GATE EE 2014 Set 1 — Question 28
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Control Systems → Frequency Response & Root Locus → Root Locus Construction
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Question
The root locus of a unity feedback system is shown in the figure
Correct answer
(C) (C(s))/(R(s)) = (K)/((s+1)(s+2)-K)
Solution
1.Identify Open-Loop Poles: From the root locus plot, the open-loop poles are at and .
2.Analyze Root Locus on the Real Axis: The root locus exists on the real axis in the regions and .
3.Determine Feedback Type: For a unity feedback system, the root locus exists on the real axis where the number of open-loop poles and zeros to the right is even for positive feedback () and odd for negative feedback ().
- To the right of , there are 0 poles (even) Locus exists (Positive Feedback).
- Between and , there is 1 pole (odd) No locus.
- To the left of , there are 2 poles (even) Locus exists (Positive Feedback).
5.Calculate Closed-Loop Transfer Function:
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