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SarkariResultOutBMS · 2024

Previous Year Question

The loop transfer function G(s)H(s) of a unity feedback system is given by G(s) H(s) = (s + 2) / ((s + 4) (s + 5) (s + 6)). How many branches of root locus will tend towards infinity?
  1. 0
  2. 1
  3. 2
  4. 3

Correct answer: C

Explanation

A root locus has one branch for each open-loop pole. The number of branches that terminate at infinity equals the number of poles minus the number of finite zeros. Here there are 3 poles and 1 zero, so 2 branches go to infinity.

Formula

Number of asymptotes = P−Z = 3−1 = 2

Step-by-step solution

Branches Tending to Infinity explanatory diagram

Correct Answer

C — 2

Concept and Reasoning

A root locus has one branch for each open-loop pole. The number of branches that terminate at infinity equals the number of poles minus the number of finite zeros. Here there are 3 poles and 1 zero, so 2 branches go to infinity.

Calculation / Key Relation

P=3

Z=1

Branches to infinity=P−Z=2

Exam Takeaway

Count poles and finite zeros before drawing the locus.

Common Mistake

Do not count the finite zero as an asymptote endpoint at infinity.

Common mistake

Do not count the finite zero as an asymptote endpoint at infinity.

Exam tip

Count poles and finite zeros before drawing the locus.

Quick method

Count poles and finite zeros before drawing the locus.