Root Locus Question and Answers

 Root Locus

1. Which one of the following statements is not correct?

a) Root loci can be used for analyzing stability and transient performance

b) Root loci provide insight into system stability and performance

c) Shape of the root locus gives idea of type of controller needed to meet design specification

d) Root locus can be used to handle more than one variable at a time

Answer: Root locus can be used to handle more than one variable at a time

2. Root locus of s(s+2)+K(s+4) =0 is a circle. What are the coordinates of the center of this circle?

a) -2,0

b) -3,0

c) -4,0

d) -5,0

Answer: -4,0

3. The main objective of drawing root locus plot is :

a) To obtain a clear picture about the open loop poles and zeroes of the system

b) To obtain a clear picture about the transient response of feedback system for various values of open loop gain K

c) To determine sufficient condition for the value of ‘K’ that will make the feedback system unstable

d) Both b and c

Answer: Both b and c

4. While increasing the value of gain K, the system becomes

a) Less stable

b) More stable

c) Unstable

d) Absolute stable

Answer: Less stable

5. The addition of open loop poles pulls the root locus towards:

a) The right and system becomes unstable

b) Imaginary axis and system becomes marginally stable

c) The left and system becomes unstable

d) The right and system becomes unstable

Answer: The right and system becomes unstable

6. Root locus is used to calculate:

a) Marginal stability

b) Absolute stability

c) Conditional stability

d) Relative stability

Answer: Relative stability

7. Routh Hurwitz criterion is better than root locus.

a) True

b) False

Answer: False

8. Consider the following statements regarding root loci:

a) All root loci start from the respective poles of G(s) H(s)

b) All root loci end at the respective zeros of G(s) H(s) or go to infinity

c) The root loci are symmetrical about the imaginary axis of the s-plane

d) All root loci start and end from the respective poles of G(s) H(s) or go to infinity

Answer: All root loci end at the respective zeros of G(s) H(s) or go to infinity

9. Number of roots of characteristic equation is equal to the number of ______________

a) Branches

b) Root

c) Stem

d) Poles

Answer: Branches

10. Which of the following statements are correct?

a) Root locus is for the negative feedback systems

b) Complementary root locus is for the positive feedback systems

c) Root locus is for the negative feedback and Complementary root locus is for the positive feedback systems

d) Complementary root locus is for the negative feedback systems

Answer: Root locus is for the negative feedback and Complementary root locus is for the positive feedback systems

11. Consider the loop transfer function K(s+6)/(s+3)(s+5) In the root locus diagram the centroid will be located at:

a) -4

b) -1

c) -2

d) -3

Answer: -2

12. Which one of the following applications software’s is used to obtain an accurate root locus for?

a) LISP

b) MATLAB

c) dBase

d) Oracle

Answer: MATLAB

13. Which one of the following is not the property of root loci?

a) The root locus is symmetrical about imaginary axis

b) They start from the open loop poles and terminate at the open loop zeroes

c) The breakaway points are determined from dK/ds = 0

d) Segments of the real axis are the part of the root locus if and only is the total number of real poles and zeroes to their right is odd.

Answer: The root locus is symmetrical about imaginary axis

14. The breakaway point calculated mathematically must always lie on the root locus.

a) True

b) False

Answer: True

15. What is the number of the root locus segments which do not terminate on zeroes?

a) The number of poles

b) The number of zeroes

c) The difference between the number of poles and zeroes

d) The sum of the number of poles and the number of the zeroes

Answer: The difference between the number of poles and zeroes

16. Which one of the following are correct?

The root locus is the path of the roots of the characteristic equation traced out in the s-plane?

a) As the input of the system is changed

b) As the output of the system is changed

c) As a system parameter is changed

d) As the sensitivity is changed

Answer: As a system parameter is changed

17. If the gain of the system is reduced to a zero value, the roots of the system in the s-plane,

a) Coincide with zero

b) Move away from zero

c) Move away from poles

d) Coincide with the poles

Answer: Coincide with the poles

18. The addition of open loop zero pulls the root loci towards:

a) The left and therefore system becomes more stable

b) The right and therefore system becomes unstable

c) Imaginary axis and therefore system becomes marginally stable

d) The left and therefore system becomes unstable

Answer: The left and therefore system becomes more stable

19. If root loci plots of a particular control system do not intersect the imaginary axis at any point, then the gain margin of the system will be:

a) 0

b) 0.707

c) 1

d) Infinite

Answer: Infinite

20. When the number of poles is equal to the number of zeroes, how many branches of root locus tends towards infinity?

a) 1

b) 2

c) 0

d) Equal to number of zeroes

Answer: 0

21. With reference to root locus, the complex conjugate roots of the characteristic equation of the O.L.T.F. given below G(s)H(s) =K(s+3)/(s+1)2, lie on

a) Straight line

b) Parabola

c) Circle

d) Semi-circle

Answer: Circle

22. Determine the centroid of the root locus for the system having G(s)H(s) = K/(s+1)(s2+4s+5)

a) -2.1

b) -1.78

c) -1.66

d) -1.06

Answer: -1.66

23. The loop transfer function of an LTI system is G(s)H(s) =K(s+1)(s+5)/s(s+2)(s+3). For K>0, the point on the real axis that does not belong to the root locus of the system is

a) -0.5

b) -2.5

c) -3.5

d) -5.5

Answer: -3.5

24. The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:

a) 0° and 270°

b) 0° and 180°

c) 90° and 270°

d) 90° and 180°

Answer: 90° and 270°

25. The intersection of asymptotes of root loci of a system with open loop transfer function G(s)H(s) = K/s(s+1)(s+3) is

a) 1.44

b) 1.33

c) -1.44

d) -1.33

Answer: -1.33

26. If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be

a) -5

b) 10

c) 5

d) -10

Answer: 10

27. The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system is

a) 4 and (-4,0)

b) 3 and (-12,0)

c) -4 and (-4,0)

d) -3 and (-12,0)

Answer: 4 and (-4,0)

28. The characteristic equation of a control system is given as 1+ K(s+4)/s(s+7)(s2+2s+2)=0. The real axis intercept for root locus asymptote is:

a) -2.25

b) -1

c) -1.67

d) 0

Answer: -1.67

29. The OLTF of a unity feedback system is K(s+2)(s+4)/(s+5)(s+6) the angle of arrival of the root loci as s =-2, and s =-4 respectively are:

a) 0°,180°

b) 180°,0°

c) 90°,180°

d) 180°, 90°

Answer: 180°,0°

30. The characteristic equation is s3+14s2+(45+K)s+K =0, centroid is located at (-x,0) then the value of x is ____________

a) 1

b) 2

c) 3

d) 4

Answer: 2

31) For a unity feedback system with G(s) = 10 / s2, what would be the value of centroid?

a. 0

b. 2

c. 5

d. 10 

ANSWER: 0

32) If poles are added to the system, where will the system tend to shift the root locus?

a. To the left of an imaginary axis

b. To the right of an imaginary axis

c. At the center

d. No shifting takes place

ANSWER: To the right of an imaginary axis

33) If the system is specified by open loop transfer function G(s)H(s) = k / s(s+3) (s + 2), how many root loci proceed to end at infinity?

a. 2

b. 3

c. 5

d. 6

ANSWER: 3

34) What should be the nature of root locus about the real axis?

a. Assymetric

b. Symmetric

c. Exponential

d. Decaying

ANSWER: Symmetric

35) Which point on root locus specifies the meeting or collision of two poles?

a. Centroid

b. Break away point

c. Stability point

d. Anti-break point

ANSWER: Break away point

36) For drawing root locus, the angle of asymptote yields the direction along which _________branches approach to infinity.

a. p + z

b. p - z

c. p / z

d. p x z

ANSWER: p - z

37) While specifying the angle and magnitude conditions, angles are added whereas magnitudes get ________

a. Subtracted

b. Multiplied

c. Divided

d. All of the above

ANSWER: Multiplied

38) Which condition is used to verify the existence of a particular point on the root locus?

a. Amplitude

b. Frequency

c. Magnitude

d. Angle

ANSWER: Angle

39) Root locus specifies the movement of closed loop poles especially when the gain of system  ________

a. Remains constant

b. Exhibit variations

c. Gives zero feedback

d. Gives infinite poles

ANSWER: Exhibit variations

40) In second order system, which among the following remains independent of gain (k)?

a. Open loop poles

b. Closed loop poles

c. Both a and b

d. None of the above

ANSWER: Open loop poles