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GATE 2026 CH – Question 25

Instrumentation and Process Control · Process modelling, transfer functions and dynamic response · 1 mark · Multiple select

A process exhibits an inverse response to a step input. Which of the following statements is/are necessarily TRUE about the process?

  1. Its transfer function has a positive zero.
  2. Its transfer function has a negative zero.
  3. The initial direction of the step response is opposite to the final steady state value.
  4. The system is unstable due to a zero in the right half of the s-plane.

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Show answer and explanation

Correct answer: (A) Its transfer function has a positive zero.; (C) The initial direction of the step response is opposite to the final steady state value.

Explanation

An inverse response (non-minimum phase behaviour) occurs when the transfer function has a zero in the right half plane, that is a positive zero, and the response first moves in the direction opposite to its final value. A right half plane zero does not make a system unstable, because stability depends on the poles, so statement D is false. A negative zero does not give an inverse response, so B is false.