Root Locus MCQ

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

1. Routh-Hurwitz criterion
2. Root locus plot
3. Bode plot
4. Nyquist criterion

2. Consider the following statements:

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

Which of the above statements are correct?

1. 1, 2, 3 and 4
2. 1, 2 and 4 only
3. 3 and 4 only
4. 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?

1. (2,0)
2. (-1,0)
3. (-2,0)
4. (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

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

5. Consider the following statements about root locus:

1. The root locus is symmetrical about real axis.
2. 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.
3. The breakaway points of the root locus are the solutions of $\frac{dK}{ds}=0$

Which of the above statements are correct?

1. 1 and 2 only
2. 1 and 3 only
3. 2 and 3 only
4. 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?

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

1. s = -∞
2. s = -3
3. s = -1.5
4. 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

1. 3 and (-4,0)
2. -3 and (-12,0)
3. -3 and (-4,0)
4. 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

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

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

1. System becomes less oscillatory
2. System stability increases
3. Root locus shifts away from imaginary axis
4. Root locus shifts towards imaginary axis

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

1. $\frac{\pi}{n+m}$
2. $\frac{2\pi}{n+m}$
3. $\frac{\pi}{n-m}$
4. $\frac{2\pi}{n-m}$

11. Consider the following statements regarding root loci plot:

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

Which of these statements are correct?

1. i and ii
2. ii and iii
3. iii and iv
4. i, ii, iii and iv

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

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

1. -2.5
2. -2
3. -1
4. -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?

1. -3, 0
2. -2, 0
3. -5, 0
4. -4, 0

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

1. System becomes oscillatory
2. Root locus shifts toward imaginary axis
3. Relative stability of the system increases
4. 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

1. product of lengths of vectors from the poles to that point
2. product of lengths of vectors from the zeroes to that point
3. ratio of product of lengths of vectors from poles to that point to the product of length of vectors from zeros to that point
4. product of lengths of vectors from all poles to zeros

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

1. The intersection of asymptotes must always be on the real axis.
2. 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?

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

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

1. Root loci can be used for analyzing stability and transient performance.
2. Root loci provide insight into system stability and performance
3. Shape of root locus gives idea of type of controller needed to meet design specification.
4. 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:

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

Which of the statements given above are correct?

1. Only ii and iii
2. Only i and ii
3. i, ii and iii
4. 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:

1. The number of separate root loci is m.
2. The number of separate root loci is n.
3. The number of root loci approaching infinity is (m – n).
4. The number of root loci approaching infinity is (m + n).

Which of the statements given above are correct?

1. i and iii
2. i and iv
3. ii and iv
4. ii and iii

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

s(s + 4) (s² + 2s + s) + K(s + 1) = 0

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

1. 0°, 180°, 300°
2. 60°, 180°, 300°
3. 0°, 120°, 240°
4. 120°, 180°, 240°