Root Locus Technique Questions and Answers

Q: Consider the following statements regarding root loci.(1) All root loci start from the respective poles of G (s) H (s)(2) All root loci end at the respective zeros of G(s) H(s) or go to infinity.(3) The root loci are symmetrical about the imaginary axis of the S-plane.Of these statements :

The keyed answer is 1 and 2 are correct.Statement 1 is true: at K = 0 the closed loop poles coincide with the open loop poles, so each branch starts at a pole of G(s)H(s). Statement 2 is true: as K grows without bound, the branches approach the open loop zeros, and the excess branches go to infinity along asymptotes.Statement 3 is false. The root locus is symmetrical about the real axis, because complex roots of a polynomial with real coefficients occur in conjugate pairs; there is no symmetry about the imaginary axis. So the options including 3 are wrong (the option printed '2 and B' is a misprint pairing).

Direction for [ Question No: 1 To 1 ] :

Assertion - Reason type questions : The following items consist of two statements, one labelled the 'Assertion (A)' and the other labelled the 'Reason (R)'. You are to examine these two statements and decide if the Assertion (A) and the Reason (R) are individually true and if so, whether the Reason is a correct explanation of the Assertion. Select your answers to these items using the codes given below and mark your answer sheet accordingly.

Assertion (A) : The part of root locus on the real axis is not dependent upon the poles and zeros which are not on the real axis.
Reason (R) : Poles and zeros which are not on the real axis always occur in conjugate pairs.

A.Both (A) and (R) are true and (R) is the correct explanation of (A).
B.Both (A) and (R) are true, but (R) is not the correct explanation of (A).
C.(A) is true and (R) is false.
D.(A) is false and (R) is true.

Exam Year(s)

UGC NET - 2013,

Answer: A

On the real axis, the root locus exists to the left of an odd number of real poles and zeros, and complex poles and zeros contribute no net angle there, because they occur in conjugate pairs whose angles cancel on the real axis. So (A) is true and (R) is true, and (R) explains (A). Complex roots always arrive as a conjugate pair, so the angle contributions of a pair to a test point on the real axis are equal and opposite and cancel, so only the real poles and zeros to the right of the point matter. This is rule that fixes the real-axis segments of the locus. The answer is both are true and (R) is the correct explanation of (A).

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Direction for [ Question No: 2 To 2 ] :

Directions : Q. Nos. 21 to 30 : The following items consist of two statements, one labelled the “Assertion (A)” and the other labelled the “Reason (R)”. You are to examine these two statements carefully and decide if the Assertion (A) and the Reason (R) are individually true and if so, whether the Reason is a correct explanation of the Assertion. Select your answers to these items using the codes given below and mark your answer accordingly.

Assertion (A) : The part of root locus on the real axis is not dependent upon the poles and zeros which are not on the real axis.

Reason (R) : Poles and zeros which are not on the real axis always occur in conjugate pairs.

A.Both (A) and (R) are true and (R) is the correct explanation of (A).
B.Both (A) and (R) are true, but (R) is not correct explanation of (A).
C.(A) is true, but (R) is false.
D.(A) is false, but (R) is true.

Exam Year(s)

UGC NET - 2012,

Answer: A

The keyed answer is that both statements are true and (R) is the correct explanation. On the real axis, a point lies on the root locus if the number of poles and zeros to its right is odd. A complex pole or zero away from the real axis comes with its conjugate, and the two angles they contribute to a point on the real axis cancel, so they do not affect the real-axis part of the locus. The conjugate-pair property in (R) is what gives that cancellation, so (R) explains (A).

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Consider the following statements regarding root loci.

(1) All root loci start from the respective poles of G (s) H (s)
(2) All root loci end at the respective zeros of G(s) H(s) or go to infinity.
(3) The root loci are symmetrical about the imaginary axis of the S-plane.

Of these statements :

A.1, 2 and 3 are correct
B.1 and 2 are correct
C.2 and B are correct
D.1 and 3 are correct

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: B

The keyed answer is 1 and 2 are correct.

Statement 1 is true: at K = 0 the closed loop poles coincide with the open loop poles, so each branch starts at a pole of G(s)H(s). Statement 2 is true: as K grows without bound, the branches approach the open loop zeros, and the excess branches go to infinity along asymptotes.

Statement 3 is false. The root locus is symmetrical about the real axis, because complex roots of a polynomial with real coefficients occur in conjugate pairs; there is no symmetry about the imaginary axis. So the options including 3 are wrong (the option printed '2 and B' is a misprint pairing).

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Root Locus Technique Questions and Answers

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