s + 2
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G(s) = 1 s2 + 3s + 2
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G(s) = 3 s2 + 3s + 2
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G(s) = 2 s3 + 3s2 + 2
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Correct Option: B
Given equation
| x = | | | x + | | 0 | | ||
| -2 | -3 | 1 |
Y = [1 , 0]x
Here,
| x = | | | and Y = | | y1 | | |
| x2 | y2 |
However from the output expression it is seen that only y1 exists i.e.,
y1 = x2 …(i)
Also,
x1 = x2 …(ii)
x2 = – 2x1 – 3x2 + u …(iii)
from equations (ii) and (iii)
x1 = – 2x1 – 3x1 + u …(iv)
By taking Laplace transform of eqn. (iv), we get
s2 x1 (s) = – 2x11or
(s2 + 3s + 2) x1 (x) = u (s)
or
| = | ||
| u(s) | s2 + 3s + 2 |
or
| G(s) = | |
| s2 + 3s + 2 |
