# Automatique by meiling Chen1 Lesson 11 Bode Diagram.

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automatique by meiling Chen1 Lesson 11 Bode Diagram

automatique by meiling Chen2 Viewpoints of analyzing control system behavior Routh-Hurwitz Root locus Bode diagram (plots) Nyquist plots Nicols plots Time domain

automatique by meiling Chen3 L.T.I system Magnitude:Phase: G(s) H(s) ＋ － Magnitude:Phase: Steady state response

automatique by meiling Chen4 Decade : Octave : Logarithmic coordinate dB

automatique by meiling Chen5 Case I : k Magnitude: Phase:

automatique by meiling Chen6 Case II : Magnitude: Phase:

automatique by meiling Chen7 Case III : Magnitude: Phase:

automatique by meiling Chen8 Case IV : Magnitude: Phase:

automatique by meiling Chen9 Case V : Magnitude: Phase:

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automatique by meiling Chen11 Case VI :

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automatique by meiling Chen13 Example : Example : page 6-24 Example : page 6-28

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automatique by meiling Chen15 n=[-3 -9] m=[1 –1 –1 –15 0] g2=tf(n,m) bode(g1,g2) g1=zpk([],[0 –2 -10],[1]) bode(g1) MATLAB Method g1 g2 g1 g2

automatique by meiling Chen16 Identification Example 6-39

automatique by meiling Chen17 Minimum phase system Type 0 : (i.e. n=0) 0dB/dec

automatique by meiling Chen18 Type I : (i.e. n=1) -20dB/dec -40dB/dec

automatique by meiling Chen19 Type 2 : (i.e. n=2) -40dB/dec -60dB/dec

automatique by meiling Chen20 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 systemStable 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 Relative stability

automatique by meiling Chen21 Open loop transfer function : Closed-loop transfer function : Open loop Stability  poles of in LHP Re Im RHP Closed-loop Stability  poles of in left side of (-1,0)

automatique by meiling Chen22 Gain crossover frequency: phase crossover frequency: P.M.>0 G.M.>0 Stable system

automatique by meiling Chen23 P.M.<0 G.M.<0 Stable system Unstable system

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