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Lesson 11

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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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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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automatique by meiling Chen

Case VI :

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automatique by meiling Chen

Example :

Example : page 6-24

Example : page 6-28

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automatique by meiling Chen

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

automatique by meiling Chen