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According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative?
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According to the Routh-Hurwitz criterion, a system is stable if: ps: A...
Routh-Hurwitz Criterion for Stability
The Routh-Hurwitz criterion is a mathematical method used to determine the stability of a system. The criterion is based on the Routh array, which is a table of coefficients derived from the characteristic equation of the system. The Routh-Hurwitz criterion states that a system is stable if certain conditions are met. Let's take a look at these conditions.
The Routh Array
The Routh array is a table of coefficients derived from the characteristic equation of the system. The characteristic equation is a polynomial equation that describes the behavior of the system. The Routh array is constructed using the coefficients of this equation. The first row of the Routh array contains the coefficients of the highest order term of the polynomial equation, while the second row contains the coefficients of the second-highest order term, and so on. The last row of the Routh array contains the coefficients of the lowest order term.
The Conditions for Stability
The Routh-Hurwitz criterion states that a system is stable if the following conditions are met:
- All the elements in the first column of the Routh array are positive.
- None of the elements in the Routh array are negative.
- There are no sign changes in the first column of the Routh array.
Explanation
The first condition ensures that the system has no unstable poles in the right-half of the s-plane. The second condition ensures that the system has no poles in the right-half of the s-plane. The third condition ensures that the system has no poles on the imaginary axis. If any of these conditions are not met, the system is unstable.
Conclusion
In conclusion, the Routh-Hurwitz criterion is a mathematical method used to determine the stability of a system. The criterion is based on the Routh array, which is a table of coefficients derived from the characteristic equation of the system. A system is stable if all the elements in the first column of the Routh array are positive, none of the elements in the Routh array are negative, and there are no sign changes in the first column of the Routh array.
The Routh-Hurwitz criterion is a mathematical method used to determine the stability of a system. The criterion is based on the Routh array, which is a table of coefficients derived from the characteristic equation of the system. The Routh-Hurwitz criterion states that a system is stable if certain conditions are met. Let's take a look at these conditions.
The Routh Array
The Routh array is a table of coefficients derived from the characteristic equation of the system. The characteristic equation is a polynomial equation that describes the behavior of the system. The Routh array is constructed using the coefficients of this equation. The first row of the Routh array contains the coefficients of the highest order term of the polynomial equation, while the second row contains the coefficients of the second-highest order term, and so on. The last row of the Routh array contains the coefficients of the lowest order term.
The Conditions for Stability
The Routh-Hurwitz criterion states that a system is stable if the following conditions are met:
- All the elements in the first column of the Routh array are positive.
- None of the elements in the Routh array are negative.
- There are no sign changes in the first column of the Routh array.
Explanation
The first condition ensures that the system has no unstable poles in the right-half of the s-plane. The second condition ensures that the system has no poles in the right-half of the s-plane. The third condition ensures that the system has no poles on the imaginary axis. If any of these conditions are not met, the system is unstable.
Conclusion
In conclusion, the Routh-Hurwitz criterion is a mathematical method used to determine the stability of a system. The criterion is based on the Routh array, which is a table of coefficients derived from the characteristic equation of the system. A system is stable if all the elements in the first column of the Routh array are positive, none of the elements in the Routh array are negative, and there are no sign changes in the first column of the Routh array.
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According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative?
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According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative?.
According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for According to the Routh-Hurwitz criterion, a system is stable if: ps: A. All the elements in the first column of the Routh array are positive B. All the elements in the last row of the Routh array are positive C. All the elements in the first row of the Routh array are positive D. None of the elements in the Routh array are negative?.
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