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GATE 2021 CH – Question 42

Instrumentation and Process Control · Closed-loop stability and frequency response · 2 marks · Multiple choice

Which of the following is NOT a necessary condition for a process under closed-loop control to be stable?

  1. Dead-time term(s) must be absent in the open-loop transfer function
  2. Roots of the characteristic equation must have negative real part
  3. All the elements in the left (first) column of the Routh array must have the same sign
  4. Open-loop transfer function must have an amplitude ratio less than 1 at the critical frequency

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Correct answer: (A) Dead-time term(s) must be absent in the open-loop transfer function

Explanation

A process with dead time **can** be stabilized by suitably chosen feedback. Dead time adds phase lag and restricts allowable controller gain, but it need not be absent. Hence A is not necessary.

For asymptotic stability, characteristic roots lie in the left half-plane; for a polynomial characteristic equation, the Routh test requires no sign changes in its first column. The critical-frequency gain criterion is the familiar stability-margin condition for the conventional open-loop-stable negative-feedback setting. **Answer: A.**