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
The root locus exists on the real axis to the left of an odd number of poles and zeros. From the figure, the root locus segments on the real axis are between and , and between and .Let's check the options:
(A) Zeros: ; Poles: . Real axis segments: and .
(B) Zeros: ; Poles: . Real axis segments: and .
(C) Zeros: ; Poles: . Real axis segments: and .All three options have the same real axis segments. However, the plot shows a breakaway point between and (which must be between two poles) and a break-in point between and .
In option (B), poles are at and , allowing for a breakaway point. There is a zero at and a pole at , and the branch starting at the pole moves towards the zero at . The complex branches from the breakaway point return to the real axis at a break-in point between and . This configuration matches the provided root locus plot.
(A) Zeros: ; Poles: . Real axis segments: and .
(B) Zeros: ; Poles: . Real axis segments: and .
(C) Zeros: ; Poles: . Real axis segments: and .All three options have the same real axis segments. However, the plot shows a breakaway point between and (which must be between two poles) and a break-in point between and .
In option (B), poles are at and , allowing for a breakaway point. There is a zero at and a pole at , and the branch starting at the pole moves towards the zero at . The complex branches from the breakaway point return to the real axis at a break-in point between and . This configuration matches the provided root locus plot.
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