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The characteristic equation of a servo system is given by 
a0s4 + a1s3 + a2s2 + a3s + a4 = 0
Now, consider the following conditions required to be satisfied by the coefficient of the above characteristic equation for the system to be stable:
1. a1 > 0 and a4 > 0
2. a1 < 0 and a4 > 0
3. a1a2< a0a3
4. a1a2 > a0a
5. 
6. 
Which of the above conditions holds true for the given system to be stable?
  • a)
    2, 3 and 6
  • b)
    1,3 and 5
  • c)
    1,4 and 5
  • d)
    2 and 4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The characteristic equation of a servo system is given bya0s4 + a1s3 +...
The Rouths array is formed as follows:

For the system to be stable, there should not be any sign change in the first column of Routh’s array.

Hence, above conditions must hold for the given system to be stable.
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The characteristic equation of a servo system is given bya0s4 + a1s3 + a2s2 + a3s + a4 = 0Now, consider the following conditions required to be satisfied by the coefficient of the above characteristic equation for the system to be stable:1. a1 > 0 and a4 > 02. a1 < 0 and a4 > 03. a1a2< a0a34. a1a2 > a0a35.6.​Which of the above conditions holds true for the given system to be stable?a)2, 3 and 6b)1,3 and 5c)1,4 and 5d)2 and 4Correct answer is option 'C'. Can you explain this answer?
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The characteristic equation of a servo system is given bya0s4 + a1s3 + a2s2 + a3s + a4 = 0Now, consider the following conditions required to be satisfied by the coefficient of the above characteristic equation for the system to be stable:1. a1 > 0 and a4 > 02. a1 < 0 and a4 > 03. a1a2< a0a34. a1a2 > a0a35.6.​Which of the above conditions holds true for the given system to be stable?a)2, 3 and 6b)1,3 and 5c)1,4 and 5d)2 and 4Correct answer is option 'C'. 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 The characteristic equation of a servo system is given bya0s4 + a1s3 + a2s2 + a3s + a4 = 0Now, consider the following conditions required to be satisfied by the coefficient of the above characteristic equation for the system to be stable:1. a1 > 0 and a4 > 02. a1 < 0 and a4 > 03. a1a2< a0a34. a1a2 > a0a35.6.​Which of the above conditions holds true for the given system to be stable?a)2, 3 and 6b)1,3 and 5c)1,4 and 5d)2 and 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The characteristic equation of a servo system is given bya0s4 + a1s3 + a2s2 + a3s + a4 = 0Now, consider the following conditions required to be satisfied by the coefficient of the above characteristic equation for the system to be stable:1. a1 > 0 and a4 > 02. a1 < 0 and a4 > 03. a1a2< a0a34. a1a2 > a0a35.6.​Which of the above conditions holds true for the given system to be stable?a)2, 3 and 6b)1,3 and 5c)1,4 and 5d)2 and 4Correct answer is option 'C'. Can you explain this answer?.
Solutions for The characteristic equation of a servo system is given bya0s4 + a1s3 + a2s2 + a3s + a4 = 0Now, consider the following conditions required to be satisfied by the coefficient of the above characteristic equation for the system to be stable:1. a1 > 0 and a4 > 02. a1 < 0 and a4 > 03. a1a2< a0a34. a1a2 > a0a35.6.​Which of the above conditions holds true for the given system to be stable?a)2, 3 and 6b)1,3 and 5c)1,4 and 5d)2 and 4Correct answer is option 'C'. 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.
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