The open-loop transfer function of a unity-feedback control system is G(s) = K/[s(s + 1)]. If the gain K is increased to infinity, then the damping ratio of the closed-loop system will tend to become
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Answer & Explanation
Correct AnswerC. 0
Quick Explanation
The closed-loop characteristic equation is s²+s+K=0. Comparing with s²+2ζωn s+ωn²=0 gives ωn=√K and ζ=1/(2√K). Therefore ζ tends to zero as K tends to infinity.
Formula / Key Relation
ζ=1/(2√K) → 0 as K→∞
Detailed Explanation
Correct Answer
C — 0
Concept and Reasoning
The closed-loop characteristic equation is s²+s+K=0. Comparing with s²+2ζωn s+ωn²=0 gives ωn=√K and ζ=1/(2√K). Therefore ζ tends to zero as K tends to infinity.
Calculation / Key Relation
ζ=1/(2√K) → 0 as K→∞
Exam Takeaway
Compare coefficients with the standard second-order form.
Common Mistake
Increasing gain does not always increase damping.
Quick Trick
Compare coefficients with the standard second-order form.
Common Mistake
Increasing gain does not always increase damping.
Exam Tip
Compare coefficients with the standard second-order form.
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