Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2019
Hard
Two non-interacting gravity-drained tanks in series: inflow q to Tank 1, draining to Tank 2 at k√h1, Tank 2 draining at k√h2. k=4 cm^2.5/s, A1=A2=28 cm². At steady state, q_ss=16 cm³/s. The transfer function relating deviation variables h̃2 (cm) to q̃ (cm³/s) is
- 2/(56s+1)²
- B2/(62s+1)²
- C2/(36s+1)²
- D2/(49s+1)²
Explanation
At steady state: h1,ss=(qss/k)²=16cm, and similarly h2,ss=16cm. Linearized resistance R=2√h_ss/k=2×4/4=2 (same for both tanks). Time constants τ1=τ2=R·A=2×28=56s. Non-interacting tanks in series: H2(s)/Q(s)=R/[(τ1s+1)(τ2s+1)]=2/(56s+1)².
Source: GATE CH 2019 (2019)
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