1. NORM BASED APPROACHES FOR INTEGRATED DESIGN OF WASTEWATER TREATMENT PLANTS Multiobjective problem considering f 1,f 22 and f 24 : Comparison of weights Wp Weights considered and parameters of the MPC controllers automatically tuned: W u =[0.00042] H p =10, H c =4 Numerical results: W u =[0.0027] H p =10, H c =2 Wp 1 less restrictive than Wp 2 Integrated Design results Multiobjective problem considering f 1,f 22 and f 24 : Comparison of different objectives for costs Substrate and flow qr 1 comparison for two cost objectives (dashed dotted line – 0.3; solid line – 1.6) Numerical results: Desired value for f 1 0.30.71.6 WuWu 0.000660.00270.0021 HpHp 710 HcHc 422 V1V1 526872629305 A193618571873 Max(s 1 )84.3778.6678.95 Max(qr 1 )205.31870.691116 Plant cost = f 1 1.36821.51271.7548 Computational time9.8710.0610.14 Substrate (s 1 ) Recycling flow (qr 1 ) Step for MPC automatic tuning: Mixed sensitivity problem where are suitable weights Constraints: Over disturbance rejection and based on l1 norms to avoid actuator saturation Multiobjective approach: M’= control sensitivity S’= output sensitivity where f i * is the desired value for each objective function Method “Goal Attainment” (MATLAB) Mario Francisco, Pastora Vega ECCE-6 Copenhagen (Denmark, September 2007) PLANT Wp 1 Wp 2 V1V1 72627307 A1857 S 1r 70 Max(s 1 )78.6676.49 Max(qr 1 )870.691021.3 Plant cost= f 1 (x)1.51271.5177 Computational time10.068.28  Study and develop an Integrated Design method including a model based predictive controller (MPC), to tune controller parameters (both real and integers) and plant parameters (dimensions, working point, etc.)  Apply this method to the Integrated Design of the activated sludge process in a wastewater treatment plant, particularizing for a linear MPC, in order to minimize substrate variations at the output General objectives INTEGRATED DESIGN Designed plants are more controllable because plant and controller are designed at the same time considering controllability aspects, and not sequentially as in classical design EFFLUENT SETTLERREACTORINFFLUENT RECYCLING Benchmark global configuration (COST project 624) (substrate, oxygen and nitrate control) Particular case considered: substrate control purge EFFLUENT INFFLUENT Biological reactors Unaerated Aerated Settler Recycling sludge Nitrate internal recycling 1 aerated reactor + 1 settler Substrate (s 1 ) and oxygen (c 1 ) controlled variables biomass (x1) limited Recycling flow (qr 1 ), purge flow (q p ), and aeration factor (fk 1 ) manipulated variables Multivariable linear predictive controller, using a state space model for prediction (MPC Toolbox MATLAB) Predictive controller index Substrate comparison for two weights (dashed dotted line – Wp 1 ; solid line – Wp 2 ) Particular formulation: Transfer functions used for Integrated Design: output sensitivity (S’), control sensitivity (M’) Block diagram: Tuning parameters: H p : Prediction horizon H c : Control horizon W u : Weight for control efforts MPC general structure for the linear case without constraints An iterative two steps optimization algorithm has been proposed due to the problem complexity and the existence of real and integer parameters Construction costs (reactor volume and settler area) Plant controllability for perfect control Objective function: M’= Control sensitivity Activated sludge process General algorithm for Integrated Design Step for MPC tuning N= mixed sensitivity Step for plant design: multiobjective approach x=(s 1,x 1,c 1,x d,x b,x r,,fk 1,qr 1,q p,V 1,A) Over the non linear differential equations of the process Controllability constraints residence timessludge age Process constraints flow relationships Constraints: etc. University of Salamanca (Spain)