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The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system is 
  • a)
    4 and (-4,0)
  • b)
    3 and (-12,0)
  • c)
    -4 and (-4,0)
  • d)
    -3 and (-12,0)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The open loop transfer function of the feedback control system is give...
Answer: a
Explanation: Number of Poles = 5
Zeroes =1
Asymptotes =P-Z =4
Centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z
Centroid = -4-4-5-6+3/4 =-4.
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Most Upvoted Answer
The open loop transfer function of the feedback control system is give...
Solution:

Root Locus:

Root locus is a graphical representation of the closed loop poles of a feedback control system as a function of a system parameter (usually gain). Root locus gives a clear understanding of the stability and performance characteristics of the system.

Given open loop transfer function is G(s) =K(s 3)/s(s 4)2(s 5)(s 6)

The closed-loop transfer function is given by

T(s) = G(s) / (1 + G(s)H(s))

Where H(s) is the feedback transfer function, which is 1 in this case.

T(s) = K(s 3) / [s(s 4)2(s 5)(s 6) + K(s 3)]

Root locus of closed-loop system:

1. Number of asymptotes:

The number of asymptotes of the root locus is given by

N = P - Z

Where P is the number of poles of the transfer function in the right half of the s-plane and Z is the number of zeros of the transfer function in the right half of the s-plane.

In this case, there are no poles or zeros in the right half of the s-plane.

Therefore, N = 0.

Number of asymptotes is 4.

2. Centroid of asymptotes:

The centroid of the asymptotes is given by

σ = (sum of poles - sum of zeros) / N

In this case, there are no zeros in the transfer function. The poles are at s = 0, s = -4, s = -5, and s = -6.

Therefore, the sum of poles = 0 - 4 - 5 - 6 = -15

σ = (-15) / 4 = -3.75

Centroid of asymptotes is (-3.75, 0).

Therefore, the correct answer is option A.
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The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system isa)4 and (-4,0)b)3 and (-12,0)c)-4 and (-4,0)d)-3 and (-12,0)Correct answer is option 'A'. Can you explain this answer?
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The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system isa)4 and (-4,0)b)3 and (-12,0)c)-4 and (-4,0)d)-3 and (-12,0)Correct answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system isa)4 and (-4,0)b)3 and (-12,0)c)-4 and (-4,0)d)-3 and (-12,0)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system isa)4 and (-4,0)b)3 and (-12,0)c)-4 and (-4,0)d)-3 and (-12,0)Correct answer is option 'A'. Can you explain this answer?.
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