Norm-based approaches for Integrated Design of WWTP
Systematic methods and tools for managing the complexity
Process Synthesis & Design (T4-1P)
Keywords: Process Design, Model Based Predictive Control, Integrated Design of Process and Control, H infinity norm, l1 norm
Abstract—
In this work the Integrated Design of the activated sludge process in a wastewater treatment plant has been performed, including a linear multivariable predictive controller with constraints. In the Integrated Design procedure, the process parameters are obtained simultaneously with the parameters of the control system by solving a multi objective constrained non-linear optimization problem, taking into account investment and operating costs. Performance indexes for optimal automatic MPC tuning are based on the weighted sum of the norm (H, l1, H2) of different closed loop transfer functions matrices of the system subject to a set of constraints. In this sense no dynamical simulation is needed and therefore the algorithm is very fast. The methodology proposed here is a general one and the formulation is a multivariable one. The use of linear models for the control also allows for the specification of any other convex performance criteria within an LMI framework to state stability conditions and some desired closed-loop behaviour. The mathematical optimization for tuning all parameters is tackled in two iterative steps. First a sequential quadratic programming (SQP) method is used to obtain plant parameters, and secondly, a special type of random search method is used to tune the controller parameters.
Motivation and objectives
The EU Urban Water Directive (2000/60/EC), define stringent requirements for urban wastewater treatment and a time frame for the step-wise implementation by the member countries. The application of the directive has lead to the construction of new plants and redesigns of the existing ones with the aim of reducing as much as possible the environmental impact. The associated costs to these actions have been very huge. In this sense, the norm imposes several objectives, to be achieved by engineers that should be pointed out. First, the design of more complex but more flexible plants considering the new environmental restrictions facilitating their adaptation to future legislations, avoiding redesigns. Second, a stricter operation and control at must be guaranteed. To achieve the above mentioned aims, its necessary the use of Integrated Design Techniques, combining Optimization and Advanced Control, together with Computer Aided Tools to allow for the simultaneous design of plants and control systems at lowest costs.
Traditionally, process design and control system design have been performed sequentially. It is only recently displayed, that a simultaneous approach to the design and control leads to significant economic benefits and improved dynamic performance during plant operation. The Integrated Design methodology allows for the evaluation of the plant parameters and control system at the same time, making the designed system more controllable [4],[9]. At design stage, controllability indicators and controllers are evaluated together with economic considerations, in order to give an optimum closed loop plant. This problem can be stated mathematically as a multi objective nonlinear programming problem with differential and algebraic constraints (NLP/DAE). Many works apply Integrated Design techniques, particularly to chemical process design, such as distillation systems or reactors, stressing the interactions of design and control [8],[11]. These works also tackle process structure selection by solving a synthesis problem. A comprehensive review of advances in the area is given by [12].
Some good examples of Integrated Design applied to the activated sludge process are given in [5, 15] where the plant dimensions, an optimal working point and the parameters of PI controllers were obtained imultaneously. Despite of the complicated dynamics of the process under design, works adding advanced controllers to the Integrated Design procedure have not been reported in the literature even though it could be a good way to improve control performance. The reason for that it could be related to the complexity of the resulting optimization problem.
Within this context, the aim of this work was to tackle problems directly related to the Integrated Design of Activated Sludge Processes and Advance Control Systems to support engineers during the complex task of designing and control Wastewater Treatment Plants. In our opinion, the field of integrated process design and control has reached a maturity level that mingles the best from process knowledge and understanding control theory on one side, with the best from numerical analysis and optimization on the other. Consequently, direct implementation of integrated methods should soon become the mainstream design procedure. The integration of Numerical Optimization, Dynamical Model Simulation and Model Based Predictive Control, is the most relevant feature of the work and, in our opinion, the key point to success in the design of flexible processes reducing the operation costs while legal specifications on the quality of the treated water are fulfilled.
In this work the Integrated Design of the activated sludge process in a wastewater treatment plant has been performed, including a linear multivariable predictive controller with constraints. In the Integrated Design procedure, the process parameters are obtained simultaneously with the parameters of the control system by solving a multi objective constrained non-linear optimization problem, taking into account investment and operating costs. Performance indexes for optimal automatic MPC tuning are based on the weighted sum of the norm (H, l1, H2) of different closed loop transfer functions matrices of the system subject to a set of constraints. In this sense no dynamical simulation is needed and therefore the algorithm is very fast.
The methodology proposed here is a general one and the formulation is a multivariable one. The use of linear models for the control also allows for the specification of any other convex performance criteria within an LMI framework to state stability conditions and some desired closed-loop behaviour.
The mathematical optimization for tuning all parameters is tackled in two iterative steps. First a sequential quadratic programming (SQP) method is used to obtain plant parameters, and secondly, a special type of random search method is used to tune the controller parameters. The loop is finished when convergence criteria is reached.. For optimization of f1 cost function, all decision
Integrated design methodology
In this work, the Integrated Design problem is stated mathematically as a constrained non-linear multi-objective optimization problem, in which economic and control objectives are considered together with some constraints. The solution of the ID problem is obtained following a constrained numerical cost optimization procedure that uses dynamic models and real data records of disturbances together with a set of predefined constraints to evaluate the plant dimensions, the optimal operation points and the control system parameters.
The cost functions include the investment, operation costs, and dynamical indexes. The constraints are selected to ensure that the process variables and some closed loop controllability measures and several closed loop performance criteria lie within specified bounds.
The methodology for the integrated design is subdivided in several steps:
1. Initial plant information: where all the information necessary is defined to carry out the WWTP design. It includes wastewater and control system characterisation (plant and control type, models, plant load,…)
2. Definition of design objectives, performance and controllability criteria and constraints: where the preliminary goals and the corresponding measurement criteria are proposed and classified according to different categories (environmental, economic, operational, control..).
3. Optimization procedure:
4. Validation of results: where the optimal plant can be simulated, several criteria evaluated, and comparison with other plants can be carried out.
Main Contributions
1) In the the proposed methodology is based on the minimization of a set of dynamical indexes which are the weighted sum of the norm (H, l1, H2) of different closed loop transfer functions matrices of the system subject to a set of constraints. In this sense no dynamical simulation is needed and therefore the algorithm is very fast
2) The methodology proposed here is a general one and the formulation is a multivariable one. The use of linear models for the control also allows for the specification of any other convex performance criteria within an LMI framework to state stability conditions and some desired closed-loop behaviour.
3) The approach has been validated on a simulated example based on a real wastewater treatment plant. Real scenarios have been considered in the simulated model by means of real data records of the main disturbances to make a more realistic analysis of the results.
4) Some computational times are compared to others approaches showing the adavantages of the proposal
References
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[2] Ali, E. and E. Zafiriou (1993). On the tuning of Nonlinear Model Predictive Control Algoritms. Proceedings of the American Control Conference, pp. 786-790.
[3] Copp, J.B. (2002). The COST Simulation Benchmark: Description and Simulator Manual. Office for Official Publications of the European Community. ISBN 92-894-1658-0.
[4] Fisher, W. R., M. F. Doherty and J. M. Douglas (1988). The Interface Between Design and Control. 1. Process Controllability. Ind. Eng. Chem. Res., 27, pp. 597-605.
[5] Francisco, M., P. Vega, O. Pérez and M. Poch (2003). Dynamic Optimization for Activated Sludge Integrated Design. European Control Conference (UK)
[6] Francisco, M., P. Vega, O. Pérez (2005). Process Integrated Design within a Model Predictive Control framework. Proceedings of IFAC World Congress (Prague)
[7] Francisco, M., P. Vega (2006). Optimal automatic tuning of model predictive controllers for the activated sludge process. Proceedings of Chemical Process Control CPC7 (Canadá)
[8] Gil, A., P. Vega and M. Francisco (2001). Integrated Design of pH processes. IASTED MIC Conference, pp 226-229.
[9] Luyben, M. L. (1993). Analyzing the Interaction Between Process Design and Process Control. Ph.D. Thesis, Princeton University.
[10] Maciejowsky, J. M. (2002). Predictive Control with Constraints. Prentice Hall.
[11] Ross, R., J.D. Perkins, E. N. Pistikopoulos, G.L.M. Koot and J.M.G. van Schijndel. (2001). Optimal design and control of a high purity industrial distillation system. Computers and Chemical Engineering, 25, pp. 141-150.
[12] Sakizlis, V., J. D. Perkins and E. N. Pistikopoulos (2004). Recent advances in optimization-based simultaneous process and control design. Computers and Chemical Engineering, 28, pp. 2069-2086.
[13] Solis, F.J. and R. J-B. Wets (1981). Minimization by random search techniques. Mathematics of Operations Research, 6, pp. 19-30.
[14] Sotomayor, O. A. Z. and C. García (2002). Model-Based Predictive Control of a pre-denitrification plant: a linear state-space model approach. Proceedings of the IFAC World Congress, Barcelona (Spain).
[15] Vega, P. and G. Gutiérrez (1999). Optimal Design Control and Operation of wastewater treatment plants. European Control Conference (Germany).
See the full pdf manuscript of the abstract.
Presented Tuesday 18, 13:30 to 17:00, in session Process Synthesis & Design (T4-1P).
