1. SacMan Control Tuning Bert Clemmens Agricultural Research Service

2. Canal Control Problem Balance supply with demand. Balance supply with demand. Maintain desired delivery rate. Maintain desired delivery rate. Above are accomplished by Above are accomplished by –Control of pool water levels which in turn requires control of pool volumes which in turn requires control of pool volumes

3. Three Aspects of Canal Automation Flow control Flow control –Ability to control flow rates at key points Feedforward control of flow rates Feedforward control of flow rates –Ability to route known major flow changes through the canal Feedback control of water levels Feedback control of water levels –Ability to adjust to disturbances and flow rate errors with downstream water-level feedback

4. Tuning Requirements Gate calibration are important, but not critical when feedback control is used. We use handbook calibration or calibrations provided by operators. Nothing special! Gate calibration are important, but not critical when feedback control is used. We use handbook calibration or calibrations provided by operators. Nothing special! Delay times for routing are important to transient performance. We manually adjust Manning n to match predicted and observed delay time for feedforward. Delay times for routing are important to transient performance. We manually adjust Manning n to match predicted and observed delay time for feedforward. We use optimal control methods to obtain water level feedback control parameters. Canal properties are determined from simulation or on- line tests. We use optimal control methods to obtain water level feedback control parameters. Canal properties are determined from simulation or on- line tests.

5. Typical Check Structure Hardware

6. Automata Hardware Gate Position Sensor Two Sensors Two Sensors –Digital Output for fine resolution of gate movement –Analog Output for coarse resolution of gate opening

7. Optical Encoder Pulsed Output Pulses count down to zero and motor stops Pulses count down to zero and motor stops 0.95 mm

8. Calibration of gates at CAIDD District has determined from experience, relationship between relative gate position change and flow rate change District has determined from experience, relationship between relative gate position change and flow rate change This is assumed linear. Then they correct when flows do not balance. This is assumed linear. Then they correct when flows do not balance. Sometimes they take into account non-linearity in initial opening. Sometimes they take into account non-linearity in initial opening. We use this calibration to determine the amount of gate movement (number of pulses) for a desired flow change. We use this calibration to determine the amount of gate movement (number of pulses) for a desired flow change. This is programmed into the SCADA system for manual control This is programmed into the SCADA system for manual control SacMan also considers upstream water level in determining gate position change SacMan also considers upstream water level in determining gate position change

9. Flow control issues Canal headgates are often not accurate for flow measurement Canal headgates are often not accurate for flow measurement Separate meter downstream can be used to adjust headgate Separate meter downstream can be used to adjust headgate Downstream Water-Level Feedback adjusts for flow errors upstream Downstream Water-Level Feedback adjusts for flow errors upstream Incremental flow control allow gradual adjustment to match downstream flows Incremental flow control allow gradual adjustment to match downstream flows Free flow gate downstream can be used to adjust head gate Free flow gate downstream can be used to adjust head gate

10. If gate is close to head-gate and is free-flowing, it can be alternative measurement device

11. Canal properties significantly affect the performance of any canal automation scheme. – –pool delay times which limits the responsiveness of the canal and thus the control possible which limits the responsiveness of the canal and thus the control possible – –pool volume changes with flow rate which influences the routing of flow changes through a canal which influences the routing of flow changes through a canal – –downstream water level response to pool volume changes over time which influences the strength of feedback corrections to water level errors which influences the strength of feedback corrections to water level errors –Reflection Wave Frequency Which is needed to avoid unstable feedback control Which is needed to avoid unstable feedback control

12. Control Engineering Practice Most industrial controllers use simpleClassical control, such as PID. Most industrial controllers use simpleClassical control, such as PID. So called Modern control theory, which uses optimization, has never caught on. So called Modern control theory, which uses optimization, has never caught on. Adaptive-classical control has received more coverage in the literature. Adaptive-classical control has received more coverage in the literature. Several simple controllers in series continues to be a difficult control problem. Several simple controllers in series continues to be a difficult control problem.

13. Optimization with State-Feedback Control of Water Levels State-Transition Relationship State-Transition Relationship –we use the Integrator-Delay Model –where, y(t) is the downstream water level at time t in response to a step change in upstream flow rate, Q, – is the pool time delay, and –A is the pool backwater surface area.

14. Integrator Delay Model Time delay, Time delay, Backwater surface area, A s Backwater surface area, A s

15. Integrator-Delay Model

16. Canals under normal depth follow this model well (SRP Arizona Canal - Pool 1)

17. State Transition Equations Derived from integrator-delay model Derived from integrator-delay model

18. Optimization with State-Feedback Control of Water Levels State-Feedback Control Law State-Feedback Control Law where u(k) is the control action (change in flow rate) at time step k, K is the controller gain matrix, and x(k) is the state vector.

19. Optimization with State-Feedback Control of Water Levels Linear Quadratic Regulator (LQR) with Penalty Function Linear Quadratic Regulator (LQR) with Penalty Function where J is the cost, e(k) is the water level error at time step k, and Q and R are penalties on the water level errors and control actions, respectively.

20. Controller Tuning Centralized PI-controller (with full gain matrix) can be found from solution of Riccati equation Centralized PI-controller (with full gain matrix) can be found from solution of Riccati equation Gradient search procedures are used to optimize other, more simple controllers, such as a series of local PI controllers Gradient search procedures are used to optimize other, more simple controllers, such as a series of local PI controllers

21. Proportional-Integral Controller We can optimally tune a PI controller with the above scheme, We can optimally tune a PI controller with the above scheme, –provided that the state vector, x(k), is properly chosen and –when only certain elements are chosen within the gain matrix, K.

22. Three local PI Controllers in series

23. Expansion of simple PI controller Additional terms are added to state vector to account for delays (as in Smith Predictor used in control theory) Additional terms are added to state vector to account for delays (as in Smith Predictor used in control theory) Off diagonal elements allow decoupling and centralized control Off diagonal elements allow decoupling and centralized control

24. Full gain Matrix Full gain Matrix –Top version highlights PI terms –Bottom version highlights delay (L) terms

25. Comparison of Controllers - Test 1-1

26. Conclusions from Optimization Series of simple PI controllers can be greatly improved upon Series of simple PI controllers can be greatly improved upon Adding Smith Predictor should improve controller performance for this canal Adding Smith Predictor should improve controller performance for this canal Decoupling or sending control signals to other pools should improve control Decoupling or sending control signals to other pools should improve control Sending information to one pool downstream and one (or more) pools upstream is a good control compromise Sending information to one pool downstream and one (or more) pools upstream is a good control compromise

27. Simulation Testing Controllers tested with CanalCAD Controllers tested with CanalCAD Tested under tuned and untuned conditions Tested under tuned and untuned conditions 12 different controllers tested for each test case 12 different controllers tested for each test case

28. Test 1-1 with NO gate movement restrictions Centralized PI Controller (PIL - + ) Change at 2 hours had feed-forward Change at 14 hours was only feed-back

29. Test 1-1 with gate movement restrictions Centralized PI Controller (PIL - + )

30. Test 1-1 untuned (gate move. restr. implied) Centralized PI Controller (PIL - + )

31. Test 1-1 untuned Simple PI Controller

32. Test 1-1 untuned PI -1 +1 Controller

33. Test 1-1 Comparison: relative to PI+S - +

34. Test 1-1 Comparison: LQR / PI+S - +

35. Test 1-2 untuned Centralized PI Controller (PIL - + )

36. Test 1-2 untuned Simple PI Controller (PI)

37. Test 1-2 untuned PI -1 +1 Controller

38. Test 1-2 untuned PIL -1 +1 Controller

39. Test 1-2 Comparison: relative to PI+S - +

40. Test 1-2 Comparison: LQR / PI+S - +

41. Conclusions Gate movement restrictions have a big influence on controller performance Gate movement restrictions have a big influence on controller performance Tuning to actual canal conditions can improve controller performance Tuning to actual canal conditions can improve controller performance Results suggest passing control actions one pool upstream and one pool downstream may be good compromise. Results suggest passing control actions one pool upstream and one pool downstream may be good compromise. While optimization suggests Smith predictor always improves performance, simulation results suggest that it often doesnt While optimization suggests Smith predictor always improves performance, simulation results suggest that it often doesnt Control with centralized PI controller comparable to traditional LQR controller Control with centralized PI controller comparable to traditional LQR controller

42. Simulation results for Upper Arizona Canal when controlling entire network Centralized PI w/ feedforward MPC w/ feedforward Centralized PI w/ feedback onlyMPC w/ feedback only

43. Manning n is used to adjust delay times for volume-based feedforward routing

44. Some canal pools do not follow the ID model. They have effectively no delay, a backwater area, and reflection waves

45. Influence of reflection waves Reflection waves can destabilize an otherwise stable controller Reflection waves can destabilize an otherwise stable controller Water level filtering can be used to Water level filtering can be used to –Minimize the influence of reflection waves on control –Remove transducer noise –Provide Anti-aliasing

46. Pseudo-random binary signal can be used to obtain frequency response of canal pool

47. Bode (Frequency) Diagram can be used to design filters Frequency Resonance Peak Actual Signal Filtered Signal Filter ID Model is straight line

48. Resulting filtered water levels

49. Manual Supervisory Control Standard Supervisory Control Features using iFix Dynamics from Intellution, Inc. Standard Supervisory Control Features using iFix Dynamics from Intellution, Inc. Added features for canal management Added features for canal management

50. Manual Supervisory Control iFix allows many types of displays (CAIDD) iFix allows many types of displays (CAIDD) Screen allows incremental flow change at gate Screen allows incremental flow change at gate