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GATE 2021 BM – Question 33

Measurements and Control Systems · Control System Transfer Functions · 1 mark · Numerical answer

For a type-2 unity-feedback system, the extrapolated initial −40 dB/decade Bode segment crosses 0 dB at 2 rad/s. Find acceleration error constant Kₐ.

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Correct answer: 4 to 4

Explanation

At low frequency, a type-two open-loop transfer function has magnitude approximately Kₐ/ω². At the extrapolated zero-decibel crossing this magnitude equals one. Therefore Kₐ/(2²)=1, so Kₐ=4. The specified slope is the signature of two integrators.

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