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LAG COMPENSATOR DESIGN

LAG COMPENSATOR DESIGN. Bode Diagrams. 20. 0. -20. -40. -60. Phase (deg); Magnitude (dB). -100. -150. -200. -180 o. -250. -1. 0. 1. 10. 10. 10. Frequency (rad/sec). Idea:. ω g. Shift gain crossover left. by pulling gain down. without changing low freq.

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LAG COMPENSATOR DESIGN

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  1. LAG COMPENSATOR DESIGN 10.4 Phase-Lag Compensation

  2. Bode Diagrams 20 0 -20 -40 -60 Phase (deg); Magnitude (dB) -100 -150 -200 -180o -250 -1 0 1 10 10 10 Frequency (rad/sec) Idea: ωg Shift gain crossover left by pulling gain down without changing low freq. Using a phase-lag compensator PM PM also introduces lagging phase 10.4 Phase-Lag Compensation

  3. Thus Must introduce a lag compensator such that Sufficient amount of attenuation is obtained at the desired frequency while keeping the phase effects small 10.4 Phase-Lag Compensation

  4. -20loga 0 dB -1/T -1/aT ωm 0O Properties of phase-lag compensator a<1 |Gc|dB Attenuation is “almost” -20loga Phase is “almost” zero at “high” frequencies Gc 10.4 Phase-Lag Compensation

  5. Procedure: Specs: steady-state error & phase margin Determine the gain compensation for desired st.st. error 1 K 10.4 Phase-Lag Compensation

  6. |KGH|dB 0 dB KGH 180o Find the frequency yielding sufficient phase 20 log a ω’g ω’g Determine the necessary attenuation Hence calculate “a” ΦD a 20loga=|KGH(jω’g)| 10.4 Phase-Lag Compensation

  7. |KGH|dB 0 dB 1/a 1 decade KGH 180o Place the zero at 1/10 of (a decade below) ’g ω’g Place the pole at 1/a of the zero 10.4 Phase-Lag Compensation

  8. 10.4 Phase-Lag Compensation

  9. |KGH|dB 0 dB KGH 180o Draw Bode for KGcGH ω’g 10.4 Phase-Lag Compensation

  10. 20 log a D Check and modify as necessary! 10.4 Phase-Lag Compensation

  11. FAILS IF Gain A LARGE a VALUE IS REQUIRED 20 log a Phase OBSERVE! 10.4 Phase-Lag Compensation

  12. 20 log a ’g D FAILS IF Gain GAIN IS STEEP MEANS LARGE a Phase 10.4 Phase-Lag Compensation

  13. ’g D FAILS IF PHASE IS FLAT Gain MEANS LARGE a Phase 10.4 Phase-Lag Compensation

  14. Phase D BEWARE ! MAY CAUSE STABILITY PROBLEMS ! 10.4 Phase-Lag Compensation

  15. End of Section Next section Restart section Restart chapter i The End General index End show 10.4 Phase-Lag Compensation

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