Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2017
Hard
The characteristic equation of a closed-loop system is 6s³+11s²+6s+(1+K)=0, K>0. The value of K beyond which the system just becomes unstable, rounded to nearest integer, is
10
Explanation
Routh array s¹ row: [11×6−6(1+K)]/11=(60−6K)/11. Marginal stability at (60−6K)=0 ⟹ K=10.
Source: GATE CH 2017 (2017)
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