GATE EE 2014 Set 1 — Question 54
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Control Systems → Stability Analysis → Routh-Hurwitz Criterion
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Question
For the given system, it is desired that the system be stable. The minimum value of for this condition is _______________.
Correct answer
0.61 to 0.63
Solution
The characteristic equation of the closed-loop system is . With :Applying the Routh-Hurwitz stability criterion:
For stability, all elements in the first column must be positive:
For and , we must have .Thus, the minimum value of is approximately 0.618.
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The roots of are .For and , we must have .Thus, the minimum value of is approximately 0.618.
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