Project ForgeInstrumentation & Process Control
Controller Modes
GATE 2019
Hard
For a closed-loop system with Kc=5 and Gp=e^(−0.1s)/(0.5s+1) (unity feedback), the phase margin (degrees) is (rounded off to one decimal place)
45.4 °(± 0.3 accepted)
Explanation
Gain crossover: 5/√(1+(0.5ω)²)=1 ⟹ ω=9.798 rad/time. Phase at ωgc=−0.1×9.798×(180/π)−arctan(0.5×9.798)=−56.14°−78.44°=−134.58°. Phase margin=180−134.58=45.4°.
Source: GATE CH 2019 (2019)
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