Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2020
Hard
A closed-loop system has Gc=Kc, Gf=10/(0.1s+1), Gp=1/(0.1s+1)². For a gain margin of 1.6, the design value of Kc is (correct to 1 decimal place)
0.5(± 0.02 accepted)
Explanation
GOL=10Kc/(0.1s+1)³. Phase crossover: 3·arctan(0.1ωpc)=180° ⟹ arctan(0.1ωpc)=60° ⟹ 0.1ωpc=√3. |GOL(ωpc)|=10Kc/(√(1+3))³=10Kc/8=1.25Kc. GM=1/|GOL(ωpc)|=1/(1.25Kc)=1.6 ⟹ Kc=0.5.
Source: GATE CH 2020 (2020)
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