PROCESS INTEGRATED DESIGN WITHIN A MODEL PREDICTIVE CONTROL FRAMEWORK Mario Francisco, Pastora Vega, Omar Pérez University of Salamanca – Spain University of Simón Bolívar – Venezuela 16 th IFAC World Congress. Prague (July 2005)

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

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

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

Objectives  Apply a particular methodology for Integrated Design to linear systems and the activated sludge process in a wastewater treatment plant  Develop and apply a method for optimal automatic tuning of Model Predictive Controllers.  Perform Integrated Design including a Linear Model Predictive Controller and a state estimator in the case of the wastewater treatment plant.  Using these techniques, minimize substrate variations at the process output, considering typical process disturbances at the input (control aim)

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

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

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

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

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

Optimal automatic tuning of MPC The optimal automatic tuning problem is stated as a non-linear mixed integer constrained optimization problem tuning parameters Performance indexes: Integral square error for both outputs: Control variations for both inputs: Weigths Penalty factor added when controller is infeasible

Optimal automatic tuning of MPC TUNING PARAMETERS H p : 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 ) Real parameters (W u, T ref ) Modified random search method for all variables

Optimization algorithm description Algorithm steps: 1.Initial point for controller parameters, variances and centre of gaussians (for random numbers generation) are chosen. 2.Two random vectors of Gaussian distributions are generated, one integer and one real. 3.Two new points are obtained by adding and removing these vectors 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. Optimization method: Modified random search method based on Solis algorithm (1981)

Tuning results (I) Results considering the linear MPC without constraints applied to a linear system Control variableOutput variable

Tuning results (II) Results considering the linear MPC with constraints applied to a linear system Control variable qr 1 Output: s1Output: c1 Soft constraints

Tuning results (III) Results considering the linear MPC with constraints applied to the activated sludge process Reference s 1ref = 55 mg/lReference s 1ref = 100 mg/l Integrated design is needed Increasing reference gives more flexibility to the plant Output: s1

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 4. Conclusions and future work Index

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

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:

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

Integrated Design results (I) Control variable qr 1 Output c 1 Output s 1

Integrated Design results (II) Integrated design (plant + controller) Results only for MPC tuning Integrated Design Improvement 125 mg/l

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

Conclusions  For optimal automatic MPC tuning: –A new algorithm for tuning horizons and weights has been developed and tried in linear plants and 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  Apply optimal automatic tuning techniques to non linear model predictive controllers.  Extend the control problem for the nitrogen loop in the activated sludge process.  Introduce some robustness due to the application of linear models to a non linear plant.  Consider benchmark performance indexes such us time of constraints violation, effluent quality index, etc.