GATE EE 2014 Set 3 — Question 28
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Control Systems → Stability Analysis → Nyquist Criterion
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Question
A single-input single-output feedback system has forward transfer function and feedback transfer function . It is given that . Which of the following is true about the stability of the system?
Correct answer
(A) The system is always stable
Solution
The characteristic equation of the feedback system is given by . For the system to be stable, all roots of this equation (closed-loop poles) must lie in the left half of the -plane. Given the condition for all in the right half plane (including the axis):
1.The term can never be zero in the right half plane because is strictly less than 1, so can never equal . This implies there are no closed-loop poles in the right half plane.
2.Furthermore, the condition implies that the open-loop transfer function cannot have any poles in the right half plane, as the magnitude would be infinite at a pole.
Since there are no open-loop poles in the right half plane and no closed-loop poles in the right half plane, the system is always stable. Thus, option (A) is correct.Continue learning with Success Tracker
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