GATE EC 2020 Set 1 — Question 50
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Control Systems → Stability Analysis → Root Locus Interpretation
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Question
The characteristic equation of a system is In the root locus plot for the given system, as varies from 0 to , the break-away or break-in point(s) lie within
Correct answer
(A) (-1, 0)
Solution
The characteristic equation is .
Rearranging for :
Break-away/break-in points occur where :
Let .
Since and , by the Intermediate Value Theorem, there is at least one root in the interval . This root corresponds to a break-away or break-in point.
Rearranging for :
Break-away/break-in points occur where :
Let .
Since and , by the Intermediate Value Theorem, there is at least one root in the interval . This root corresponds to a break-away or break-in point.
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