Lesson 11
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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

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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


Lesson 11

G(s)

H(s)

L.T.I system

Magnitude:

Phase:

Steady state response

Magnitude:

Phase:

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Lesson 11

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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automatique by meiling Chen


Lesson 11

Example :

Example : page 6-24

Example : page 6-28

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Lesson 11

automatique by meiling Chen


Lesson 11

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

automatique by meiling Chen


Lesson 11

Identification

Example 6-39

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Lesson 11

Minimum phase system

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

0dB/dec

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Lesson 11

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

-20dB/dec

-40dB/dec

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Lesson 11

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

-40dB/dec

-60dB/dec

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Lesson 11

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

automatique by meiling Chen


Lesson 11

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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Lesson 11

Gain crossover frequency:

phase crossover frequency:

G.M.>0

Stable system

P.M.>0

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Lesson 11

G.M.<0

Unstable system

Stable system

P.M.<0

Unstable system

automatique by meiling Chen


Lesson 11

automatique by meiling Chen


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