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

2. Toni Barjas Blanco - 26th Benelux Meeting on Systems and Control - March 15th, 2007 2 Problem Description Principles of MPC Model of the Demer Uncontrollability Results Conclusion and Future Works Outline

3. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 3 Introduction

4. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 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. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 5 Model Predictive control: Principles Real-life analogy:

6. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 6 State Space Model Linear State Space Model: Nonlinear State Space Model: State: water levels, discharges, volumes Input: gate positions Disturbance input: rainfall

7. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 7 Model Predictive Control: Principles Mathematical formulation: s.t. Initial state

8. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 8 Model Predictive control Advantages: Disadvantages: Constraints Predictive Rainfall due to horizon Multiple Objectives Priorities Computational complexity

9. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 9 Model of the Demer Possible modelling strategies: Black box: based on data Physical : physical laws Grey box : Combination of previous strategies In this work Grey box modelling from historical data (1998 and 2002)  Reservoir Type

10. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 10 Schematical overview bassin

11. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 11 Resultaten Schulensmeer Demer Schulenslake Gate K7Gate A

12. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 12 Resultaten Schulensmeer Hopw qK7 Hs qA Hafw

13. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 13 Model Validation

14. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 14 Expert knowledge Water administration: Experience : Debatable w.r.t. optimality 1.Can be usefull to take into account e.g. N 2.Drastical change can be frightening Experience  Guidelines about filling order reservoirs

15. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 15 Expert knowledge in MPC Constraint priorization: Ensures satisfaction high priority constraints 1.Divide the constraints in sets with different priority 2.Solve MPC control problem with all constraints 3.If infeasible  remove lowest priority contraints and resolve MPC control problem, increasing weights of variables corresponding to removed constraint set 4.Until a feasible solution  apply first calculated input

16. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 16 Uncontrollability problem Typical use of MPC  control to a reference value In flooding prevention: 1.Control to reference value less important 2.Avoid flooding  Nonlineair behaviour is very important Most difficult nonlinearity example No derivatives

17. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 17 Fuzzy model for derivatives model estimator MPC Fuzzy model y x u x ^ ^ A,B (Linearized system matrices)

18. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 18 Results (Historical rainfall 1998) Three-position controller (currently in use): MPC with priorities: Control to 21.5 m Hopw en Hs < 23m TAW Hafw < 22.75m

19. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 19 Results (Fictituous data based on data from 1998) Three-position controller (currently in use): MPC with priorities:

20. Toni Barjas Blanco - 4th International Symposium on Flood Defence - May 6 th -8 th, 2008 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