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SarkariResultOutBMS · 2024

Previous Year Question

A unity-feedback second order control system is characterised by G(s) = K/(Js2 + Bs) Which of the following transient response specification will be unaffected by the variation in parameter K?
  1. Damped natural frequency
  2. Maximum overshoot
  3. Rise time
  4. Settling time

Correct answer: D

Explanation

For the unity-feedback characteristic equation Js²+Bs+K=0, ωn=√(K/J) and ζ=B/(2√(JK)). Their product ζωn=B/(2J) is independent of K. Since the 2% settling time is approximately 4/(ζωn), settling time is unaffected by K.

Formula

Ts≈4/(ζωn)=8J/B

Step-by-step solution

Specification Unaffected by K explanatory diagram

Correct Answer

D — Settling time

Concept and Reasoning

For the unity-feedback characteristic equation Js²+Bs+K=0, ωn=√(K/J) and ζ=B/(2√(JK)). Their product ζωn=B/(2J) is independent of K. Since the 2% settling time is approximately 4/(ζωn), settling time is unaffected by K.

Calculation / Key Relation

Ts≈4/(ζωn)=8J/B

Exam Takeaway

Look for a specification depending on the product ζωn.

Common Mistake

Do not assume every transient specification changes when the loop gain changes.

Common mistake

Do not assume every transient specification changes when the loop gain changes.

Exam tip

Look for a specification depending on the product ζωn.

Quick method

Look for a specification depending on the product ζωn.