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Instrumentation & Process Control
Controller Modes
GATE 2009
Hard

For a tank of cross-sectional area 100cm² with inlet flow rate Qi (cm³/s) and outlet flow rate Qo=3√H (H = liquid height in cm), the transfer function H̄(s)/Q̄i(s) (deviation variables) of the process around the steady state point Qi,s=18cm³/s, Hs=36cm, is

  • A1/(100s+1)
  • B2/(200s+1)
  • C3/(300s+1)
  • 4/(400s+1)

Explanation

Linearizing Qo=3√H at Hs=36: dQo/dH=3/(2√36)=0.25=1/R, so R=4 (resistance). A·dH'/dt=Qi'−H'/R ⟹ τ=A·R=100×4=400. Transfer function: R/(τs+1)=4/(400s+1).

Source: GATE CH 2009 (2009)

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