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Instrumentation & Process Control
Controller Modes
GATE 2009
Hard

The characteristic equation of a closed loop system using a proportional controller with gain Kc is 12s³+19s²+8s+1+Kc=0. At the onset of instability, the value of Kc is

  • 35/3
  • B10
  • C25/3
  • D20/3

Explanation

Routh array s¹ row=(19×8−12×(1+Kc))/19=(140−12Kc)/19. Onset of instability: 140−12Kc=0 ⟹ Kc=140/12=35/3.

Source: GATE CH 2009 (2009)

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