Control System – Concepts of Stability MCQ

1. A system with characteristic equation,

s4 + 2s3 + 11s2 + 18s + 18 = 0

will have closed-loop poles such that,

  1. all poles lie in the left half of the s-plane and no pole lies on imaginary axis.
  2. all poles lie in the right half of the s-plane
  3. two poles lie symmetrically on the imaginary axis of the s-plane
  4. all four poles lie on the imaginary axis of the s-plane.
Answer
Answer. c

2. The characteristic polynomial of a feedback control system is given by

R(s) = s5 + 2s4 + 2s3 + 4s2 + 11s + 10

For this system, the numbers of roots that lie in the left hand and right-hand of s-plane respectively, are

  1. 5 and 0
  2. 4 and 1
  3. 3 and 2
  4. 2 and 3
Answer
Answer. c

3. The open-loop transfer function of negative feedback is

$G(s)H(s)=\frac{K}{s(s+5)(s+12)}$

For ensuring system stability the gain K should be in the range

  1. 0 < K < 60
  2. 0 < K < 600
  3. 0 < K < 1020
  4. K > 1020
Answer
Answer. c

4. The closed-loop transfer function of a system is

$\frac{C(s)}{R(s)}=\frac{s-2}{s^3+8s^2+19s+12}$

The system is

  1. Stable
  2. Unstable
  3. Conditionally stable
  4. Critically stable
Answer
Answer. a

5. The frequency of sustained oscillation for marginal stability, for a control system

$G(s)H(s)=\frac{2k}{s(s+1)(s+5)}$

and operating with negative feedback is

  1. $\sqrt{5}$ r/s
  2. $\sqrt{6}$ r/s
  3. 5 r/s
  4. 6 r/s
Answer
Answer. a

6. When gain K of the open-loop transfer function of order greater than unity is varied from zero to infinity, the closed-loop system

  1. may become unstable
  2. stability may improve
  3. stability may not be affected
  4. will become highly stable
Answer
Answer. a

7. None of the poles of a linear control system lies in the right-half of s-plane. For a bounded input, the output of this system

  1. is always bounded
  2. could be unbounded
  3. always tends to zero
  4. None of the above
Answer
Answer. d

8. How many roots of the following equation lie in the right-half of s-plane?

2s4 + s3 + 2s2 + 5s + 10 = 0

  1. 4
  2. 3
  3. 2
  4. 1
Answer
Answer. c

9. The characterisitic equation of a feedback system is

s3 + Ks2 + 5s + 10 = 0.

For a stable system, the value of K should be greater than

  1. 4
  2. 3
  3. 2
  4. 1
Answer
Answer. c

10. The characterisitic equation of a feedback system is

s4 + s3 + 2s2 + 4s + 15 = 0.

The number of roots in the right half of the s-plane is

  1. 4
  2. 2
  3. 3
  4. 1
Answer
Answer. b

11. A unity feedback system has forward transfer function

$G(s)=\frac{K}{s(s+3)(s+10)}$

The range of K for the system to be stable is

  1. 0 < K < 390
  2. 0 < K < 39
  3. 0 < K < 3900
  4. None of the above
Answer
Answer. a

12. The characteristic equation of a control system is given below:

Q(s) = s4 + s3 +3s2 + 2s + 5 = 0

The system is

  1. stable
  2. critically stable
  3. conditionally stable
  4. unstable
Answer
Answer. d

13. Consider the following statements in connection with pole location

  1. A distinct pole always lies on the real axis.
  2. A dominant constant pole has a large time.

Which of the above statements is/are correct?

  1. Both i and ii
  2. Neither i nor ii
  3. i only
  4. ii only
Answer
Answer. a

14. Consider the following statements in connection with the closed-loop poles of feedback control system

  1. Poles on jω-axis will make the output amplitude neither decaying nor growing in time.
  2. Dominant closed-loop poles occur in the form of a complex conjugate pair.
  3. The gain of a higher-order system is adjusted so that there will exist a pair of complex conjugate closed-loop poles on jω-axis.
  4. The presence of complex conjugate closed-loop poles reduces the effects of such non-linearities as dead zones, backlash and coulomb friction.
  1. ii, iii and iv only
  2. ii only
  3. i, ii and iv only
  4. i, ii, iii and iv
Answer
Answer. d

15. The feedback control system represented by the open-loop transfer function

$G(s)H(s)=\frac{10(s+2)}{(s+1)(s+3)(s-5)}$ is

  1. stable
  2. unstable
  3. marginally stable
  4. insufficient data
Answer
Answer. b

16. The unit step response of a system is [1 – e-t (1 + t)] u(t). What is the nature of the system in turn of stability?

  1. Stable
  2. Unstable
  3. Oscillatory
  4. Critically stable
Answer
Answer. a

17. The characteristic equation of a feedback control system is given by:

s3 + 6s2 +9s + 4 = 0

What is the number of roots in the left-half of the s-plane?

  1. three
  2. two
  3. zero
  4. one
Answer
Answer. a

18. Consider the following statements:

  1. A system is said to be stable if its output is bounded for any input.
  2. A system is stable if all the roots of the characteristic equation lie in the left half of the s-plane.
  3. A system is stable if all the roots of the characteristic equation have negative real parts.
  4. A second-order system is always stable for finite positive values of open-loop gain.

Which of the above statements is/are correct?

  1. ii, iii and iv
  2. i only
  3. ii and iii only
  4. iii and iv only
Answer
Answer. c

19. Which one of the following statement is correct for the open-loop transfer function?

$G(s)=\frac{K(s+3)}{s(s-1)}$ for K > 1 is

  1. Open-loop system is stable but the closed-loop system is unstable.
  2. Open-loop system is unstable but the closed-loop system is stable.
  3. Both open-loop and closed-loop systems are unstable.
  4. Both open-loop and closed-loop systems are stable.
Answer
Answer. b

20. What is the range of K for which the open-loop transfer function

$G(s)=\frac{K}{s^2 (s+a)}$

represents an unstable closed-loop system?

  1. K > 0
  2. K = 0
  3. K < 0
  4. -∞ < K < ∞
Answer
Answer. d
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