(a) A feedback control system has the following characteristic equation. 5³+(4+ K) s² + 6s+ 8(K + 2) = 0 What is the maximum value of K before the system starts to oscillate? Determine, (i) the frequency of oscillation (ii) the value of the roots when the system oscillates. (b) Determine the range of values of K (K> 0) such that the characteristic equation, 5³ + 3(K + 1) s² + (7K+5) s+ (4K + 7) = 0, has roots more negative than s = - 1.
(a) A feedback control system has the following characteristic equation. 5³+(4+ K) s² + 6s+ 8(K + 2) = 0 What is the maximum value of K before the system starts to oscillate? Determine, (i) the frequency of oscillation (ii) the value of the roots when the system oscillates. (b) Determine the range of values of K (K> 0) such that the characteristic equation, 5³ + 3(K + 1) s² + (7K+5) s+ (4K + 7) = 0, has roots more negative than s = - 1.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![(a) A feedback control system has the following characteristic equation.
5³+(4+ K) s² + 6s+ 8(K + 2) = 0
What is the maximum value of K before the system starts to oscillate? Determine,
(i)
the frequency of oscillation
(ii)
the value of the roots when the system oscillates.
(b) Determine the range of values of K (K> 0) such that the characteristic equation,
s³ + 3(K + 1) s² + (7K+ 5) s+ (4K + 7) = 0, has roots more negative than s = - - 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1770a0c6-60a2-4197-ba3a-e76b7f379658%2F1a5cde22-5260-44c1-8294-421927dbb25e%2F46s3rc_processed.png&w=3840&q=75)
Transcribed Image Text:(a) A feedback control system has the following characteristic equation.
5³+(4+ K) s² + 6s+ 8(K + 2) = 0
What is the maximum value of K before the system starts to oscillate? Determine,
(i)
the frequency of oscillation
(ii)
the value of the roots when the system oscillates.
(b) Determine the range of values of K (K> 0) such that the characteristic equation,
s³ + 3(K + 1) s² + (7K+ 5) s+ (4K + 7) = 0, has roots more negative than s = - - 1.
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