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An open loop transfer function of a unity feedback control system has two finite zeros, two poles at origin and two pairs of complex conjugate poles. The slope of high frequency asymptote in Bode magnitude plot will be
  • a)
    +40 dB/decade
  • b)
    0 dB/decade
  • c)
    −40 dB/decade
  • d)
    −80 dB/decade
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
An open loop transfer function of a unity feedback control system has ...
No. of poles, n = 6
No. of zeros, m = 2
Slope of high frequency asymptote
= −20 (n−m)
= −20 (6−2)
= −80 dB/decade
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Most Upvoted Answer
An open loop transfer function of a unity feedback control system has ...
Given information:
- Open loop transfer function of a unity feedback control system
- Two finite zeros, two poles at origin and two pairs of complex conjugate poles

To find:
- Slope of high frequency asymptote in Bode magnitude plot

Solution:
1. Draw the Bode magnitude plot for the given transfer function.
- At high frequencies, the magnitude plot will be dominated by the complex conjugate poles.
- Each complex conjugate pole pair contributes a slope of -40 dB/decade.
- Therefore, the total slope due to complex conjugate poles will be -80 dB/decade.

2. Determine the contribution of finite zeros and poles at origin.
- Finite zeros do not affect the slope of the magnitude plot.
- Poles at origin contribute a slope of -20 dB/decade each.
- Therefore, the total slope due to poles at origin will be -40 dB/decade.

3. Add the contributions of all the components to get the total slope.
- Slope of high frequency asymptote = slope due to complex conjugate poles + slope due to poles at origin
- Slope of high frequency asymptote = -80 dB/decade + (-40 dB/decade)
- Slope of high frequency asymptote = -120 dB/decade

Therefore, the correct answer is option D, 80 dB/decade.
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An open loop transfer function of a unity feedback control system has two finite zeros, two poles at origin and two pairs of complex conjugate poles. The slope of high frequency asymptote in Bode magnitude plot will bea)+40 dB/decadeb)0 dB/decadec)−40 dB/decaded)−80 dB/decadeCorrect answer is option 'D'. Can you explain this answer?
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