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Green Team Speed System

Green Team Speed System. Proportional Only Controller Design and Experimental 11-09-05 Dustin Fraley DeAndre Strong Stephanie Wilson. Outline. Description of Speed System Previous work Step Response Frequency Response Root Locus Proportional only controller response curves Model

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Green Team Speed System

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  1. Green TeamSpeed System Proportional Only Controller Design and Experimental 11-09-05 Dustin Fraley DeAndre Strong Stephanie Wilson

  2. Outline • Description of Speed System • Previous work • Step Response • Frequency Response • Root Locus • Proportional only controller response curves • Model • Experimental • Results • Conclusions

  3. / Motor SRC SCZ 1 Generator 1 ST 1 Speed System Diagram

  4. M(t) C(t) Speed System Input (%) Output (RPM) SSOC Input-Output Relationship

  5. M(t) C(t) Ke-t0 Input (%) Output (RPM) Step Response Input-Output Relationship τ– Time Constant (s) = 0.2 t0 – Dead Time (s) = 0.1 K – Gain (RPM/%) = 17

  6. M(t) C(t) Ke-t0 Input (%) Output (RPM) Frequency Response Input-Output Relationship τ – Time Constant (s) t0 – Dead Time (s) K – Gain (RPM/%)

  7. tau - t0 - tau -0.2 s t0 – 0.1 s

  8. Step and Frequency Response Experiments Conclusions • FOPDT Parameters • t = 0.2 s • to = 0.1 s • K = 17 RPM/% • order about 1st • fu = 3.5 Hz • Kcu= 0.3%/RPM

  9. Feedback Controller

  10. Characteristic Equation (CE) Padés Approximation

  11. Control Gain Locations fu = 24/2Π= 3.82 Hz KC-CD=0.02 %/RPM KQD=0.19 %/RPM KCU=0.3 %/RPM Over-damped Under-damped Unstable

  12. Root Locus Conclusions • Ultimate Kcu= 0.3 • Quarter Decay Kc = 0.19 • Critically Damping KCD = 0.02 • Underdamped 0.02<Kc<0.3 • Overdamped 0<Kc<0.02 *all units are % / RPM

  13. Determination of fu • Bode plots • fu = 3.5 Hz • Characteristic Equation (CE) • fu = 4 Hz • Root Locus • fu = 3.8 Hz

  14. P-only Controller Analysis Model FOPDT Parameters • t = 0.2 s • to = 0.1 s • K = 17 RPM/% • Values found for • Ultimate (Marginal Stability) • Quarter Decay • Critical Damping • Overdamped

  15. Set Point Output Decay Ratio – 1 Oscillatory Settling Time – Never Offset - CBD

  16. Set Point Output Decay Ratio – 0.25 Oscillatory Settling Time – 1.25 s Offset – 71 RPM

  17. Set Point Output Decay Ratio – 0 Monotonic Settling Time – 0.5 s Offset – 219 RPM

  18. Set Point Output Decay Ratio – 0 Monotonic Settling Time – 0.5 s Offset – 230 RPM

  19. Controller Operating Curve for Model m bar = 63% r(t) = 1100 RPM delta r = 300 RPM

  20. P-only Controller Analysis Experimental FOPDT Parameters • t = 0.2 s • to = 0.1 s • K = 17 RPM/% • Values found for • Ultimate (Marginal Stability) • Quarter Decay • Critical Damping • Overdamped

  21. Set Point Output SIW 11-5-05

  22. Set Point Output RPM SIW 11-5-05

  23. Set Point Output RPM SIW 11-5-05

  24. Set Point Output SIW 11-5-05

  25. could not be determined

  26. Model vs. Experimental • Decay Ratio • Settling • Offset

  27. FVT = delta R*(1-KCK/(1+KCK))

  28. Conclusions • Low Kc values • Model and experimental responses are analogous • Higher Kc values • Experimental responses never settle • Recommended Kc = 0.19 (%/RPM) • High offset (75 RPM)

  29. Proportional-Integral Feedback Controller

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