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Consider the following characteristic equation of a system:
s3 + 2Ks2 + (K+ 2) s+ 4 = 0
Which one of the following is correct?
s3 + 2Ks2 + (K+ 2) s+ 4 = 0
Which one of the following is correct?
- a)The system is stable for all positive values of K.
- b)The system is unstable for all values of K.
- c)The system is stable for values of K > 0.73.
- d)The system is stable for value of K < 0.73.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the following characteristic equation of a system:s3+ 2Ks2+ (...
Given characteristic equation is,
s2 + 2Ks2 + (K + 2)s + 4 = 0
Routh’s array is:
For stability, 2K > 0 or K > 0
Now, K2 + 2K - 2 = 0 or, K = 0.73, -2.73
For K > 0.73, K2 + 2 K - 2 > 0
(since K should be > 0)
Hence, system will be stable if K > 0.73.
s2 + 2Ks2 + (K + 2)s + 4 = 0
Routh’s array is:
For stability, 2K > 0 or K > 0
Now, K2 + 2K - 2 = 0 or, K = 0.73, -2.73
For K > 0.73, K2 + 2 K - 2 > 0
(since K should be > 0)
Hence, system will be stable if K > 0.73.
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Community Answer
Consider the following characteristic equation of a system:s3+ 2Ks2+ (...
Understanding Stability in Control Systems
To determine the stability of the system described by the characteristic equation:
s^3 + 2Ks^2 + (K + 2)s + 4 = 0
we need to analyze the roots of this polynomial for varying values of K.
Routh-Hurwitz Stability Criterion
The Routh-Hurwitz criterion helps in assessing the stability of a system by checking the conditions on the coefficients of the characteristic polynomial. For the system to be stable, all roots must have negative real parts.
Formulating the Routh Array
1. Write down the coefficients:
- a0 = 1 (s^3)
- a1 = 2K (s^2)
- a2 = K + 2 (s^1)
- a3 = 4 (s^0)
2. Construct the Routh array and check the first column for sign changes, which indicates the number of roots with positive real parts.
Finding Stability Conditions
To ensure stability, all elements in the first column of the Routh array must be positive. This leads us to derive inequalities involving K:
- 2K > 0 implies K > 0
- (K + 2) > 0 implies K > -2
- 4 > 0 holds true for all K.
However, for K, we need to also ensure that the first column remains positive as we analyze K further.
Critical Value of K
Through the analysis, we find that the critical point for stability occurs around K = 0.73. At this point, the roots transition from having negative real parts to positive, indicating the boundary of stability.
Conclusion
Thus, the system is stable for K < 0.73="" and="" becomes="" unstable="" for="" k="" /> 0.73. Hence, the correct answer is:
C) The system is stable for values of K > 0.73.
To determine the stability of the system described by the characteristic equation:
s^3 + 2Ks^2 + (K + 2)s + 4 = 0
we need to analyze the roots of this polynomial for varying values of K.
Routh-Hurwitz Stability Criterion
The Routh-Hurwitz criterion helps in assessing the stability of a system by checking the conditions on the coefficients of the characteristic polynomial. For the system to be stable, all roots must have negative real parts.
Formulating the Routh Array
1. Write down the coefficients:
- a0 = 1 (s^3)
- a1 = 2K (s^2)
- a2 = K + 2 (s^1)
- a3 = 4 (s^0)
2. Construct the Routh array and check the first column for sign changes, which indicates the number of roots with positive real parts.
Finding Stability Conditions
To ensure stability, all elements in the first column of the Routh array must be positive. This leads us to derive inequalities involving K:
- 2K > 0 implies K > 0
- (K + 2) > 0 implies K > -2
- 4 > 0 holds true for all K.
However, for K, we need to also ensure that the first column remains positive as we analyze K further.
Critical Value of K
Through the analysis, we find that the critical point for stability occurs around K = 0.73. At this point, the roots transition from having negative real parts to positive, indicating the boundary of stability.
Conclusion
Thus, the system is stable for K < 0.73="" and="" becomes="" unstable="" for="" k="" /> 0.73. Hence, the correct answer is:
C) The system is stable for values of K > 0.73.
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Consider the following characteristic equation of a system:s3+ 2Ks2+ (K+ 2) s+ 4 = 0Which one of the following is correct?a)The system is stable for all positive values of K.b)The system is unstable for all values of K.c)The system is stable for values of K > 0.73.d)The system is stable for value of K < 0.73.Correct answer is option 'C'. Can you explain this answer?
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Consider the following characteristic equation of a system:s3+ 2Ks2+ (K+ 2) s+ 4 = 0Which one of the following is correct?a)The system is stable for all positive values of K.b)The system is unstable for all values of K.c)The system is stable for values of K > 0.73.d)The system is stable for value of K < 0.73.Correct 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 Consider the following characteristic equation of a system:s3+ 2Ks2+ (K+ 2) s+ 4 = 0Which one of the following is correct?a)The system is stable for all positive values of K.b)The system is unstable for all values of K.c)The system is stable for values of K > 0.73.d)The system is stable for value of K < 0.73.Correct 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 Consider the following characteristic equation of a system:s3+ 2Ks2+ (K+ 2) s+ 4 = 0Which one of the following is correct?a)The system is stable for all positive values of K.b)The system is unstable for all values of K.c)The system is stable for values of K > 0.73.d)The system is stable for value of K < 0.73.Correct answer is option 'C'. Can you explain this answer?.
Consider the following characteristic equation of a system:s3+ 2Ks2+ (K+ 2) s+ 4 = 0Which one of the following is correct?a)The system is stable for all positive values of K.b)The system is unstable for all values of K.c)The system is stable for values of K > 0.73.d)The system is stable for value of K < 0.73.Correct 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 Consider the following characteristic equation of a system:s3+ 2Ks2+ (K+ 2) s+ 4 = 0Which one of the following is correct?a)The system is stable for all positive values of K.b)The system is unstable for all values of K.c)The system is stable for values of K > 0.73.d)The system is stable for value of K < 0.73.Correct 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 Consider the following characteristic equation of a system:s3+ 2Ks2+ (K+ 2) s+ 4 = 0Which one of the following is correct?a)The system is stable for all positive values of K.b)The system is unstable for all values of K.c)The system is stable for values of K > 0.73.d)The system is stable for value of K < 0.73.Correct answer is option 'C'. Can you explain this answer?.
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