The unit impulse response of a unit feedback control system is given by- ct-te-t-2e-t-t- 0 the open loop transfer funciton is equal to

Close loop T.F = Limpulse response =L( te^ t+2e^ t)= 1(s+1)^2+2(s+1) C.L.T.F=2s+1(s+1)^2 ∵ C.L.T.F=O.L.T.F1+O.L.T.F nbsp; for unity feedback i.e.,C.L.T.F=G ...

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Control Systems

Review on Laplace Transform-2

The unit impu...

Question

The unit impulse response of a unit feedback control system is given by: $c (t) = - t e^{- t} + 2 e^{- t}, (t \geq 0)$ the open loop transfer funciton is equal to

\frac{s + 1}{(s + 2)^{2}}

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\frac{2 s + 1}{s^{2}}

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\frac{s + 1}{(s + 1)^{2}}

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\frac{s + 1}{s^{2}}

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Solution

The correct option is B $\frac{2 s + 1}{s^{2}}$
Close loop T.F = $L$ {impulse response}
$= L (- t e^{- t} + 2 e^{- t}) = \frac{- 1}{(s + 1)^{2}} + \frac{2}{(s + 1)}$

$C . L . T . F = \frac{2 s + 1}{(s + 1)^{2}}$

$∵ C . L . T . F = \frac{O . L . T . F}{1 + O . L . T . F}$ for unity feedback

$i . e ., C . L . T . F = \frac{G (s)}{1 + G (s)} |_{H (s) = 1}$

$∴ G (s) = \frac{C . L . T . F}{1 - C . L . T . F} |_{H (s) = 1}$

On putting the value of C.L.T.F
We get,
$G (s) = \frac{2 s + 1}{s^{2}}$

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The unit impulse response of a unit feedback control system is given by: c(t)=−te−t+2e−t,(t≥0) the open loop transfer funciton is equal to

The correct option is B 2s+1s2Close loop T.F = L{impulse response} =L(−te−t+2e−t)=−1(s+1)2+2(s+1) C.L.T.F=2s+1(s+1)2 ∵C.L.T.F=O.L.T.F1+O.L.T.F for unity feedback i.e.,C.L.T.F=G(s)1+G(s)|H(s)=1 ∴G(s)=C.L.T.F1−C.L.T.F|H(s)=1 On putting the value of C.L.T.F We get, G(s)=2s+1s2

The unit impulse response of a unit feedback control system is given by: $c (t) = - t e^{- t} + 2 e^{- t}, (t \geq 0)$ the open loop transfer funciton is equal to