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GATE 2014 EC (EC3) – Question 58

Control Systems · Bode and Root-Locus Plots · 2 marks · Multiple choice

The root-locus plot has its pole/zero marks and arrows removed. Which transfer function corresponds to it?

Diagram for GATE 2014 EC (EC3) question 58
  1. $(s+1)/((s+2)(s+4)(s+7))$
  2. $(s+4)/((s+1)(s+2)(s+7))$
  3. $(s+7)/((s+1)(s+2)(s+4))$
  4. $(s+1)(s+2)/((s+7)(s+4))$

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Show answer and explanation

Correct answer: (B) $(s+4)/((s+1)(s+2)(s+7))$

Explanation

The real-axis branches occupy intervals−7to−4and−2to−1. The two branches leaving between−2and−1approach vertical asymptotes with centroid−3. For **(s+4)/[(s+1)(s+2)(s+7)],B**, poles are−1,−2,−7and the zero is−4; centroid=[−1−2−7−(−4)]/2=−3. A has the same real-axis intervals but centroid−6.