GATE 2020 CH – Question 33

Instrumentation and Process Control · Process modelling, transfer functions and dynamic response · 1 mark · Numerical answer

A negative unity-feedback loop has controller $G_c=0.2[1+1/(0.5s)]$ and process $G_p=10/[(s+1)(2s+1)]$ as shown. For a unit step in setpoint yₛₚ, find the steady-state output change y, to one decimal place.

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Correct answer: 0.9 to 1.1

Explanation

The controller includes integral action, so its DC gain is infinite. The characteristic polynomial is $s(s+1)(2s+1)+2s+4=2s^3+3s^2+3s+4$, whose Routh first column is positive, confirming stability. Thus the type-one loop has zero steady step error. The final output change equals the unit setpoint change, y = 1.0.

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