1. Which of the following is considered a time-domain technique in control systems?

- Routh-Hurwitz criterion
- Root locus plot
- Bode plot
- Nyquist criterion

2. Consider the following statements:

- Adding a zero to the G(s)H(s) tends to push root locus to the left.
- Adding a pole to the G(s)H(s) tends to push root locus to the right.
- Complementary root locus refers to root loci with positive K.
- Adding a zero to the forward path transfer function reduces the maximum overshoot of the system.

Which of the above statements are correct?

- 1, 2, 3 and 4
- 1, 2 and 4 only
- 3 and 4 only
- 1, 2 and 3 only

3. The open-loop transfer function of a feedback control system is given by

$G(s)H(s)=\frac{K(s+8)}{s(s+4)(s^2+4s+8)}$

In the root locus diagram of the system, the asymptotes of the root loci for large values of K meet at a point in the s-plane. Which one of the following is the set of coordinates of that point?

- (2,0)
- (-1,0)
- (-2,0)
- (0,0)

4. A unity feedback system has open-loop transfer function

$G(s)=\frac{K(s+4)}{(s+1)(s+2)}$

The portions of the real axis that lie on the root loci are between

- s = 0 and s = -1
- s = 0 and s = -2; beyond s = -4
- s = -1 and s = -2; s = -4 and -∞
- s = -2 and s = -4; s = -4 and +∞

5. Consider the following statements about root locus:

- The root locus is symmetrical about real axis.
- If a root locus branch moves along the real axis from an open-loop pole to zero or to infinity, this root locus branch is called real root branch.
- The breakaway points of the root locus are the solutions of $\frac{dK}{ds}=0$

Which of the above statements are correct?

- 1 and 2 only
- 1 and 3 only
- 2 and 3 only
- 1, 2 and 3

6. Which of the following points is not on the root locus of a system with the given open-loop transfer function?

$G(s)H(s)=\frac{K}{s(s+1)(s+3)}$

- s = -∞
- s = -3
- s = -1.5
- s = -j1.73

7. The characteristic equation of a control system is given by

s(s+4)(s+5)(s+6)+K(s+3) = 0

The number of asymptotes and the centroid of the asymptotes of this control system are

- 3 and (-4,0)
- -3 and (-12,0)
- -3 and (-4,0)
- 3 and (4,0)

8. The open-loop transfer function of the feedback control system is given by

$G(s)=\frac{K}{(s + 1)(s + 2)(s + 3)}$

The breakaway point in its root locus will be

- beyond -3
- between 0 and -1
- between -1 and -2
- between -2 and -3

9. Addition of open-loop poles results into which of the following?

- System becomes less oscillatory
- System stability increases
- Root locus shifts away from imaginary axis
- Root locus shifts towards imaginary axis

10. The angle between two adjacent asymptotes in a root locus diagram is

- $\frac{\pi}{n+m}$
- $\frac{2\pi}{n+m}$
- $\frac{\pi}{n-m}$
- $\frac{2\pi}{n-m}$

11. Consider the following statements regarding root loci plot:

- When gain K is zero, the roots coincide with the poles.
- When K is increased, the roots move away from the poles.
- A root locus diagram is always symmetric about the imaginary axis.
- The number of branches terminates on infinity is open loop poles plus zeros.

Which of these statements are correct?

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

12. The breakaway point in the root loci plot for the loop transfer function

$G(s)=\frac{K}{s(s+3)^{2}}$

- -2.5
- -2
- -1
- -0.5

13. Root locus of s(s + 2) + K(s +4) = 0 is a circle. What are the co-ordinates of the centre of this circle?

- -3, 0
- -2, 0
- -5, 0
- -4, 0

14. Which one of the following describes correctly the effect of adding a zero to the system?

- System becomes oscillatory
- Root locus shifts toward imaginary axis
- Relative stability of the system increases
- Operating range of K for stable operation decreases

15. Which one of the following is correct?

The value of the system gain at any point on a root locus can be obtained as a

- product of lengths of vectors from the poles to that point
- product of lengths of vectors from the zeroes to that point
- ratio of product of lengths of vectors from poles to that point to the product of length of vectors from zeros to that point
- product of lengths of vectors from all poles to zeros

16. Consider the following statements made on the basis of root locus analysis:

- The intersection of asymptotes must always be on the real axis.
- The asymptotes of root loci refer to the angle of root loci when gain K is zero.

Which of the statements given above is/are correct?

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

17. Which one of the following statement is not correct?

- Root loci can be used for analyzing stability and transient performance.
- Root loci provide insight into system stability and performance
- Shape of root locus gives idea of type of controller needed to meet design specification.
- Root locus can be used to handle more than one variable at a time.

18. Consider the following statements in connection with the addition of a pole to the forward path transfer function:

- Closed-loop system becomes less stable.
- Rise time of the system increases.
- Bandwidth of the system increases.

Which of the statements given above are correct?

- Only ii and iii
- Only i and ii
- i, ii and iii
- Only i and iii

19. The open loop transfer function of a feedback system has m poles and n zeros (m > n).

Consider the following statements:

- The number of separate root loci is m.
- The number of separate root loci is n.
- The number of root loci approaching infinity is (m – n).
- The number of root loci approaching infinity is (m + n).

Which of the statements given above are correct?

- i and iii
- i and iv
- ii and iv
- ii and iii

20. The characteristic equation of a control system is given by

s(s + 4) (s^{2} + 2s + s) + K(s + 1) = 0

What are the angles of the asymptotes for the root loci for K ≥ 0?

- 0°, 180°, 300°
- 60°, 180°, 300°
- 0°, 120°, 240°
- 120°, 180°, 240°