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Determine the stability range of k for a feedback control system having characteristic equation -
s4 + 2s3 + 10s2 + (k − 10)s + k = 0
s4 + 2s3 + 10s2 + (k − 10)s + k = 0
- a)28 > k > 5
- b)13.1 > k > 22.9
- c)13.1 < k < 22.9
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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Determine the stability range of k for a feedback control system havin...
Concept:
Routh-Hurwitz Stability Criterion
The necessary condition is that the coefficients of the characteristic polynomial should be positive. This implies that all the roots of the characteristic equation should have negative real parts.
The sufficient condition is that all the elements of the first column of the Routh array should have the same sign. This means that all the elements of the first column of the Routh array should be either positive or negative.
Calculation:
Given;
Characteristic equation:
s4 + 2s3 + 10s2 + (k − 10)s + k = 0
For the system to be stable:
The necessary condition is that the coefficients of the characteristic polynomial should be positive.
(K-10) > 0
K > 10
The sufficient condition is that all the elements of the first column of the Routh array should have the same sign. This means that all the elements of the first column of the Routh array should be either positive or negative.
Condition: (K > 10) ∩ (K < 13.10) ∩ (K < 22.89)
Pictorially
In the shaded region all the conditions will be satisfy
Condition for stability: (10 < K < 13.10)
Routh-Hurwitz Stability Criterion
The necessary condition is that the coefficients of the characteristic polynomial should be positive. This implies that all the roots of the characteristic equation should have negative real parts.
The sufficient condition is that all the elements of the first column of the Routh array should have the same sign. This means that all the elements of the first column of the Routh array should be either positive or negative.
Calculation:
Given;
Characteristic equation:
s4 + 2s3 + 10s2 + (k − 10)s + k = 0
For the system to be stable:
The necessary condition is that the coefficients of the characteristic polynomial should be positive.
(K-10) > 0
K > 10
The sufficient condition is that all the elements of the first column of the Routh array should have the same sign. This means that all the elements of the first column of the Routh array should be either positive or negative.
Condition: (K > 10) ∩ (K < 13.10) ∩ (K < 22.89)
Pictorially
In the shaded region all the conditions will be satisfy
Condition for stability: (10 < K < 13.10)
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Determine the stability range of k for a feedback control system havin...
- 6k)s - 20k = 0.
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Determine the stability range of k for a feedback control system having characteristic equation -s4 + 2s3 + 10s2 + (k − 10)s + k = 0a)28 > k > 5b)13.1 > k > 22.9c)13.1 < k < 22.9d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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Determine the stability range of k for a feedback control system having characteristic equation -s4 + 2s3 + 10s2 + (k − 10)s + k = 0a)28 > k > 5b)13.1 > k > 22.9c)13.1 < k < 22.9d)None of the aboveCorrect answer is option 'D'. 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 Determine the stability range of k for a feedback control system having characteristic equation -s4 + 2s3 + 10s2 + (k − 10)s + k = 0a)28 > k > 5b)13.1 > k > 22.9c)13.1 < k < 22.9d)None of the aboveCorrect answer is option 'D'. 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 Determine the stability range of k for a feedback control system having characteristic equation -s4 + 2s3 + 10s2 + (k − 10)s + k = 0a)28 > k > 5b)13.1 > k > 22.9c)13.1 < k < 22.9d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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