Filling Pond Control Minimizing Water loss on Scipio River

1. Filling Pond Control Minimizing Water loss on Scipio River (Comparison between PI Controller and Fractional Order Controllers) By Nicolas MONEGIER DU SORBIER

2. Outline • 1.Introduction • 2.System Specifications • 3.System Modeling and Parameters Calculation • 4.System Control & Simulations (PI, Piα,PIIα) • 5.Comparison : PI vs Piα vsPIIα Controllers • 6.Conclusion

3. 1. Introduction • The aim of this project was to control the filling of each pond of the Scipio Open Channel in the right time, minimizing the water loss at the end of the canal. • The most difficult was that only a positive action was available on the system. • Many controllers were tested in this project to find the best one.

4. 2. System Specification Sensors and actuators can be used just one time each hour. Gate height, Diversion water level and Pond water Level are available for each Pond. Gate height, Water level and Outflow are available for the Reservoir.

5. 3.System Modeling and Parameters Calculation

6. Diversion Flow Calculation • For each diversion gate, the flow was calculated using the derivative of the pond volume variations. • Thus, the points related to the gate height, the diversion pond height and the flow were plotted. • Seeing these plots, so many points had very low flows for many values of gate heights and diversion pond heights. That is why a Look-up Table, based on 5 values of diversion pond heights and 5 values of gate heights, was made for the model. • So for each cell of the Look-up Table, the average was taken in the neighborhood of the point.

7. Reservoir Flow Calculation

8. Johnnie’s Diversion Flow Calculation

9. Tom’s Diversion Flow Calculation

10. City’s Diversion Flow Calculation

11. Cemetary’s Diversion Flow Calculation

12. Diversion Flow Modeling

13. Time Delay Calculation • To Calculate the Time Delay between the reservoir and each diversion, the Rootcanal software was used: http://www.neng.usu.edu/bie/faculty/merkley/BIE6300.htm • Through Google Earth the topographic datas of the Scipio channel were obtained to model it on this software (elevations, distances) • Thus, 3 Look-Up Tables were made to calculate the delay relative to the Reservoir outflow for each part of the canal. • So each part of the canal was represented by a delay : y (t)= u (t-τ)

14. Time Delay Calculation

15. Delay Modeling For each part of the canal, Delays were modeled like this : But for parts between diversions and Ponds, Delays were modeled by constant delays. Johnnie’s Pond Delay=0.2 hours, Tom’s Pond Delay=0.2 hours City’s Pond Delay=0.1 hours and Cemetary’s Pond Delay=0.5 hours

16. Pond Volume Calculation Where q (t) is the flow and C the initial Pond Volume

17. Model Overview

18. 4. System Control & Simulations (PI, Piα,PIIα)

19. Pond PI Controller

20. Reservoir PI Controller

21. Johnnie’s Pond (PI)

22. Tom’s Pond (PI)

23. City’s Pond (PI)

24. Cemetary’s Pond (PI)

25. Reservoir (PI) For PI Global error=156830 m 3 and Water loss = 8158 m3

26. Johnnie’s Pond in Use (PI)

27. Tom’s Pond in Use (PI)

28. City’s Pond in Use (PI)

29. Cemetary’s Pond in Use (PI)

30. Reservoir in Use (PI) For PI Global error=168450 m 3 and Water loss =7868 m3

31. Pond PIα Controller

32. Reservoir PIα Controller

33. Johnnie’s Pond (PIα)

34. Tom’s Pond (PIα)

35. City’s Pond (PIα)

36. Cemetary’s Pond (PIα)

37. Reservoir (PIα) For α = 0.3 Global error=156950 m 3 and Water loss = 8066 m3 For α = 0.6 Global error=157320 m 3 and Water loss = 8026 m3 For α = 0.8 Global error=164330 m 3 and Water loss = 7447 m3

38. Johnnie’s Pond in Use (PIα)

39. Tom’s Pond in Use (PIα)

40. City’s Pond in Use (PIα)

41. Cemetary’s Pond in Use (PIα)

42. Reservoir in Use (PIα) For α = 0.3 Global error=161750 m 3 and Water loss = 7912 m3 For α = 0.6 Global error=163620 m 3 and Water loss = 7176 m3 For α = 0.8 Global error=168010 m 3 and Water loss = 7745 m3

43. Pond PIIα Controller

44. Reservoir PIIα Controller

45. Johnnie’s Pond (PIIα)

46. Tom’s Pond (PIIα)

47. City’s Pond (PIIα)

48. Cemetary’s Pond (PIIα)

49. Reservoir (PIIα) For α = 0.3 Global error=155680 m 3 and Water loss = 7369 m3 For α = 0.7 Global error=158170 m 3 and Water loss = 8118 m3

50. Johnnie’s Pond in Use (PIIα)