1. Flow Rate Control System Proportional Only Controller April 2, 2006 U.T.C. Engineering 329

2. Yellow Team Jimy George Jeff Lawrence Taylor Murphy Jennifer Potter

3. Outline Flow System Background Previous Work Proportional Control Modeling Results Conclusions

4. Flow System Setup

5. Block Diagram

6. Steady State Operation

7. SSOC

8. Step Response Results K (lb/min/%) =0.26 τ (sec) =0.46 t 0 (sec) =0.42

9. Frequency Response Experiment

10. Bode Plots Kcu (%/(lb/min) =10.00 K ((lb/min)/%) =0.24 τ (sec) =0.27 t 0 (sec) =0.35 m (order) =1.14 fu (Hz) =0.95

11. Model Bode Plot K (lb/min/%) =0.22 t0 (sec) =0.35 Tau (sec)=0.25 f u =0.95

12. Model Bode Plot K (lb/min/%) =0.22 t0 (sec) =0.35 Tau (sec)=0.25 K cu =10

13. FOPDT Parameters K = 0.24 (lb/min)/% τ = 0.28 sec t 0 = 0.4 sec

14. Closed Loop Transfer Function

15. Root Locus Parameters K CD =0.08 K QD =6.6 K CU =10 f u =1.24 *all units for K are % / (lb/min)

16. ζ Locations Response to Step Change in Set PointSymbolAverage Critical DampingK CD 0.08 1/500th DecayK C500 1.8 1/10 DecayK C10 4.8 Quarter DecayK QD 6.6 UltimateK CU 10

17. Results From Root Locus Ultimate Quarter Decay Critically Damped Underdamped Overdamped Kc = 10 Kc = 6.6 Kc = 0.08 0.08 < Kc < 10 0 < Kc < 0.08 *all units are % / (lb/min)

18. Predicted Ultimate Frequency and Ultimate Gain Bode PlotLuyben Method Routh Method Direct Substitution K CU = 10% / (lb/min) K CU = 9.6% / (lb/min) K CU = 10% / (lb/min) F u =0.87 HzF u =0.67 Hzn/aF u = 1.24 Hz

19. Model Results for K CD Offset Offset = 4.9 lb/min Decay Ratio = 0 Settling Time = 0.8 s K CD = 0.10% / (lb/min) Set Point Output Settling Time

20. Model Results for K QD Offset Offset = 1.9 lb/min Decay Ratio = 0.25 Settling Time = 3.9 s K QD = 6.6%/ (lb/min) Settling Time Set Point Output

21. Model Results for K CU Offset = 1 lb/min Decay Ratio = 1 Settling Time = never K CU = 10%/ (lb/min) Output Set Point Offset

22. Proportional Only Model Results K C (%*min/lb)Offset (lb/min) Critical Damping0.104.9 1/500th Decay1.83.5 1/10 Decay4.82.3 Quarter Decay6.61.9 Ultimate101.5

23. Experimental Results for K CD Offset = 4.9 lb/min Decay Ratio = 0 Settling Time = 0.8 s K CD = 0.10% / (lb/min) Settling Time Offset

24. Experimental Results for K QD Offset = 2.4 lb/min Decay Ratio = 0.25 Settling Time = 4.5 s K QD = 0.10% / (lb/min) Offset Settling Time

25. Experimental Results for K CU Offset = 1.2 lb/min Decay Ratio = 1 Settling Time = never K CD = 10% / (lb/min) Offset

26. Proportional Only Experimental Results K C (%*min/lb)Offset (lb/min) Critical Damping0.104.9 1/500th Decay1.83.7 1/10 Decay3.52.9 Quarter Decay 5 2.4 Ultimate101.2

27. Comparison of Results Critical Damping 1/500th Decay 1/10th Decay 1/4th Decay Ultimate Root Locus 0.081.84.86.610 P-Only Model 0.101.84.86.610 P-Only Experimental 0.101.83.5510

28. Conclusion For Kc needed Overdamped0 < Kc < 0.10 Critically DampedKc = 0.10 Underdamped0.10< Kc < 10 Quarter Decay Kc = 5.0