GATE EE 2025 Set 1 — Question 29
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Control Systems → Frequency Response & Root Locus → Root Locus Construction
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Question
The open-loop transfer function of the system shown in the figure, isFor , which of the following real axis point(s) is/are on the root locus?
Correct answer
(A) -1; (C) -6
Solution
The root locus exists on the real axis at points to the left of an odd number of open-loop poles and zeros.
Given , the open-loop singularities are:
(A) is in Yes.
(B) is in No.
(C) is in Yes.
(D) is in No.
Given , the open-loop singularities are:
- Zeros at and
- Poles at and
- Segment : 1 singularity to the right (odd) On Root Locus.
- Segment : 2 singularities to the right (even) Not on Root Locus.
- Segment : 3 singularities to the right (odd) On Root Locus.
- Segment : 4 singularities to the right (even) Not on Root Locus.
(A) is in Yes.
(B) is in No.
(C) is in Yes.
(D) is in No.
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