Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2014
Medium
A process with transfer function Gp=2/(s−1) is to be controlled by a feedback proportional controller with a gain Kc. If the transfer functions of all other elements in the control loop are unity, then which ONE of the following conditions produces a stable closed loop response?
- AKc = 0.25
- B0 < Kc < 0.25
- C0.25 < Kc < 0.5
- Kc > 0.5
Explanation
Closed loop characteristic equation: 1+Kc·Gp=0 ⟹ (s−1)+2Kc=0 ⟹ s=1−2Kc. For stability the pole must be negative: 1−2Kc<0 ⟹ Kc>0.5.
Source: GATE CH 2014 (2014)
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