Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2015
Hard
Which transfer function, for a unit step change in disturbance at t=0, shows a STABLE response with a NEGATIVE initial slope?
- G(s)=1/(s+1)−2/(s+4)
- BG(s)=1/(s+1)+2/(s+4)
- CG(s)=1/(s+1)+2/(s−4)
- DG(s)=1/(s−1)+2/(s−4)
Explanation
Only option A has both poles stable (−1,−4). For a step input, y'(0+)=lim(s→∞)s²·G(s)/s=1−2=−1<0, a negative initial slope. Other options either have unstable poles (C,D) or a positive initial slope (B: 1+2=3).
Source: GATE CH 2015 (2015)
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