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Lesson 11

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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  1. Lesson 11 Bode Diagram automatique by meiling Chen

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

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

  4. Decade : Octave : Logarithmic coordinate dB automatique by meiling Chen

  5. Case I : k Magnitude: Phase: automatique by meiling Chen

  6. Case II : Magnitude: Phase: automatique by meiling Chen

  7. Case III : Magnitude: Phase: automatique by meiling Chen

  8. Case IV : Magnitude: Phase: automatique by meiling Chen

  9. Case V : Magnitude: Phase: automatique by meiling Chen

  10. automatique by meiling Chen

  11. Case VI : automatique by meiling Chen

  12. automatique by meiling Chen

  13. Example : Example : page 6-24 Example : page 6-28 automatique by meiling Chen

  14. automatique by meiling Chen

  15. 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

  16. Identification Example 6-39 automatique by meiling Chen

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

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

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

  20. 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

  21. 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

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

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

  24. automatique by meiling Chen

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