GATE EC 2022 Set 1 — Question 22
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Control Systems → Stability Analysis → Root Locus Interpretation
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Question
The root-locus plot of a closed-loop system with unity negative feedback and transfer function in the forward path is shown in the figure. Note that is varied from 0 to .
Select the transfer function that results in the root-locus plot of the closed-loop system as shown in the figure.
Correct answer
(A) G(s) = (1)/((s + 1)⁵)
Solution
The root-locus plot shows 5 branches going to infinity, which implies that the number of poles minus the number of zeros is . The asymptotes intersect at a centroid . The angles of the asymptotes are . For option (A), , we have poles at and zeros. Thus, . The centroid is calculated as:The angles of the asymptotes are:This matches the provided root-locus plot perfectly. Other options result in different centroids or branch counts.
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