Evaluation of River Flood Regulation using Model Predictive Control

1. K. U. LEUVEN 4th International Symposium on Flood Defence May 6th-8th, 2008 Evaluation of River Flood Regulation using Model Predictive Control Patrick Willems Toni Barjas Blanco P.K. Chiang Bart De Moor Jean Berlamont SCD Research Division ESAT- K. U. Leuven

2. Outline • Problem Description • Principles of MPC • Model of the Demer • Uncontrollability • Results • Conclusion and Future Works

3. Introduction

4. Introduction • Current control strategy (three-position controller): • If-then-else rules • Based on current state • Takes no rain predictions into account • Simulations  far from optimal • Better Alternative: • Model Predictive Control (MPC)

5. Model Predictive control: Principles • Real-life analogy:

6. State Space Model • Linear State Space Model: • Nonlinear State Space Model: State: water levels, discharges, volumes Disturbance input: rainfall Input: gate positions

7. Model Predictive Control: Principles • Mathematical formulation: s.t. Initial state

8. Model Predictive control • Advantages: • Constraints • Predictive Rainfall due to horizon • Multiple Objectives • Priorities • Disadvantages: • Computational complexity

9. Model of the Demer • Possible modelling strategies: • Black box: based on data • Physical : physical laws • Grey box : Combination of previous strategies Grey box modelling from historical data (1998 and 2002)  Reservoir Type • In this work

10. Schematical overview bassin

11. Resultaten Schulensmeer Gate A Gate K7 Schulenslake Demer

12. Resultaten Schulensmeer Hafw Hs qA qK7 Hopw

13. Model Validation

14. Expert knowledge • Water administration: • Experience : • Debatable w.r.t. optimality • Can be usefull to take into account e.g. N • Drastical change can be frightening • Experience  Guidelines about filling order reservoirs

15. Expert knowledge in MPC • Constraint priorization: • Divide the constraints in sets with different priority • Solve MPC control problem with all constraints • If infeasible  remove lowest priority contraints and resolve MPC control problem, increasing weights of variables corresponding to removed constraint set • Until a feasible solution  apply first calculated input Ensures satisfaction high priority constraints

16. Uncontrollability problem • Typical use of MPC  control to a reference value • In flooding prevention: • Control to reference value less important • Avoid flooding  Nonlineair behaviour is very important Most difficult nonlinearity example No derivatives

17. Fuzzy model for derivatives u y model ^ x estimator MPC ^ x A,B (Linearized system matrices) Fuzzy model

18. Hopw en Hs < 23m TAW Hafw < 22.75m Control to 21.5 m Results (Historical rainfall 1998) Three-position controller (currently in use): MPC with priorities:

19. Results (Fictituous data based on data from 1998) Three-position controller (currently in use): MPC with priorities:

20. Conclusions and future works • Conclusion: • Model Predictive Control outperformed three-position controller • Future works: • Extend MPC to control the whole model • Estimate state with moving horizon estimator • Robust MPC wrt uncertainty rain prediction and modelling errors