GATE EC 2025 Set 1 — Question 26
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Control Systems → Stability Analysis → Root Locus Interpretation
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Question
Consider the unity-negative-feedback system shown in Figure (i) below, where gain . The root locus of this system is shown in Figure (ii) below. For what value(s) of will the system in Figure (i) have a pole at ?
Correct answer
(C) For no positive value of K
Solution
From Figure (ii), the open-loop poles are at and the open-loop zeros at , so(up to a positive constant absorbed in ).Angle condition at (needed for to be a closed-loop pole for some ):
- zeros: , ; sum
- poles: , ; sum
- (A) and (B) : neither places a pole at .
- (D): clearly false.
- (C): correct.
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