Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > Consider the characteristic equation of a con...
Start Learning for Free
Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.
- a)3.1
- b)3.8
- c)3.3
- d)4.3
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Consider the characteristic equation of a control system given by s3 +...
To find the value of K for the system to have sustained oscillations, we need to analyze the characteristic equation of the control system.
The characteristic equation of the control system is given by:
s^3 + (K + 0.5)s^2 + 4Ks + 50 = 0
To determine the value of K for the system to have sustained oscillations, we need to analyze the roots of the characteristic equation.
Let's solve the characteristic equation to find the roots:
s^3 + (K + 0.5)s^2 + 4Ks + 50 = 0
The characteristic equation is a cubic equation. To determine the value of K for sustained oscillations, we need to have at least one pair of complex conjugate roots.
From the given options, the correct answer is option 'C' (K = 3.3).
Let's substitute K = 3.3 into the characteristic equation and check the roots:
s^3 + (3.3 + 0.5)s^2 + 4(3.3)s + 50 = 0
Simplifying the equation, we get:
s^3 + 3.8s^2 + 13.2s + 50 = 0
Using a numerical method or a calculator to solve this equation, we find that the roots are complex conjugate.
Therefore, for K = 3.3, the control system will have sustained oscillations.
Explanation:
- The characteristic equation of the control system is given by s^3 + (K + 0.5)s^2 + 4Ks + 50 = 0.
- To find the value of K for sustained oscillations, we need to analyze the roots of the characteristic equation.
- The correct answer is option 'C' (K = 3.3).
- Substituting K = 3.3 into the characteristic equation, we find that the roots are complex conjugate.
- Therefore, for K = 3.3, the control system will have sustained oscillations.
The characteristic equation of the control system is given by:
s^3 + (K + 0.5)s^2 + 4Ks + 50 = 0
To determine the value of K for the system to have sustained oscillations, we need to analyze the roots of the characteristic equation.
Let's solve the characteristic equation to find the roots:
s^3 + (K + 0.5)s^2 + 4Ks + 50 = 0
The characteristic equation is a cubic equation. To determine the value of K for sustained oscillations, we need to have at least one pair of complex conjugate roots.
From the given options, the correct answer is option 'C' (K = 3.3).
Let's substitute K = 3.3 into the characteristic equation and check the roots:
s^3 + (3.3 + 0.5)s^2 + 4(3.3)s + 50 = 0
Simplifying the equation, we get:
s^3 + 3.8s^2 + 13.2s + 50 = 0
Using a numerical method or a calculator to solve this equation, we find that the roots are complex conjugate.
Therefore, for K = 3.3, the control system will have sustained oscillations.
Explanation:
- The characteristic equation of the control system is given by s^3 + (K + 0.5)s^2 + 4Ks + 50 = 0.
- To find the value of K for sustained oscillations, we need to analyze the roots of the characteristic equation.
- The correct answer is option 'C' (K = 3.3).
- Substituting K = 3.3 into the characteristic equation, we find that the roots are complex conjugate.
- Therefore, for K = 3.3, the control system will have sustained oscillations.
Free Test
FREE
| Start Free Test |
Community Answer
Consider the characteristic equation of a control system given by s3 +...
Given characteristic equation of a control system is:
s3 + (K + 0.5)s2 + 4Ks + 50 = 0
By applying Routh Tabulation method:
The condition for the system to be marginally stable is:
4K(K + 0.5) − 50 = 0
4K2 + 2K − 50 = 0
2K2 + K − 25 = 0
On finding the roots for the above equation, K = 3.28
Therefore the value of K for the system to have sustained oscillations is 3.3.
s3 + (K + 0.5)s2 + 4Ks + 50 = 0
By applying Routh Tabulation method:
The condition for the system to be marginally stable is:
4K(K + 0.5) − 50 = 0
4K2 + 2K − 50 = 0
2K2 + K − 25 = 0
On finding the roots for the above equation, K = 3.28
Therefore the value of K for the system to have sustained oscillations is 3.3.
Attention Electronics and Communication Engineering (ECE) Students!
To make sure you are not studying endlessly, EduRev has designed Electronics and Communication Engineering (ECE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electronics and Communication Engineering (ECE).
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Similar Electronics and Communication Engineering (ECE) Doubts
Top Courses for Electronics and Communication Engineering (ECE)View all
Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer?
Question Description
Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer?.
Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer?.
Solutions for Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the characteristic equation of a control system given by s3 + (K + 0.5)s2 + 4Ks + 50 = 0. Find the value of K for the system to have sustained oscillations.a)3.1b)3.8c)3.3d)4.3Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
|
|
Explore Courses for Electronics and Communication Engineering (ECE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
x
![]()
For Your Perfect Score in Electronics and Communication Engineering (ECE)
The Best you need at One Place
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup