8) Which of these statements are True? The breakaway point for the root-locus with a = 1.5 is at s = -1.5 The root locus obtained by varying K always lies on the left half of the complex s-plane for all values of a > 0. The root-locus will have 1 branch going to infinity regardless of the value of a. The centroid will remain constant regardless of the value of a.

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Q8 only . multiple answers question
Common data for Q7, Q8, Q9:
The characteristic equation of a system is given by:
s(s? + 2s + a) + K(s + 1) = 0
The gain K is varied in the range 0, 00) to obtain
the root locus for different values of a > 0.
7) The angle of departure(in degrees) from
one of the complex open-loop
poles(when they exist) vary w.r.t. a as: 2|
(represents the absolute value of a complex
number)
90 – tan (l/2, ), a > 2
tan- (|V1 - al), a >1
180 – tan-1(IV1- a), a < 1
2-a
tan-(/1), a < 2
8) Which of these statements are True?
The breakaway point for the root-locus with
1.5 is at s = -1.5
The root locus obtained by varying K
always lies on the left half of the complex
s-plane for all values of a > 0.
The root-locus will have 1 branch going to
infinity regardless of the value of a.
The centroid will remain constant
regardless of the value of a.
Transcribed Image Text:Common data for Q7, Q8, Q9: The characteristic equation of a system is given by: s(s? + 2s + a) + K(s + 1) = 0 The gain K is varied in the range 0, 00) to obtain the root locus for different values of a > 0. 7) The angle of departure(in degrees) from one of the complex open-loop poles(when they exist) vary w.r.t. a as: 2| (represents the absolute value of a complex number) 90 – tan (l/2, ), a > 2 tan- (|V1 - al), a >1 180 – tan-1(IV1- a), a < 1 2-a tan-(/1), a < 2 8) Which of these statements are True? The breakaway point for the root-locus with 1.5 is at s = -1.5 The root locus obtained by varying K always lies on the left half of the complex s-plane for all values of a > 0. The root-locus will have 1 branch going to infinity regardless of the value of a. The centroid will remain constant regardless of the value of a.
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