Question

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

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

Hint:

For closed-loop stability, focus on the Routh-Hurwitz criterion, root locations, and absence of unstable poles.

Answer 1

The Correct Option is A

To ensure stability in closed-loop control, certain conditions must hold:

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).