Transfer function of a first order system is given byGs-1Ts-1Impulse response of the system is

nbsp; nbsp; nbsp; nbsp; nbsp; G(s)=1(Ts+1) Given that, nbsp; nbsp; nbsp;R(s)=1 nbsp; nbsp; nbsp; nbsp; nbsp; C(s)=R(s).G ...

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Control Systems

Step Response of First Order System

Transfer func...

Question

Transfer function of a first order system is given by $G (s) = \frac{1}{T s + 1}$

Impulse response of the system is

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Solution

The correct option is C
$G (s) = \frac{1}{(T s + 1)}$

Given that, $R (s) = 1$

$C (s) = R (s) . G (s)$

$C (s) = \frac{1}{(T s + 1)} = \frac{1}{T (s + \frac{1}{T})}$
Taking inverse Laplace transform of above equation, we get

$C (t) = \frac{1}{T} e^{- t / T}$

$A t, t = 0, C (t) = \frac{1}{T}$

$t = \infty, C (t) = 0$

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Transfer function of a first order system is given byG(s)=1Ts+1 Impulse response of the system is

The correct option is C G(s)=1(Ts+1) Given that, R(s)=1 C(s)=R(s).G(s) C(s)=1(Ts+1)=1T(s+1T) Taking inverse Laplace transform of above equation, we get C(t)=1Te−t/T At,t=0,C(t)=1T t=∞,C(t)=0

Transfer function of a first order system is given by $G (s) = \frac{1}{T s + 1}$

Impulse response of the system is