GATE EC 2017 Set 1 — Question 47
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Control Systems → Stability Analysis → Root Locus Interpretation
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Question
A linear time invariant (LTI) system with the transfer functionis connected in unity feedback configuration as shown in the figure.
For the closed loop system shown, the root locus for intersects the imaginary axis for . The closed loop system is stable for
Correct answer
(A) K 1.5
Solution
To determine the stability of the closed-loop system, we first find the characteristic equation:Substituting the given transfer function :For a second-order system to be stable, all coefficients must have the same sign. Assuming :
1.
2.
3.
Combining these conditions for , the system is stable when . At , the coefficient becomes zero, and the roots lie on the imaginary axis, which is consistent with the problem statement.Continue learning with Success Tracker
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