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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

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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

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

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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)

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

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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

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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

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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

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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

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

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

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

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

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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

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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

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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

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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)

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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

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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:

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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

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