1. Green Team Speed 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. Speed System Diagram SRC 1 ST 1 Motor / Generator SCZ 1

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

6. Step Response Input-Output Relationship Ke -t 0 M(t) Input (%) C(t) Output (RPM) τ – Time Constant (s) = 0.2 t 0 – Dead Time (s) = 0.1 K – Gain (RPM/%) = 17

7. Frequency Response Input-Output Relationship Ke -t 0 M(t) Input (%) C(t) Output (RPM) τ – Time Constant (s) t 0 – Dead Time (s) K – Gain (RPM/%)

8. tau - t 0 - tau -0.2 s t 0 – 0.1 s

10. Step and Frequency Response Experiments Conclusions  FOPDT Parameters  = 0.2 s t o = 0.1 s K = 17 RPM/%  order about 1st  f u = 3.5 Hz  K cu = 0.3%/RPM

11. Feedback Controller

12. Characteristic Equation (CE) Padés Approximation

13. Control Gain Locations K C-CD =0.02 %/RPM K CU =0.3 %/RPM K QD =0.19 %/RPM Over-damped Under-dampedUnstable f u = 24/2 Π = 3.82 Hz

14. Root Locus Conclusions  Ultimate K cu = 0.3  Quarter Decay K c = 0.19  Critically Damping K CD = 0.02  Underdamped 0.02<K c <0.3  Overdamped 0<K c <0.02 *all units are % / RPM

15. Determination of f u  Bode plots f u = 3.5 Hz  Characteristic Equation (CE) f u = 4 Hz  Root Locus f u = 3.8 Hz

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

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

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

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

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

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

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

29. Set Point Output SIW 11-5-05

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

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

32. Set Point Output SIW 11-5-05

33. could not be determined

34. Model vs. Experimental  Decay Ratio  Settling  Offset

37. FVT = delta R*(1-K C K/(1+K C K))

38. Conclusions  Low K c values Model and experimental responses are analogous  Higher K c values Experimental responses never settle  Recommended K c = 0.19 (%/RPM) High offset (75 RPM)

39. Proportional-Integral Feedback Controller