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 ] :

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).

Discuss in Forum

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).

Discuss in Forum

Loading…

Topics

Other Subjects

Tags: Root Locus Technique Questions and Answers || Root Locus Technique MCQ Questions and Answers || Root Locus Technique GK Questions and Answers || Root Locus Technique GK MCQ Questions || Root Locus Technique Multiple Choice Questions and Answers || Root Locus Technique GK || GK on Root Locus Technique || Control Systems Questions and Answers || Control Systems MCQ Questions and Answers || Control Systems GK Questions and Answers || GK on Control Systems

Root Locus Technique Questions and Answers

Direction for [ Question No: 1 To 1 ] :

Topics

Other Subjects

About Us

Stay informed about all important Dates & Notifications