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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

slide3

G(s)

H(s)

L.T.I system

Magnitude:

Phase:

Steady state response

Magnitude:

Phase:

automatique by meiling Chen

slide4

Decade :

Octave :

Logarithmic coordinate

dB

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slide5

Case I : k

Magnitude:

Phase:

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slide6

Case II :

Magnitude:

Phase:

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slide7

Case III :

Magnitude:

Phase:

automatique by meiling Chen

slide8

Case IV :

Magnitude:

Phase:

automatique by meiling Chen

slide9

Case V :

Magnitude:

Phase:

automatique by meiling Chen

slide11

Case VI :

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slide13

Example :

Example : page 6-24

Example : page 6-28

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slide15

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

slide16

Identification

Example 6-39

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slide17

Minimum phase system

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

0dB/dec

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slide18

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

-20dB/dec

-40dB/dec

automatique by meiling Chen

slide19

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

-40dB/dec

-60dB/dec

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slide20

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

slide21

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

automatique by meiling Chen

slide22

Gain crossover frequency:

phase crossover frequency:

G.M.>0

Stable system

P.M.>0

automatique by meiling Chen

slide23

G.M.<0

Unstable system

Stable system

P.M.<0

Unstable system

automatique by meiling Chen

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