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Find the number of asymptotes for the given open-loop transfer function of a unity feedback system:
G(s) = ((s + 2) (s+3) (s + 4)) / ((s + 5) (s+6) (s + 1))
- a)1
- b)0
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Find the number of asymptotes for the given open-loop transfer functio...
Solution:
The number of asymptotes of a transfer function is equal to the number of poles minus the number of zeros at infinity.
In this given transfer function, the degree of the numerator is 3 and the degree of the denominator is also 3.
Therefore, the transfer function can be written as:
G(s) = (s^2 + 2s + 3) / (s^2 + 6s + 5)
The poles of the transfer function are the roots of the denominator polynomial, which are s = -1 and s = -5.
The zeros of the transfer function are the roots of the numerator polynomial, which are complex conjugate pairs.
Since the degrees of the numerator and denominator are the same, there are no zeros at infinity.
Therefore, the number of asymptotes is:
Number of asymptotes = Number of poles - Number of zeros at infinity
= 2 - 0
= 2
Hence, the correct option is B) 0.
The number of asymptotes of a transfer function is equal to the number of poles minus the number of zeros at infinity.
In this given transfer function, the degree of the numerator is 3 and the degree of the denominator is also 3.
Therefore, the transfer function can be written as:
G(s) = (s^2 + 2s + 3) / (s^2 + 6s + 5)
The poles of the transfer function are the roots of the denominator polynomial, which are s = -1 and s = -5.
The zeros of the transfer function are the roots of the numerator polynomial, which are complex conjugate pairs.
Since the degrees of the numerator and denominator are the same, there are no zeros at infinity.
Therefore, the number of asymptotes is:
Number of asymptotes = Number of poles - Number of zeros at infinity
= 2 - 0
= 2
Hence, the correct option is B) 0.
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Community Answer
Find the number of asymptotes for the given open-loop transfer functio...
The number of asymptotes in a given system is equal to the number of branches approaching infinity. So, the formula to calculate the number of asymptotes is P -Z. Here, P and Z represent the poles and zeroes.
We know that poles and zeroes are calculated by equating the denominator and numerator to zero. So, for the given open-loop transfer function, we get:
P = 3
Z = 3
So, the number of zeroes at infinity = 3 - 3 = 0
Hence, the correct answer is an option (b).
P = 3
Z = 3
So, the number of zeroes at infinity = 3 - 3 = 0
Hence, the correct answer is an option (b).
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Find the number of asymptotes for the given open-loop transfer function of a unity feedback system:G(s) = ((s + 2) (s+3) (s + 4)) / ((s + 5) (s+6) (s + 1))a)1b)0c)2d)3Correct answer is option 'B'. Can you explain this answer?
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