Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2010
Hard
A block diagram has R(s)→0.2→[sum +/−]→Gc=2(1+0.2s)/(1+0.02s)→Gp=2/(s²+11s+1)→Y(s), with unity-scaled feedback of 0.2 from Y(s) to the summing junction. The steady state gain of the closed loop system, between output Y(s) and set point R(s), is
- A5/9
- 4/9
- C1/3
- D2/9
Explanation
At s=0: Gc(0)=2, Gp(0)=2, so the forward-path steady-state gain (from the summer to Y) is Gc(0)Gp(0)=4. Y/R=(0.2×4)/(1+4×0.2)=0.8/1.8=4/9.
Source: GATE CH 2010 (2010)
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