Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2011
Hard
A PID controller output is p(t)=30+5e(t)+1.25∫₀ᵗe(t)dt+15de(t)/dt. The transfer function of the controller is
- A5(12s²+4s+1)/(3s)
- B5(12s²+3s+1)/(3s)
- 5(12s²+4s+1)/(4s)
- D5(12s²+3s+1)/(4s)
Explanation
Matching to standard PID p(t)=p̄+Kc[e+(1/τI)∫e dt+τD de/dt]: Kc=5, Kc/τI=1.25⟹τI=4, Kc·τD=15⟹τD=3. Gc(s)=Kc[1+1/(τIs)+τDs]=Kc(τIτDs²+τIs+1)/(τIs)=5(4×3×s²+4s+1)/(4s)=5(12s²+4s+1)/(4s).
Source: GATE CH 2011 (2011)
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