Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2015
Hard
A feedback control block diagram: Gc(s)=0.5s, Gf(s)=0.2/(1.5s+1), Gp(s)=1/(0.5s), Gm(s)=1. A unit step change is made in the setpoint at t=0. The time (min) for h to reach 50% of its ultimate value, rounded to 2 decimal places, is
0.87 min(± 0.03 accepted)
Explanation
Gc·Gf·Gp=0.5s×0.2/(1.5s+1)×1/(0.5s)=0.2/(1.5s+1) (the 0.5s terms cancel). Closed loop=0.2/(1.5s+1.2)=(1/6)/(1.25s+1), a first-order system with τ=1.25min. Time to 50%: t=τln2=1.25×0.693=0.87min.
Source: GATE CH 2015 (2015)
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