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Lesson 9

Automatic control 2. Analysis. Lesson 9. Root locus. Poles and zeros. zeros poles. pole. zero. Closed-loop transfer function :. Negative damped. Undamped. Underdamped. Critically damped. Overdamped. Root locus. k. G(s). ＋. －. H(s). poles. Open loop transfer function.

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Lesson 9

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  1. Automatic control 2. Analysis Lesson 9 Root locus automatic control by meiling CHEN

  2. Poles and zeros zeros poles pole zero automatic control by meiling CHEN

  3. Closed-loop transfer function : automatic control by meiling CHEN

  4. automatic control by meiling CHEN

  5. automatic control by meiling CHEN

  6. Negative damped Undamped Underdamped Critically damped Overdamped automatic control by meiling CHEN

  7. Root locus k G(s) ＋ － H(s) poles automatic control by meiling CHEN

  8. Open loop transfer function Using open loop transfer function + system parameters to analyze the closed-loop system response Draw the s-plan root locus automatic control by meiling CHEN

  9. Root locus properties: • The locus segments are symmetrical about the real axis. • (iii) automatic control by meiling CHEN

  10. each locus from poles to zeros for excess zeros or poles, locus segments extend from infinity. if Root locus construction (i) Loci Branches (1) (2) automatic control by meiling CHEN

  11. (ii) Real axis segments Poles + zeros = odd Poles + zeros = even automatic control by meiling CHEN

  12. (iii) Asymptotic angles automatic control by meiling CHEN

  13. (iv) Centroid of the asymptotes example Zero : 0 Poles: -2, -3+j3, -3-j3 automatic control by meiling CHEN

  14. (v) Breakaway and entry points example The characteristic function of closed loop system automatic control by meiling CHEN

  15. (vi) Angle of departure and approach example Angle of departure from the pole: automatic control by meiling CHEN

  16. example Angle of approach to the zero: automatic control by meiling CHEN

  17. (vii) The cross point of root locus and Im-axis example The characteristic function of closed loop system: automatic control by meiling CHEN

  18. + - (i) (iii) (ii) automatic control by meiling CHEN

  19. automatic control by meiling CHEN

  20. MATLAB method gh=zpk([],[0 –2 -10],[1]) rltool(gh) n=[-3 -9] m=[1 –1 –1 –15 0] gh=tf(n,m) rltool(gh) automatic control by meiling CHEN

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