GATE Exam > GATE Questions > Find the location of roots of characteristic ...
Start Learning for Free
Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation as
s
5+s4+4s3+4s2+4s+4=0- a)1 pole in LHS of s plane multiple poles on imaginary axis; unstable
- b)1 pole in RHS of s plane, 4 poles on imaginary axis; stable
- c)2 pole in RHS & 1 pole in LHS of s plane, 2 poles on imaginary axis; unstable
- d)1 pole in RHS of s plane 4 poles on imaginary axis; unstable
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Find the location of roots of characteristic equation and stability fo...
R – H criteria
s3 row turns out to be zero
Forming auxiliary equation A(s) = 0 = s4 + 4s2 + 4
Again s1 row turns out to be zero
Forming auxiliary equation & differentiating it we get s1 row term
A’1 (s) = 2s2 + 4
A’1 (s) = 4s
For frequency of oscillations
s4 + 4s2 + 4 = 0
(s2 + 2)2 = 0
s1, s2 = ±
s3, s4
multiple roots on jw axis so system is unstable
Forming auxiliary equation A(s) = 0 = s4 + 4s2 + 4
Again s1 row turns out to be zero
Forming auxiliary equation & differentiating it we get s1 row term
A’1 (s) = 2s2 + 4
A’1 (s) = 4s
For frequency of oscillations
s4 + 4s2 + 4 = 0
(s2 + 2)2 = 0
s1, s2 = ±
s3, s4multiple roots on jw axis so system is unstable
Most Upvoted Answer
Find the location of roots of characteristic equation and stability fo...
Analysis of the Closed Loop System:
- The characteristic equation of the closed-loop system is given as $s^5+s^4+4s^3+4s^2+4s+4=0$.
Location of Roots:
- By analyzing the characteristic equation, we can see that there is only 1 pole in the left-hand side (LHS) of the s-plane.
- Additionally, there are multiple poles on the imaginary axis.
Stability Analysis:
- Having a pole in the left-hand side (LHS) of the s-plane indicates instability in the system.
- The presence of multiple poles on the imaginary axis further confirms the unstable nature of the system.
Therefore, the closed-loop system described by the given characteristic equation has 1 pole in the LHS of the s-plane and multiple poles on the imaginary axis, making it unstable.
- The characteristic equation of the closed-loop system is given as $s^5+s^4+4s^3+4s^2+4s+4=0$.
Location of Roots:
- By analyzing the characteristic equation, we can see that there is only 1 pole in the left-hand side (LHS) of the s-plane.
- Additionally, there are multiple poles on the imaginary axis.
Stability Analysis:
- Having a pole in the left-hand side (LHS) of the s-plane indicates instability in the system.
- The presence of multiple poles on the imaginary axis further confirms the unstable nature of the system.
Therefore, the closed-loop system described by the given characteristic equation has 1 pole in the LHS of the s-plane and multiple poles on the imaginary axis, making it unstable.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer?
Question Description
Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer?.
Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Find the location of roots of characteristic equation and stability for closed loop system having characteristic equation ass5+s4+4s3+4s2+4s+4=0a)1 pole in LHS of s plane multiplepoles on imaginary axis; unstableb)1 pole in RHS of s plane, 4poles on imaginary axis; stablec)2pole in RHS & 1pole in LHS of s plane, 2poles on imaginary axis; unstabled)1 pole in RHS of s plane 4 poles on imaginary axis; unstableCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© 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