Which of the following is NOT a necessary condition for a process under closed-loop control to be stable?
Show Hint
- Dead-time term(s) must be absent in the open-loop transfer function
- Roots of the characteristic equation must have negative real part
- All the elements in the left (first) column of the Routh array must have the same sign
- Open-loop transfer function must have an amplitude ratio less than 1 at the critical frequency
The Correct Option is A
Solution and Explanation
Step 1: Review necessary conditions for stability.
- The absence of dead-time (A) improves control system performance.
- The Routh-Hurwitz criterion (C) ensures stability by checking sign changes.
- Negative real parts of the characteristic equation roots (B) are essential for stability.
Step 2: Incorrect statement.
(D) The amplitude ratio condition at the critical frequency is not a necessary condition for stability. It is a criterion for gain margin analysis, not stability itself.
Thus, the correct answer is (D).
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