1. INTEGRATED DESIGN OF WASTEWATER TREATMENT PROCESSES USING MODEL PREDICTIVE CONTROL Mario Francisco, Pastora Vega University of Salamanca – Spain European Control Conference. (Kos, July 2007)

2. 2 Index 1. Introduction and objectives 1.1 Classical Design 1.2 Integrated Design 1.3 Objectives 2. Description of the activated sludge process 3. Optimal automatic tuning of model predictive controller 4. Integrated Design problem 5. Conclusions and future work

3. 3 Introduction: Classical design Selection of the process units and interconnection Calculation of plant parameters and steady state Control system selection and tuning All this minimizing construction and operational costs Process engineer Control engineer Sequential procedure

4. 4 Introduction: Integrated Design Structure selection ( PLANT + MPC CONTROL ) Definition of the optimization problem (Costs, controllability indexes, model, constraints) Calculation of the optimum design parameters (plant, controllers, steady state point) Plant and controller are designed at the same time

5. 5 Objectives  Develop a method for optimal automatic tuning of Model Based Predictive Controllers (MPC) using dynamic and norm based performance indexes.  Develop Integrated Design techniques that use this new automatic tuning method.  Apply this methodology to the activated sludge process in a wastewater treatment plant, in order to obtain optimal plants that minimize substrate variations at the process output, considering typical process disturbances at the input.  Introduce some benchmark plant characteristics for better interpretation of results (disturbances, indexes)

6. 6 1. Introduction and objectives 2. Description of the activated sludge process 2.1 Process 2.2 Disturbances 2.3 Closed loop configuration 3. Optimal automatic tuning of model predictive controller 4. Integrated Design problem 5. Conclusions and future work Index

7. 7 Description of the process EffluentSettlerBioreactor Influent Recycling Benchmark configuration (control of substrate, oxygen, nitrogen) Substrate and oxygen control problem waste EFFLUENT INFFLUENT Bioreactors Unaerated aerated Settler Recycling sludge Nitrate internal recycling

8. 8 Process disturbances: input flow and substrate Substrate concentration at the plant input (s i ) Flow rate at the plant input (q i ) Real data from a wastewater plant Benchmark disturbances

9. 9 General MPC controller structure s 1,c 1 controlled x 1 constrained qr 1,fk 1,q p manipulated variables Standard linear multivariable MPC controller, using state space model for prediction (MPC Toolbox MATLAB) MPC controller index MPC constraints

10. 10 1. Introduction and objectives 2. Description of the activated sludge process 3. Optimal automatic tuning of model predictive controller 3.1 Optimization problem 3.2 Tuning parameters 3.3 Algorithm description 3.4 Tuning results 4. Integrated Design problem 5. Conclusions and future work Index

11. 11 Optimal automatic tuning of MPC The optimal automatic tuning problem is stated as a non-linear mixed integer constrained optimization problem (MINLP) Penalty factor added when controller is infeasible c = tuning parameters Performance indexes Integral square error for both outputs Index based on the  norm of the error signals H  norm of the closed loop disturbances transfer function Indexes for disturbance rejection Pumping energy Aeration energy Benchmark indexes for operational costs

12. 12 Optimal automatic tuning of MPC TUNING PARAMETERS H p : Maximum prediction horizon H w : Minimum prediction horizon H c : Control horizon W u : Weights of the changes of manipulated variables T ref : Time constants of the exponential reference trajectories Integer parameters (H p, H c, H w ) Real parameters (W u, T ref, s 1ref ) Modified random search method for all variables S 1ref : Optimal reference for substrate

13. 13 Optimization algorithm description Algorithm steps Modified random search method for tuning MPC parameters 2. A random vector ξ(k) of Gaussian distribution is generated, with integer and real elements. 1. An initial point for controller parameters, variances and centre of gaussians (for random numbers generation) is chosen. 3. Two new points are obtained by adding and removing this vector to the current point. 4. Cost function is evaluated at the original point and at new points, and the algorithm chooses the point with smallest cost. 5. If some convergence criteria is satisfied, stop the algorithm, otherwise return to step 2. Variances are decreased.

14. 14 Tuning results (I) Results considering ISE as performance index With constraints over PE, AE (solid lines) and without these constraints (dashed-dotted lines) TABLE I INDEXISE+PE,AEISE Wu(1)0.00150 Wu(2)00 Wu(3)8.303310 T ref 0.3560 HpHp 2512 HcHc 10 HwHw 31 f 2 =W n * ISE0.17370.09030 PE190.15276.84 AE470.36502.83 0.06540.0032 S 1r 73.5560.50 Computational time (min) 39.9129.34 Control variable: qr 1 Output variable: s 1 Control effors are smaller in the first case Fixed plant V 1 =7668 A=2970.88

15. 15 Tuning results (II) Results considering as performance index Results considering (solid lines) compared with ISE (dashed-dotted lines) TABLE I INDEXISE Wu(1)00 Wu(2)00 Wu(3)109.8648 T ref 00 HpHp 125 HcHc 105 HwHw 11 f 2 =W n * ISE0.090300.1045 PE276.84299.94 AE502.83511.47 0.00325.9191e-6 S 1r 60.5058.45 Computational time (min)129.342.22 Control variable: qr 1 Output variable: s 1 Results are similar but computa- tional time is smaller

16. 16 1. Introduction and objectives 2. Description of the activated sludge process 3. Optimal automatic tuning of model predictive controller 4. Integrated Design problem 4.1 Two steps approach 4.2 Optimization problem 4.3 Integrated Design results 5. Conclusions and future work Index

17. 17 Integrated Design problem Integrated Design of plant and MPC: Two iterative steps approach Step 2: Controller parameters fixed, plant design (NLP/DAE problem) Step 1: Optimal MPC tuning previously explained (MINLP problem)

18. 18 Optimization problem Optimization problem: non-linear constrained problem (NLP /DAE). Solved using SQP algorithm Construction costs (reactor volume and settler area) Operational costs (reactor aeration and pumps) Objective function: The weights wi (i = 1,…,4) are selected from CAPDET model (benchmark) w 1 =1; w 2 =3.1454 w 3 =1; w 4 =1

19. 19 Optimization problem Constraints on the non- linear differential equations of the plant : Controllability constraints: Residence time Mass loads Sludge age Process constraints: Relationships between flows where INDEX= performance index (ISE, norms, etc.)

20. 20 Control variable qr 1 Output s 1 TABLE III INTEGRATED DESIGN RESULTS WITH ISE INDEXISE+ PE,AEISE WuWu [10 0 0.28][0.0001 0.0001 10] T ref 3.880 H p, H c, H w 5,2,1 V1V1 87867153 A18002062 S 1r 70 f 2 =W n * ISE0.96280.1175 Plant cost= f 1 (x)1.26841.5499 PE120.40180.72 AE217.08280.59 Control variable q p Results considering ISE as performance index Substrate variations are much smaller when constraints over PE,AE are not considered With constraints over PE, AE (solid lines) and without these constraints (dashed-dotted lines) Integrated Design results (I)

21. 21 Control variable qr 1 Output s 1 Results considering as performance index TABLE IV INTEGRATED DESIGN RESULTS WITH INDEX+ PE,AE WuWu [0 7.34 9.93][0 0 6.23] T ref 1.970 H p, H c, H w 7, 7, 15, 5, 1 V1V1 92177100 A1800 f 2 =W n * ISE1.37070.1110 Plant cost= f 1 (x)1.26471.0393 0.01363.3958e-5 PE126.19194.48 AE226.89290.32 Integrated Design results (II) With constraints over PE, AE (solid lines) and without these constraints (dashed-dotted lines) Results are similar but computational time is smaller

22. 22 Integrated Design results (III) Integrated Design: (plant + MPC) Results only for MPC tuning: Results with Integrated Design Improvement Results with Improvement in operational and construction costs V 1 =7668 A=2970.88 PE=299.9 AE=511.5 V 1 =7099.9 A=1800 PE=194.4 AE=290.3 A comparison between automatic tuning and Integrated Design results Dashed-dotted lines Output s 1

23. 23 1. Introduction and objectives 2. Description of the activated sludge process 3. Optimal automatic tuning of model predictive controller 4. Integrated Design problem 5. Conclusions and future work Index

24. 24 Conclusions and future work  For optimal automatic MPC tuning: –A new algorithm for tuning horizons and weights has been developed, considering dynamic and norm based indexes –It has been tried in the activated sludge process, with good results.  For Integrated Design of plant and MPC: –The design procedure produces better controllable plants than the classical procedure. –The designed plant satisfies all basic working requirements, is optimum cost (optimum units), and furthermore it attenuates the substrate load disturbances. Future work: –Consider different norm based performance indexes (mixed sensitivity problems based on H  and l1 norms of sensitivity transfer functions) –Include some robust stability and performace indexes.