Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2011
Hard
For the PID controller Gc(s)=5(12s²+4s+1)/(4s) and process Gp(s)=10/(200s+1), the characteristic equation of the closed loop is
- A6s²+102s+1=0
- 700s²+102s+25=0
- C100s²−196s−25=0
- D240s³+812s²+204s+1=0
Explanation
1+GcGp=0 ⟹ 4s(200s+1)+50(12s²+4s+1)=0 ⟹ 800s²+4s+600s²+200s+50=0 ⟹ 1400s²+204s+50=0, dividing by 2: 700s²+102s+25=0.
Source: GATE CH 2011 (2011)
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