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# Lesson 11 - PowerPoint PPT Presentation

Lesson 11. Bode Diagram. Viewpoints of analyzing control system behavior. Routh-Hurwitz Root locus Bode diagram (plots) Nyquist plots Nicols plots Time domain. G(s). ＋. －. H(s). L.T.I system. Magnitude:. Phase:. Steady state response. Magnitude:. Phase:. Decade :. Octave :.

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### Lesson 11

Bode Diagram

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• Routh-Hurwitz

• Root locus

• Bode diagram (plots)

• Nyquist plots

• Nicols plots

• Time domain

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H(s)

L.T.I system

Magnitude:

Phase:

Magnitude:

Phase:

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Octave :

Logarithmic coordinate

dB

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Case I : k

Magnitude:

Phase:

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Case II :

Magnitude:

Phase:

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Case III :

Magnitude:

Phase:

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Case IV :

Magnitude:

Phase:

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Case V :

Magnitude:

Phase:

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Case VI :

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Example : page 6-24

Example : page 6-28

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g1=zpk([],[0 –2 -10],[1])

bode(g1)

g1

g2

g2

n=[-3 -9]

m=[1 –1 –1 –15 0]

g2=tf(n,m)

bode(g1,g2)

g1

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Example 6-39

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Type 0 : (i.e. n=0)

0dB/dec

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-20dB/dec

-40dB/dec

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-40dB/dec

-60dB/dec

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A transfer function is called minimum phase when all the poles and zeros are LHP and non-minimum-phase when there are RHP poles or zeros.

Minimum phase system

Stable

The gain margin (GM) is the distance on the bode magnitude plot from the amplitude at the phase crossover frequency up to the 0 dB point. GM=-(dB of GH measured at the phase crossover frequency)

The phase margin (PM) is the distance from -180 up to the phase at the gain crossover frequency. PM=180+phase of GH measured at the gain crossover frequency

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Closed-loop transfer function :

Open loop Stability  poles of in LHP

Im

Closed-loop Stability 

poles of in left side of (-1,0)

RHP

Re

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phase crossover frequency:

G.M.>0

Stable system

P.M.>0

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Unstable system

Stable system

P.M.<0

Unstable system

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