# A unity feedback second order control system is characterized by the open loop transfer function $\left( s \right) = \frac{K}{{s\left( {Js + B} \righ 0 votes 88 views closed A unity feedback second order control system is characterized by the open loop transfer function \(\left( s \right) = \frac{K}{{s\left( {Js + B} \right)}}$

J = moment of inertia, B = damping constant and K = system gain

The transient response specification which is not affected by system gain variation is
1. Peak overshoot
2. Rise time
3. Settling time
4. Time to peak overshoot

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Correct Answer - Option 3 : Settling time

The open-loop transfer function of a unity feedback 2nd order system is,

$G\left( s \right) = \frac{k}{{s\left( {Js + B} \right)}}\;$

Closed-loop transfer function:

$H\left( s \right) = \frac{k}{{s\left( {Js + B} \right) + k}}$

$H\left( s \right) = \frac{{k/J}}{{{s^2} + \frac{B}{J}s + \frac{k}{J}}}$

Now, compare it with the standard equation:

$H\left( s \right) = \frac{{{\omega _n}}}{{{s^2} + 2\xi {\omega _n}s + \omega _n^2}}$

Now, settling time

$= \frac{1}{{\xi {\omega _n}}} = \frac{1}{{\frac{B}{{2J}}}} = \frac{{2J}}{B}$

Hence only settling time is not affected by system gain k.