1. A system with characteristic equation,

s^{4} + 2s^{3} + 11s^{2} + 18s + 18 = 0

will have closed-loop poles such that,

- all poles lie in the left half of the s-plane and no pole lies on imaginary axis.
- all poles lie in the right half of the s-plane
- two poles lie symmetrically on the imaginary axis of the s-plane
- 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) = s^{5 }+ 2s^{4} + 2s^{3} + 4s^{2} + 11s + 10

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

- 5 and 0
- 4 and 1
- 3 and 2
- 2 and 3

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

- 0 < K < 60
- 0 < K < 600
- 0 < K < 1020
- K > 1020

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

- Stable
- Unstable
- Conditionally stable
- Critically stable

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

- $\sqrt{5}$ r/s
- $\sqrt{6}$ r/s
- 5 r/s
- 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

- may become unstable
- stability may improve
- stability may not be affected
- 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

- is always bounded
- could be unbounded
- always tends to zero
- None of the above

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

2s^{4} + s^{3} + 2s^{2} + 5s + 10 = 0

- 4
- 3
- 2
- 1

9. The characterisitic equation of a feedback system is

s^{3} + Ks^{2} + 5s + 10 = 0.

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

- 4
- 3
- 2
- 1

10. The characterisitic equation of a feedback system is

s^{4} + s^{3} + 2s^{2} + 4s + 15 = 0.

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

- 4
- 2
- 3
- 1

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

- 0 < K < 390
- 0 < K < 39
- 0 < K < 3900
- None of the above

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

Q(s) = s^{4} + s^{3} +3s^{2} + 2s + 5 = 0

The system is

- stable
- critically stable
- conditionally stable
- unstable

13. Consider the following statements in connection with pole location

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

Which of the above statements is/are correct?

- Both i and ii
- Neither i nor ii
- i only
- ii only

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

- Poles on jω-axis will make the output amplitude neither decaying nor growing in time.
- Dominant closed-loop poles occur in the form of a complex conjugate pair.
- 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.
- The presence of complex conjugate closed-loop poles reduces the effects of such non-linearities as dead zones, backlash and coulomb friction.

- ii, iii and iv only
- ii only
- i, ii and iv only
- i, ii, iii and iv

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

- stable
- unstable
- marginally stable
- 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?

- Stable
- Unstable
- Oscillatory
- Critically stable

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

s^{3} + 6s^{2} +9s + 4 = 0

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

- three
- two
- zero
- one

18. Consider the following statements:

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

Which of the above statements is/are correct?

- ii, iii and iv
- i only
- ii and iii only
- iii and iv only

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

- Open-loop system is stable but the closed-loop system is unstable.
- Open-loop system is unstable but the closed-loop system is stable.
- Both open-loop and closed-loop systems are unstable.
- Both open-loop and closed-loop systems are stable.

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?

- K > 0
- K = 0
- K < 0
- -∞ < K < ∞