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For an under damped second order control system, if damping increases, the settling time :

  • A.Decreases
  • B.Remain Unaffected
  • C.Is proportional to square of damping
  • D.Increases

Answer: A

The settling time decreases.

For an underdamped second-order system the response settles within an envelope \(e^{-\zeta\omega_{n}t}\), and the settling time on the 2% criterion is about

\[ t_{s} \approx \frac{4}{\zeta\omega_{n}} \]

For a fixed natural frequency \(\omega_{n}\), a larger damping ratio \(\zeta\) makes the envelope decay faster, so \(t_{s}\) falls. It varies inversely with \(\zeta\), not with its square, and it is certainly affected by damping.

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