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
The closed loop transfer function of the system is
Correct answer
(C) (C(s))/(R(s)) = (K)/((s+1)(s+2)-K)
Solution
1.Open-loop poles: the plot marks points (open-loop poles) at and , and shows no open-loop zeros. So with (unity feedback).
2.Real-axis locus in the plot: the branches leave the poles outward, occupying and ; the segment between and is not on the locus.
3.Feedback type: for negative feedback (, ) a real-axis point is on the locus when the number of real poles and zeros to its right is odd; for positive feedback () when it is even.
- Right of : 0 poles (even) — on the locus.
- Between and : 1 pole (odd) — not on the locus.
- Left of : 2 poles (even) — on the locus.
4.Closed-loop transfer function:
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