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If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number of
- a)breakaway point
- b)unstable poles
- c)separate root loci
- d)asymptotes
Correct answer is option 'D'. Can you explain this answer?
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If the open-loop transfer function is a ratio of a numerator polynomia...
n-m
Difference between poles and zeros gives number of asymptotes
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If the open-loop transfer function is a ratio of a numerator polynomia...
The open-loop transfer function of a control system is the ratio of the output of the system to the input, without any feedback. It is represented as a ratio of two polynomials, with the numerator polynomial of degree m and the denominator polynomial of degree n.
In this context, the integer (n-m) represents the difference in degrees between the numerator and denominator polynomials. It has a specific significance in control systems and is related to the behavior of the system.
Explanation:
1. Open-loop Transfer Function: The open-loop transfer function is given by the ratio of the numerator polynomial to the denominator polynomial. It represents the relationship between the input and the output of the system in the absence of feedback.
2. Degree of Polynomials: The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the numerator polynomial has a degree of m and the denominator polynomial has a degree of n.
3. Difference in Degrees: The integer (n-m) represents the difference in degrees between the numerator and denominator polynomials. It is calculated by subtracting the degree of the numerator from the degree of the denominator.
4. Asymptotes: In control systems, the open-loop transfer function can have asymptotes. Asymptotes are lines that the root locus follows as the gain of the system approaches infinity. The number of asymptotes is equal to the difference in degrees between the numerator and denominator polynomials.
5. Interpretation: The integer (n-m) represents the number of asymptotes in the root locus plot. It indicates the number of straight lines that the root locus follows as the gain of the system increases. These asymptotes provide valuable information about the stability and behavior of the system.
Therefore, the correct answer is option 'D' - asymptotes. The integer (n-m) in the open-loop transfer function represents the number of asymptotes in the root locus plot.
In this context, the integer (n-m) represents the difference in degrees between the numerator and denominator polynomials. It has a specific significance in control systems and is related to the behavior of the system.
Explanation:
1. Open-loop Transfer Function: The open-loop transfer function is given by the ratio of the numerator polynomial to the denominator polynomial. It represents the relationship between the input and the output of the system in the absence of feedback.
2. Degree of Polynomials: The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the numerator polynomial has a degree of m and the denominator polynomial has a degree of n.
3. Difference in Degrees: The integer (n-m) represents the difference in degrees between the numerator and denominator polynomials. It is calculated by subtracting the degree of the numerator from the degree of the denominator.
4. Asymptotes: In control systems, the open-loop transfer function can have asymptotes. Asymptotes are lines that the root locus follows as the gain of the system approaches infinity. The number of asymptotes is equal to the difference in degrees between the numerator and denominator polynomials.
5. Interpretation: The integer (n-m) represents the number of asymptotes in the root locus plot. It indicates the number of straight lines that the root locus follows as the gain of the system increases. These asymptotes provide valuable information about the stability and behavior of the system.
Therefore, the correct answer is option 'D' - asymptotes. The integer (n-m) in the open-loop transfer function represents the number of asymptotes in the root locus plot.
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If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number ofa)breakaway pointb)unstable polesc)separate root locid)asymptotesCorrect answer is option 'D'. Can you explain this answer?
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If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number ofa)breakaway pointb)unstable polesc)separate root locid)asymptotesCorrect 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 If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number ofa)breakaway pointb)unstable polesc)separate root locid)asymptotesCorrect 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 If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number ofa)breakaway pointb)unstable polesc)separate root locid)asymptotesCorrect answer is option 'D'. Can you explain this answer?.
If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number ofa)breakaway pointb)unstable polesc)separate root locid)asymptotesCorrect 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 If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number ofa)breakaway pointb)unstable polesc)separate root locid)asymptotesCorrect 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 If the open-loop transfer function is a ratio of a numerator polynomial of degree 'm' and a denominator polynomial of degree 'n' then the integer (n-m) represents the number ofa)breakaway pointb)unstable polesc)separate root locid)asymptotesCorrect answer is option 'D'. Can you explain this answer?.
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