MAGIC: Model-Based Actuation for Ground Irrigation Control

Transcription

1 MAGIC: Model-Based Actuation for Ground Irrigation Control Daniel Winkler, Robert Wang, Francois Blanchette, Miguel Á. Carreira-Perpiñán, Alberto E. Cerpa University of California, Merced 1

2 Fresh water is not abundant... Folsom Lake Kern River 2

3 Lawn (Turf) Coverage In continental United States alone: 128,000 square kilometers Estimated 3x more than corn 9 Billion gallons/day to irrigate!! 13,600 olympic swimming pools 3.3 hours of Niagara Falls flow 3

4 Systems aren t great It s easy to find irrigation systems that aren t doing their jobs properly Primary offenses: Underwatering Bad quality Overwatering Bad efficiency 4

5 Irrigation System Architecture ur c so W at er Water Valve e Generally, valves are installed like this: 5

6 Irrigation System Architecture Depending on the size of the system, the valves may be placed on each run, like this: W at er so ur c e Water Valves 6

7 Irrigation System Architecture Water needs are not necessarily constant everywhere! 3cm 6cm 3cm W at er Water Requirements so ur c e Water Valves 7

8 Irrigation System Architecture Water needs are not necessarily constant everywhere! 3cm 3cm 3cm 6cm 3cm 3cm 3cm 3cm ur c so Water Requirements W at er Water Valve e 3cm 8

9 Our proposed solution: Distributed Actuation The MAGIC Node Wireless mote Solenoid Soil Moisture Sensor 9

10 Our proposed solution: Distributed Actuation Sensor Readings 3cm 3cm Model-Based Schedule Optimization 3cm 6cm 3cm 3cm 3cm 3cm so W at er Water Requirements Individualized Valve Schedules ur c e 3cm 10

11 Current Control Strategies Trial-and-error (most common by far) Sensor-based Weather-based Rain-detection only Evapotranspiration (ET) Give 45 minutes a try & Increase until turf seems to stay healthy Control Valve 11

12 Current Control Strategies Trial-and-error (most common by far) Sensor-based Weather-based Rain-detection only Very Dry? Irrigate 45 minutes Evapotranspiration (ET) Already Saturated? Irrigate 15 minutes Control Valve 12

13 Local Weather Station Current Control Strategies Trial-and-error (most common by far) Sensor-based Weather-based Rain-detection only State-of-the-art Evapotranspiration (ET) Based on today s temperature, sun exposure, humidity, rain, and wind, you should irrigate 36 minutes Control Valve 13

14 How can we generate schedules for MAGIC nodes? This method does have potential, but some flaws exist... Helps, but extra effort required of the groundskeepers wouldn t be sustainable Weather data won t provide us info for valves that are close spatially 14

15 Reactive control using sensors - what moisture conditions are we reacting to? 15

16 Reactive control using sensors - what moisture conditions are we reacting to? 16

17 Sensors + model of moisture movement - what moisture conditions are we reacting to? 17

18 Model-based Schedule Optimization k=7 F k= k=9 k=5 k=4 K k=8 k=6 t= k= Nt k=2 PDE Model Equations Soil Moisture k=3 18

19 Soil moisture movement model PDE Model built from first principles Full details/justifications in the paper 19

20 Soil moisture movement model K sprinklers in total Does sprinkler k reach me? Is sprinkler k on or off? 20

21 Soil moisture movement model Conversion factors between height (H) and volumetric content ( ) 21

22 Soil moisture movement model Surface fluid velocity Sub-Surface fluid velocity 22

23 Soil moisture movement model Darcy s Law: Flow through porous media Sub-surface velocity: 23

24 Soil moisture movement model Darcy s Law: Flow through porous media Sub-surface velocity: 24

25 Soil moisture movement model Darcy s Law: Flow through porous media Sub-surface velocity: Surface velocity: 25

26 Soil moisture movement model Bringing the terms all together, the final model is defined as follows: 26

27 Soil moisture movement model Non-linearities in model problematic for optimization No guarantee of global minimum (non-convex feasible set) Non-linear optimization is considerably slower 27

28 Model Linearization Linearization Error Shift of Origin 28

29 Model Linearization Constant Linear Replicated on each model variable (Substituted for readability) 29

30 Model discretization Moving variables from a continuous to a discrete space For example: 30

31 Model discretization 31

32 Linear, discretized 32

33 Initial / Boundary Conditions Get initial soil moisture conditions from current soil measurements! Dirichlet boundary conditions Fix function value on boundary Others could be used... Boundary conditions fixed on H, chosen to be as small as reasonable 33

34 Optimization Problem Definition k=7 (Sprinkler limitations) k=8 k=9 k=5 k=4 k=6 k=1 PDE Model Equations k=2 k=3 34

35 Optimization Problem Definition (Soil limitations) PDE Model Equations 35

36 Optimization Problem Definition (Plant limitations) PDE Model Equations 36

37 Optimization Problem Definition (Model constraints) PDE Model Equations 37

38 System Deployment UC Merced s Bowl 38

39 System Analysis - Water Consumption 12.3% less water used vs evapotranspiration 23.4% less water used vs trial-and-error Rain! 39

40 System Analysis - Quality of Irrigation Evapotranspiration (Control) 68.1 Combined hours below Below this threshold, turf start withering! MAGIC 16.7 Combined hours below 4.08x less vs ET 3.23x less vs trial-and-error 40

41 System Analysis - Moisture Distribution MAGIC Evapotranspiration Trial and Error Average water distribution, interpolated 41

42 Return on Investment (ROI) analysis Unit Cost Even with 20% business markup, ROI in months! 42

43 Node power management 2+ year lifetime (current prototype) 14+ year lifetime with smarter radio use 43

44 Future goals Explicit weather inclusion Sensor error -> model functionality Optimal sprinkler placement in new irrigation systems Data-driven model generation 44

45 Conclusions Distributed Actuation - MAGIC node allows us to actuate individual sprinkler heads according to schedules we provide Model-Based Schedule Optimization Compute schedules that minimize water usage but satisfy minimum moisture requirements Across 7-weeks of deployment, MAGIC system is found to improve irrigation efficiency 12.3% % while improving irrigation quality up to 4x!! 45