(369r) Integrating Economic Targets for Simultaneous Structural and Operational Decision-Making in the Design of the Control Recipe

Improving plant management and decision-making is a promising area of potential industrial development. A flexible plant management provides benefits regarding safety, environment and economical issues. Also, it permits dealing with more complex and versatile systems, as well as adapting the process to market fluctuations. The process systems engineering approach aims to integrate the decision support system along the different hierarchical levels of decision-making (Rengaswamy, 1995), and it can be done either by serial solution of the different subproblems involved within the enterprise framework, or by the integrated resolution of the overall formulation of the whole problem with more advanced methodology.

This work aims at performing control recipe optimization integrating decisions which are typically considered at different levels in the framework of batch processes. Firstly, while defining control recipes, process design is simultaneously solved at the operational level. This means that operating conditions, set points, basic control parameters and resulting manipulated variables acting above the process are decided. The second type of problem which is attempted is the decision upon structural variables in a given plant. This means that the selected equipment, flow structure and characterization of the operational stages in the process cell are degrees of freedom, which allows improving the process configuration to the optimal one. Consequently, the focus of this work is optimizing the procedural specification within a process cell in a multipurpose batch plant. That will be of great interest, especially in the production of several components whose processing interacts due to competitive reactions and because different operating conditions are required to obtain the products efficiently. In such cases the integrated decision-making that is proposed will provide higher flexibility, leading to potentially better solutions, especially in the cases where uncertainty in product demands is significant. In order to achieve this goal, it is essential that the decision-making at this level takes into account the optimization of economic targets, instead of targets based on operational parameters traditionally considered at this hierarchical level. The goal is still to obtain the maximum profit, achieving both the minimum material and operational costs and the minimum processing time.

The process design problem can be formulated and solved attending to several approaches, such as mathematical programming, heuristics, metaheuristics or black-box methods. In this work, dynamic optimization (DO) and general disjunctive programming (GDP) are employed, which is known as mixed-logic dynamic optimization (MLDO). Previous works introducing MLDO approach have been reported, solving process design problems that require qualitative as well as quantitative knowledge. Bemporad & Morari (1999) proposed a framework for modeling and controlling systems by interdependent physical laws, logic rules, and operating constraints, denoted as mixed logical dynamical (MDL) systems. Oldenburg et al. (2002, 2003) solved the optimal configuration, sequencing and operation of batch equipment units. Nyström et al. (2006) also solved the optimal operation and sequencing of multiple units for continuously operated processes. The MLDO approach was also used to solve product grade transition and production scheduling in continuous operation processes (Nyström et al., 2005 and Prata et al., 2008).

The MLDO approach is used in this work to solve the optimal configuration (i.e. structural decisions) and profile of manipulated variables (i.e. operational decisions) to produce the requested products in the process cell, meeting a specified objective function. The methodology that has been used consists in defining a discrete-continuous model that represents the process cell using GDP. Firstly, a superstructure that includes all possible pieces of equipment and configurations is set. To specify which pieces of equipment are active and which are dismissed for processing a given batch, Boolean variables associated to each unit are used. These may be related using logical propositions to include previous knowledge and system restrictions (Raman & Grossmann, 1994, Türkay & Grossmann, 1996). Secondly, the dynamic behavior of each equipment unit is represented by differential and algebraic equations (DAE) where process variables, control variables and parameters are related. Summarizing, GDP problems capture both the qualitative (logical) and quantitative (DAE system) part of the problem (Vecchietti & Grossmann, 2000). Afterwards, the GDP problem is reformulated as a mixed-integer dynamic optimization (MIDO) problem by replacing the Boolean variables by binary ones and the disjunctions by ?big-M? relaxations (Williams, 1985). The obtained MIDO problem is solved using a direct-simultaneous approach by full discretization of state and control variable profiles, obtaining a mixed-integer nonlinear programming (MINLP) problem. The discretization is implemented using orthogonal collocation methods, based on Lagrange polynomials in shifted Legendre roots (Či?niar, 2005). The MINLP solution is obtained with the global optimization solver BARON (Tawarmalani & Sahinidis, 2004), using an objective function which aims at maximizing profit and is defined using the costs of products and operations. The results collect optimal configuration and operation for several scenarios, which are defined by the following variables and parameters: product demands, time horizon and unitary costs including cost of raw materials and final products, fixed operational costs and variable operational costs. Moreover, to highlight the improvement achieved with this combined resolution of structural and operational decisions, the objective function is compared for two different cases: 1) predefined control recipes and tuned control algorithms, using fixed operation sequences, and 2) not-predefined control recipes, using adaptable operational and structural strategies.

To exemplify and evaluate the usefulness of solving the integrated structural and operational problem, a case study is solved throughout the described methodology. The process consists of three competitive reactions to produce two different products. The process cell is composed by two reactors. Additionally, the necessary splitters and mixers are represented in the flowsheet, providing flexibility to process design. Three subsystems or configurations can be selected: a) operation with one single reactor, b) operation with two reactors in serial, or c) operation with two reactors in parallel.

Finally, it should be noticed that advantages of solving the joint operational and structural decisions are due to the adaption of operational strategies of a given physical system to: i) new requirements in production regarding long-term decisions (for example, introduction of new products to be processed or new procedures and plant policies) and ii) short-term adaption of operation strategies to process requirements (for example, market fluctuations, changes in planning or response to faults).

Acknowledgements

Financial support received from the Spanish Ministerio de Ciencia e Innovación (FPU grant and research projects DPI2006-05673 & DPI2009-09386) are gratefully acknowledged. Funding from the European Commission (FEDER) is also appreciated. Also, we thank Professor Dr. Wolfgang Marquardt and Kathrin Frankl at University RWTH-Aachen for fruitful advices.

References

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