Bode Plots

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• Bode Plots

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Advantage of Working with Frequency Response in
terms of Bode Plots

• Bode plots of systems in series (or tandem)
  simply add which is quite convenient.
• Bodes important phase-gain relationship is given
  in terms of logarithms of phase and gain.

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Advantage of Working with Frequency Response in
terms of Bode Plots

• A much wider range of system behavior (from low
  to high frequency behavior) can be displayed on a
  single plot.
• Bode plots can be determined experimentally.
• Dynamic compensator design can be based entirely
  on Bode plots.

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Bode Form of the Transfer Function

• Bode form all one
• K0 is transfer function magnitude at very low
  frequencies.

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Classes of terms of transfer functions

• (1)
• (2)
• (3)

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Class1singularities at the origin
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Class2 first-order term

• a) For
• b) For
• we call the break point
• below magnitude is approximately constant 1
• above magnitude is like class 1

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Exp
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phase

• a) For
• b) For
• c) For

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Exp
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Class3second order term

• Break point
• Peak amplitude
• magnitude change slop 40dB or -40dB
• phase change 1800 or -1800

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Matlabs Bode Plots

• bode(num,den)

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Example
U0sin?t
Y(t)
G(s)
L
1/(s2s3)
U0 ?/(s2 ?2)
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Result (response of G(s)1/(s2s3)to sint )
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Example

• KG110/s(s20.4s4)
• KG20.01(s20.01s1)/s2(s2/4)0.02(s/2)1

• numG10
• denG1 0.4 4 0
• bode(numG,denG)

• numG0.011 0.01 1
• denG0.25 0.01 1 0 0
• bode(numG,denG)