Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2012
Hard
The characteristic equation for a system is s³+9s²+26s+12(2+Kc)=0. Using the Routh test, the value of Kc that will keep the system on the verge of instability is
- A20.9
- B18.4
- 17.5
- D15.3
Explanation
With c=12(2+Kc): Routh array's s¹ row = (9×26−1×c)/9=(234−c)/9. Verge of instability: 234−c=0 ⟹ c=234 ⟹ 12(2+Kc)=234 ⟹ 2+Kc=19.5 ⟹ Kc=17.5.
Source: GATE CH 2012 (2012)
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