Stability Criteria (Routh-Hurwitz, Nyquist) — MCQs – EE

1. The main purpose of stability analysis in control systems is to determine whether:
(A) The system output increases with input
(B) The system output remains bounded for bounded input
(C) The system output decreases continuously
(D) The system has zero steady-state error

2. A system is said to be stable if all the roots of its characteristic equation lie:
(A) On the right-half of the s-plane
(B) On the imaginary axis
(C) On the left-half of the s-plane
(D) On the real axis

3. The Routh–Hurwitz criterion determines system stability without:
(A) Solving for roots of the characteristic equation
(B) Using Nyquist plots
(C) Using time-domain response
(D) Using transfer functions

4. The Routh array is formed using the coefficients of:
(A) The open-loop transfer function
(B) The closed-loop transfer function
(C) The characteristic equation
(D) The time response

5. A system is unstable if any element in the first column of the Routh array:
(A) Is positive
(B) Changes sign
(C) Is zero
(D) Is constant

6. In the Routh–Hurwitz criterion, the number of sign changes in the first column indicates:
(A) The number of left-half-plane poles
(B) The number of right-half-plane poles
(C) The number of imaginary roots
(D) The number of zero roots

7. If all elements of the first column of the Routh array are positive, the system is:
(A) Stable
(B) Unstable
(C) Marginally stable
(D) Oscillatory

8. If any row of the Routh array becomes entirely zero, it indicates:
(A) Asymptotic stability
(B) Symmetrical roots on the imaginary axis
(C) All poles in the left-half-plane
(D) Damped oscillations

9. When the first element of a row in the Routh array is zero, it can be replaced by:
(A) A small positive number (ε)
(B) A large number
(C) A negative number
(D) A constant gain

10. The Routh–Hurwitz criterion is applicable only to:
(A) Linear time-variant systems
(B) Linear time-invariant systems
(C) Nonlinear systems
(D) Discrete systems

11. A system is said to be marginally stable if:
(A) All poles are in the right-half-plane
(B) At least one pair of poles lies on the imaginary axis and none in the right-half-plane
(C) All poles are on the imaginary axis
(D) There are no poles in the left-half-plane

12. The Nyquist stability criterion is based on:
(A) Time-domain response
(B) Frequency response
(C) Root locus
(D) Bode plot

13. The Nyquist plot is a graph between:
(A) Magnitude and phase
(B) Real and imaginary parts of the open-loop transfer function
(C) Time and frequency
(D) Amplitude and gain

14. The Nyquist criterion determines:
(A) The damping ratio
(B) The stability of a closed-loop system
(C) The steady-state error
(D) The bandwidth

15. In the Nyquist plot, the critical point corresponds to:
(A) (0, 0)
(B) (1, 0)
(C) (–1, 0)
(D) (–2, 0)

16. In Nyquist stability analysis, each clockwise encirclement of the critical point (–1, 0) represents:
(A) A left-half-plane pole
(B) A right-half-plane pole
(C) A zero on the real axis
(D) A stable system

17. If the Nyquist plot does not encircle the point (–1, 0) and there are no open-loop poles in the right-half-plane, the system is:
(A) Stable
(B) Unstable
(C) Marginally stable
(D) Critically damped

18. If a Nyquist plot encircles the critical point in the clockwise direction once, the system has:
(A) One right-half-plane pole
(B) One left-half-plane pole
(C) Zero poles
(D) Infinite poles

19. The Nyquist criterion can be used for:
(A) Only stable open-loop systems
(B) Both stable and unstable open-loop systems
(C) Only systems with imaginary roots
(D) Nonlinear systems only

20. The gain margin and phase margin of a system are obtained from:
(A) Nyquist plot
(B) Time-domain response
(C) Root locus
(D) Routh array