GATE EC 2014 Set 3 — Question 58
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Control Systems → Stability Analysis → Root Locus Interpretation
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Question
In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?
Correct answer
(B) (s+4)/((s+1)(s+2)(s+7))
Solution
From the figure the marked real-axis points are at about ; the real-axis locus is the segment and the thick segment ; the branches leaving break away and bend into two vertical asymptotes at .All four options give the same real-axis segments, so use the other features:
- Breakaway between and requires both to be poles (or both zeros for a break-in). In (A) is a zero and a pole, so the locus on just runs from pole to zero with no breakaway. (A) is out.
- (D) has two poles and two zeros, so there are no asymptotes; the locus cannot go to infinity. Out.
- (C): poles , zero : , centroid , so the asymptotes would be the axis, not . Out.
- (B): poles , zero : the branches from and break away and follow asymptotes at with centroid , and the branch from goes to the zero at along the thick segment. This matches the plot.
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