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

Outline 1.Introduction 2.System Specifications 3.System Modeling and Parameters Calculation 4.System Control & Simulations (PI, Pi α, PII α ) 5.Comparison : PI vs Pi α vs PII α Controllers 6.Conclusion

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.

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.

3.System Modeling and Parameters Calculation

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.

Reservoir Flow Calculation Height (feet) / Gate(feet)

Johnnie’s Diversion Flow Calculation Height (feet) / Gate(feet)

Tom’s Diversion Flow Calculation Height (feet) / Gate(feet)

City’s Diversion Flow Calculation Height (feet) / Gate(feet)

Cemetary’s Diversion Flow Calculation Height (feet) / Gate(feet)

Diversion Flow Modeling

Time Delay Calculation To Calculate the Time Delay between the reservoir and each diversion, the Rootcanal software was used: 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 )

Time Delay Calculation Flow (in m^3/s) Johnnie Diversion (in min) Tom Diversion (in min) City/Cemetary Diversion (in min)

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

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

Model Overview

4. System Control & Simulations (PI, Pi α, PII α )

Pond PI Controller

Reservoir PI Controller

Johnnie’s Pond (PI)

Tom’s Pond (PI)

City’s Pond (PI)

Cemetary’s Pond (PI)

Reservoir (PI) For PI Global error= m 3 and Water loss = 8158 m 3

Johnnie’s Pond in Use (PI)

Tom’s Pond in Use (PI)

City’s Pond in Use (PI)

Cemetary’s Pond in Use (PI)

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

Pond PI α Controller

Reservoir PI α Controller

Johnnie’s Pond (PI α )

Tom’s Pond (PI α )

City’s Pond (PI α )

Cemetary’s Pond (PI α )

Reservoir (PI α ) For α = 0.6 Global error= m 3 and Water loss = 8026 m 3 For α = 0.8 Global error= m 3 and Water loss = 7447 m 3 For α = 0.3 Global error= m 3 and Water loss = 8066 m 3

Johnnie’s Pond in Use (PI α )

Tom’s Pond in Use (PI α )

City’s Pond in Use (PI α )

Cemetary’s Pond in Use (PI α )

Reservoir in Use (PI α ) For α = 0.6 Global error= m 3 and Water loss = 7176 m 3 For α = 0.8 Global error= m 3 and Water loss = 7745 m 3 For α = 0.3 Global error= m 3 and Water loss = 7912 m 3

Pond PII α Controller

Reservoir PII α Controller

Johnnie’s Pond (PII α )

Tom’s Pond (PII α )

City’s Pond (PII α )

Cemetary’s Pond (PII α )

Reservoir (PII α ) For α = 0.3 Global error= m 3 and Water loss = 7369 m 3 For α = 0.7 Global error= m 3 and Water loss = 8118 m 3

Johnnie’s Pond in Use (PII α )

Tom’s Pond in Use (PII α )

City’s Pond in Use (PII α )

Cemetary’s Pond in Use (PII α )

Reservoir in Use (PII α ) For α = 0.3 Global error= m 3 and Water loss = 6979 m 3 For α = 0.7 Global error= m 3 and Water loss = 7891 m 3

5. Comparison : PI vs Pi α vs PII α

Johnnie’s Pond in Use (PI vs Pi α vs PII α )

Tom’s Pond in Use (PI vs Pi α vs PII α )

City’s Pond in Use (PI vs Pi α vs PII α )

Cemetary’s Pond in Use (PI vs Pi α vs PII α )

Reservoir in Use (PI vs Pi α vs PII α ) For PI α α = 0.6 Global error= m 3 and Water loss = 7176 m 3 For PII α α = 0.3 Global error= m 3 and Water loss = 6979 m 3 For PI Global error= m 3 and Water loss = 7868 m 3

Comparison NormalConditionUsingCondition Value (m^3)PI relativeValue (m^3)PI relative PI Global Error % ,00% PI Water Loss %78680,00% PIα Global Error % % Piα Water Loss % % PIIα Global Error % % PIIα Water Loss % %

6. Conclusion The efficiency, for this system, of the PII α controller compared to others controllers was shown in this study. Also an other strategy based on cooperative control could be applied but this one is hard to control due to the system complexity.

References “Rootcanal software” by Dr. MERKLEY Biological & Irrigation Engineering Department (USU,Logan) “Open-Channel flows” by Subhash C. JAIN “Introduction to Hydrology” by Warren VIESSMAN and Gary L. LEWIS

Thanks Thanks to all for listening to my presentation Particular thanks to Dr. Chen for making me come to Logan and to Christophe for his help during this project