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In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of
1. a pair of real roots with opposite sign
2. complex conjugate roots on the imaginary axis
3. a pair of complex conjugate roots with opposite real parts
Which of the above statements are correct?
- a)Only 2
- b)2 and 3
- c)Only 3
- d)1, 2 and 3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In the formation of Routh-Hurwitz array for a polynomial, all the elem...
Routh-Hurwitz Stability Criterion: It is used to test the stability of an LTI system.
The characteristic equation for a given open-loop transfer function G(s) is
1 + G(s) H(s) = 0
According to the Routh tabulation method,
The system is said to be stable if there are no sign changes in the first column of the Routh array
The number of poles lies on the right half of s plane = number of sign changes
A row of zeros in a Routh table:
This situation occurs when the characteristic equation has
- a pair of real roots with opposite sign (±a)
- complex conjugate roots on the imaginary axis (± jω)
- a pair of complex conjugate roots with opposite real parts (-a ± jb, a ± jb)
The procedure to overcome this as follows:
- Form the auxiliary equation from the preceding row to the row of zeros
- Complete Routh array by replacing the zero row with the coefficients obtained by differentiating the auxiliary equation.
- The roots of the auxiliary equation are also the roots of the characteristic equation.
- The roots of the auxiliary equation occur in pairs and are of the opposite sign of each other.
- The auxiliary equation is always even in order.
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In the formation of Routh-Hurwitz array for a polynomial, all the elem...
Real roots with opposite sign:
- When all elements of a row in the Routh-Hurwitz array are zero, it indicates that the corresponding polynomial has a pair of real roots with opposite signs.
- This means that the polynomial has one root with a positive value and the other root with a negative value.
Complex conjugate roots on the imaginary axis:
- If the entire row in the Routh-Hurwitz array is zero, it does not indicate the presence of complex conjugate roots on the imaginary axis.
- The premature termination of the array does not provide information about the location of complex roots on the imaginary axis.
Complex conjugate roots with opposite real parts:
- The presence of a pair of complex conjugate roots with opposite real parts can be inferred from the premature termination of the Routh-Hurwitz array.
- This situation occurs when all elements of a row in the array are zero, suggesting the existence of complex roots with opposite real parts.
Therefore, the correct answer is option 'D', which includes all three statements. The Routh-Hurwitz array can provide valuable information about the nature and location of roots of a polynomial, helping in analyzing the stability of a system in control theory.
- When all elements of a row in the Routh-Hurwitz array are zero, it indicates that the corresponding polynomial has a pair of real roots with opposite signs.
- This means that the polynomial has one root with a positive value and the other root with a negative value.
Complex conjugate roots on the imaginary axis:
- If the entire row in the Routh-Hurwitz array is zero, it does not indicate the presence of complex conjugate roots on the imaginary axis.
- The premature termination of the array does not provide information about the location of complex roots on the imaginary axis.
Complex conjugate roots with opposite real parts:
- The presence of a pair of complex conjugate roots with opposite real parts can be inferred from the premature termination of the Routh-Hurwitz array.
- This situation occurs when all elements of a row in the array are zero, suggesting the existence of complex roots with opposite real parts.
Therefore, the correct answer is option 'D', which includes all three statements. The Routh-Hurwitz array can provide valuable information about the nature and location of roots of a polynomial, helping in analyzing the stability of a system in control theory.
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In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?a)Only 2b)2 and 3c)Only 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?a)Only 2b)2 and 3c)Only 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?a)Only 2b)2 and 3c)Only 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?.
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?a)Only 2b)2 and 3c)Only 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?a)Only 2b)2 and 3c)Only 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?a)Only 2b)2 and 3c)Only 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?.
Solutions for In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of1. a pair of real roots with opposite sign2. complex conjugate roots on the imaginary axis3. a pair of complex conjugate roots with opposite real partsWhich of the above statements are correct?a)Only 2b)2 and 3c)Only 3d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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