Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2014
Hard
Consider a closed-loop feedback control system with Km=1.5, Gc=Kc, Gv=0.5, Gp=−2/s, Gd=−2/s, Gm=2. A proportional controller is being used with Kc=−4. If a step change in disturbance of magnitude 2 affects the system, then the magnitude of the offset is _____
0.5(± 0.02 accepted)
Explanation
Loop gain L=Gc·Gv·Gp·Gm=Kc×0.5×(−2/s)×2=−2Kc/s. With Kc=−4: L=8/s. C(s)/D(s)=Gd/(1+L)=(−2/s)/[(s+8)/s]=−2/(s+8). For a step D(s)=2/s: C(s)=−4/[s(s+8)]. Steady state C(∞)=lim(s→0) s·C(s)=−4/8=−0.5. Offset (magnitude, setpoint constant at 0) = |0−(−0.5)|=0.5.
Source: GATE CH 2014 (2014)
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