INTEGRATED DESIGN OF WASTEWATER TREATMENT PROCESSES USING MODEL PREDICTIVE CONTROL

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. Index • Introduction and objectives 1.1 Classical Design 1.2 Integrated Design 1.3 Objectives • Description of the activated sludge process • Optimal automatic tuning of model predictive controller • Integrated Design problem • Conclusionsand future work

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

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

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

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

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

9. General MPC controller structure qr1,fk1,qpmanipulated variables s1,c1 controlled x1 constrained Standard linear multivariable MPC controller, using state space model for prediction (MPC Toolbox MATLAB) MPC controller index MPC constraints

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

11. Performance indexes Integral square error for both outputs Indexes for disturbance rejection Index based on the norm of the error signals H norm of the closed loop disturbances transfer function Benchmark indexes for operational costs Pumping energy Aeration energy 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

12. Optimal automatic tuning of MPC TUNING PARAMETERS Hp : Maximum prediction horizon Hw : Minimum prediction horizon Hc : Control horizon Wu: Weights of the changes of manipulated variables Tref: Time constants of the exponential reference trajectories S1ref: Optimal reference for substrate Integer parameters (Hp, Hc, Hw) Modified random search method for all variables Real parameters (Wu, Tref, s1ref)

13. Optimization algorithm description Modified random search method for tuning MPC parameters Algorithm steps 1. An initial point for controller parameters, variances and centre of gaussians (for random numbers generation) is chosen. 2. A random vectorξ(k)of Gaussian distribution is generated, with integer and real elements. 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. Tuning results (I) Results considering ISE as performance index With constraints over PE, AE (solid lines) and without these constraints (dashed-dotted lines) Fixed plant V1=7668 A=2970.88 Output variable: s1 Control effors are smaller in the first case Control variable: qr1

15. Tuning results (II) Results considering as performance index Results considering (solid lines) compared with ISE (dashed-dotted lines) Output variable: s1 Results are similar but computa-tional time is smaller Control variable: qr1

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

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

18. Optimization problem Optimization problem: non-linear constrained problem (NLP /DAE). Solved using SQP algorithm Objective function: Construction costs (reactor volume and settler area) Operational costs (reactor aeration and pumps) The weights wi (i = 1,…,4) are selected from CAPDET model (benchmark) w1=1; w2=3.1454 w3=1; w4=1

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

20. Integrated Design results (I) Results considering ISE as performance index With constraints over PE, AE (solid lines) and without these constraints (dashed-dotted lines) Control variable qp Control variable qr1 Output s1 Substrate variations are much smaller when constraints over PE,AE are not considered

21. Integrated Design results (II) Results considering as performance index With constraints over PE, AE (solid lines) and without these constraints (dashed-dotted lines) Control variable qr1 Output s1 Results are similar but computational time is smaller

22. Integrated Design results (III) A comparison between automatic tuning and Integrated Design results Results only for MPC tuning: Results with Output s1 V1=7668 A=2970.88 PE=299.9 AE=511.5 Dashed-dotted lines Integrated Design Improvement Output s1 Improvement in operational and construction costs Integrated Design: (plant + MPC) V1=7099.9 A=1800 PE=194.4 AE=290.3 Results with Dashed-dotted lines

23. Index • Introductionand objectives • Description of the activated sludge process • Optimal automatic tuning of model predictive controller • Integrated Design problem • Conclusions and future work

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.