GATE EC 2015 Set 1 — Question 30
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Control Systems → Stability Analysis → Root Locus Interpretation
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Question
A unity negative feedback system has the open-loop transfer function . The value of the gain at which the root locus crosses the imaginary axis is _______.
Correct answer
12 to 12
Solution
1.Characteristic Equation:
The characteristic equation is . For unity feedback, .2.Routh-Hurwitz Stability Criterion:
Construct the Routh array:- : 1, 3
- : 4, K
- :
- : K
The root locus crosses the imaginary axis when the system is marginally stable. This occurs when a row of the Routh array (usually the row) becomes zero.
Thus, the value of gain is 12.
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