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Which one of the following characteristic equations of result in the stable operation of the feedback system?
- a)s3 + 4s2 + s − 6 = 0
- b)s3 + s2 + 5s + 6 = 0
- c)s3 + 4s2 + 10s + 11 = 0
- d)s4 + s3 + 2s2 + 4s + 6 = 0
Correct answer is option 'C'. Can you explain this answer?
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Which one of the following characteristic equations of result in the s...
For stable operation, all coefficients of the characteristic equation should be real and have the same sign and none of the coefficients should be zero.
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Which one of the following characteristic equations of result in the s...
Characteristics equations are used to determine the stability of a feedback system. Stability is crucial in ensuring that the system operates in a controlled and predictable manner. A stable system will reach a steady state and remain there, while an unstable system will exhibit oscillations or diverge.
To determine the stability of a system, we need to analyze the roots of the characteristic equation. The roots represent the poles of the system transfer function and indicate the behavior of the system.
In this question, we are given four characteristic equations, and we need to identify the one that results in stable operation.
Let's analyze each equation one by one:
a) s^3 + 4s^2 + s + 6 = 0
b) s^3 + s^2 + 5s + 6 = 0
c) s^3 + 4s^2 + 10s + 11 = 0
d) s^4 + s^3 + 2s^2 + 4s + 6 = 0
To determine the stability, we need to find the roots of these equations. If all the roots have negative real parts, the system is stable.
Analyzing the options:
a) The equation has a positive constant term (6), which indicates that at least one root will have a positive real part. Therefore, this equation does not result in stable operation.
b) The equation has a positive constant term (6), which indicates that at least one root will have a positive real part. Therefore, this equation does not result in stable operation.
c) The equation has a negative constant term (11), which indicates that all the roots will have negative real parts. Therefore, this equation results in stable operation.
d) The equation has a positive constant term (6) and a higher-order term (s^4), which indicates that at least one root will have a positive real part. Therefore, this equation does not result in stable operation.
Hence, the correct answer is option 'C': s^3 + 4s^2 + 10s + 11 = 0, which results in stable operation.
To determine the stability of a system, we need to analyze the roots of the characteristic equation. The roots represent the poles of the system transfer function and indicate the behavior of the system.
In this question, we are given four characteristic equations, and we need to identify the one that results in stable operation.
Let's analyze each equation one by one:
a) s^3 + 4s^2 + s + 6 = 0
b) s^3 + s^2 + 5s + 6 = 0
c) s^3 + 4s^2 + 10s + 11 = 0
d) s^4 + s^3 + 2s^2 + 4s + 6 = 0
To determine the stability, we need to find the roots of these equations. If all the roots have negative real parts, the system is stable.
Analyzing the options:
a) The equation has a positive constant term (6), which indicates that at least one root will have a positive real part. Therefore, this equation does not result in stable operation.
b) The equation has a positive constant term (6), which indicates that at least one root will have a positive real part. Therefore, this equation does not result in stable operation.
c) The equation has a negative constant term (11), which indicates that all the roots will have negative real parts. Therefore, this equation results in stable operation.
d) The equation has a positive constant term (6) and a higher-order term (s^4), which indicates that at least one root will have a positive real part. Therefore, this equation does not result in stable operation.
Hence, the correct answer is option 'C': s^3 + 4s^2 + 10s + 11 = 0, which results in stable operation.
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Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?
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Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?.
Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?.
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Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Which one of the following characteristic equations of result in the stable operation of the feedback system?a)s3 + 4s2 + s − 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s + 11 = 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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