# 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.

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

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

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

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

The system is

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

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

and operating with negative feedback is

1. r/s
2. r/s
3. 5 r/s
4. 6 r/s

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

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

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

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

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

11. A unity feedback system has forward transfer function

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

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

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

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

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

is

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

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

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

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

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

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.

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

represents an unstable closed-loop system?

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