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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

Lesson 11

Bode Diagram

automatique by meiling Chen


Viewpoints of analyzing control system behavior
Viewpoints of analyzing control system behavior

  • Routh-Hurwitz

  • Root locus

  • Bode diagram (plots)

  • Nyquist plots

  • Nicols plots

  • Time domain

automatique by meiling Chen


G(s)

H(s)

L.T.I system

Magnitude:

Phase:

Steady state response

Magnitude:

Phase:

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Decade :

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 :

Example : page 6-24

Example : page 6-28

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MATLAB Method

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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Identification

Example 6-39

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Minimum phase system

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

0dB/dec

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Type I : (i.e. n=1)

-20dB/dec

-40dB/dec

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Type 2 : (i.e. n=2)

-40dB/dec

-60dB/dec

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Relative stability

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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Open loop transfer function :

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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Gain crossover frequency:

phase crossover frequency:

G.M.>0

Stable system

P.M.>0

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G.M.<0

Unstable system

Stable system

P.M.<0

Unstable system

automatique by meiling Chen



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