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Which one of the following statements regarding ‘Root locus’ is not correct?

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  1. By the addition of poles to the left half, the root locus shifts towards the right-hand side, and the stability of the system decreases
  2. By addition of zero towards left, the root locus shifts towards left half, since root locus shifts towards left half, the relative stability of control system increases
  3. By the addition of zero towards the left side, the root locus shifts towards the left half, the relative stability remains the same
  4. By addition of poles to the left half, the system stability decreases, while by addition of zeros towards left half, the stability of system increases

Answer (Detailed Solution Below)

Option 3 : By the addition of zero towards the left side, the root locus shifts towards the left half, the relative stability remains the same
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Detailed Solution

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Effect of addition of zero to the system:

  • The angle of asymptotes increases and this root locus shift towards the left side of the s-plane slightly more
  • Breakaway point shifts towards the left in the s plane
  • The system becomes more stable i.e. less oscillatory
  • The range of ‘K’ value of stability increases
  • The relative stability increases

 

Effect of addition of pole to the system:

  • The angle of asymptotes decreases and this root locus shift towards the right side of the s-plane slightly more
  • Breakaway point shifts towards the right in the s plane
  • The system becomes less stable i.e. more oscillatory
  • The range of ‘K’ value of stability decreases
  • The relative stability decreases
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