Economics-based NMPC strategies for the operation and control of a continuous catalytic distillation process
Highlights
► Optimal operation and feedback control are combined using nonlinear model-based optimizations with different schemes. ► The potential benefits of two different economics-driven NMPC formulations are explored and discussed. ► As a case study, the rigorous process model of the catalytic esterification of methanol with acetic acid is considered. ► The performances of the pure tracking, the economics-oriented tracking and the economics-optimizing NMPCs are compared. ► The economics-optimizing NMPC can better enhance the process economical operations without scarifying product specifications.
Introduction
Economics-driven optimization based on rigorous first-principles models has been increasingly integrated into the operation of chemical processes in order to improve the competitiveness of these processes. Decisions on the most profitable conditions are usually made based on infrequent optimizations of stationary rigorous first-principles models (real-time optimization, RTO [1]). However, it has been recognized that the neglect of the dynamic process behavior in these models can lead to feasibility issues and performance degradation [1]. The inclusion of rigorous dynamic models in the decision-making policies makes it possible to overcome these difficulties and therefore higher process efficiency and profitability can be achieved. This can be realized by using different strategies of economics-based nonlinear model-predictive control (NMPC) or dynamic real-time optimization (D-RTO) schemes [2]. A historical view of the changing role of process control in operation and profit/loss measures together with the perspective of how process control has influenced business decision-making were presented in [3]. A novel framework for online full optimizing control of chemical processes was proposed in [4]. In [5], a motivation is given on how model predictive control techniques and dynamic process optimization can be integrated to improve the economic performance of chemical processes. In [6] an economics optimizing NMPC controller to optimize and control a complex dynamical model of a continuous catalytic distillation process for the production of methyl acetate using four control inputs and two controlled outputs has been proposed. In that work the “glcSolve” – DIRECT global optimization algorithm [7], [8] was used. Although the number of the objective function evaluations in the global optimizer “glcSolve” – DIRECT can be restricted to meet real-time requirements, “glcSolve” sometimes generates undesired and unjustifiable jumps in the controller response. In the work proposed here, different control structures and the local SQP optimization solver SNOPT [9] are used instead to obtain smooth controller responses. Additionally, we investigate the economics-oriented tracking NMPC scheme from [10].
The remainder of the paper is organized as follows: the next section gives a short overview on NMPC and the mathematical formulation of different NMPC strategies. In Section 3, a brief description of the catalytic distillation process, its mathematical modeling and the numerical strategy used for the model solution are presented. The control structures considered in this work are described in Section 4. Section 5 discusses the objective functions that are used in the different controllers. The control algorithm structure is shown in Section 6. In Section 7 we discuss the performance of these NMPC strategies. The paper finishes with Section 8 in which a general conclusion and directions for future work are presented.
Section snippets
Nonlinear model-predictive control
Over the last two decades, linear MPC has increasingly been implemented in the chemical industry [11]. Its strengths are its ability to naturally handle constraints and multi-input multi-output (MIMO) systems. It also enables the incorporation of general economic optimization criteria into feedback control [12].
A drawback of linear MPC is that linear models describe the dynamics of the process accurately only in the vicinity of the point at which the model was linearized or identified. This
Process description
During the last decades, integrated reaction and separation processes have become an area of intense research and several industrial processes have been realized because they provide a convenient way of alleviating kinetic and/or thermodynamic constraints that are usually present in the more traditional sequential configuration, which limit the extent of reaction and also the purity of the products [26], [27], [28], [29]. Moreover, integrated processes are energetically more efficient and
Control study
In Idris and Engell [6], it was proposed to use a MIMO-control structure for this process considering the reflux ratio, the heat supplied to the reboiler and the feed flow rates of the reactants as the manipulated variables, while the purity of MeAc in the distillate and the conversion of MeOH are the controlled variables. In this article, we use two alternative control structures in order to explore the potential of the system. These MIMO control structures are investigated using the
Economic NMPC strategies
The formulation of the economical function considered here is as follows:which can be rewritten mathematically as:where Ψ(k) is the profit function value at the time [k], Nf is the number of feed streams, is the product flow rate at time [k], CP is the product unit price, is the boil-up rate at time [k], CE is the price per energy unit, are the feed flow rates at time [k], and CR,j are the unit
Structure of the simulation environment
The control algorithm illustrated in Fig. 6 was implemented in gPROMS, MATLAB and TOMLAB (see [48]). An Excel spreadsheet is used to update the initial conditions and the control inputs at each iteration. The differential-algebraic equations of the optimization model and the plant model are integrated using the gPROMS’ DAE solver DASOLV, while the optimization is conducted in the TOMLAB optimization environment using the SNOPT NLP solver.
The objective functions and the constraints are
Control performance and discussion
The performance of the pure tracking controller, of the economics-oriented tracking controller and of the economics optimizing controllers for the control structures CS(1) and CS(2) are depicted in Fig. 7, Fig. 8. All controllers are able to achieve the control goals.
In control structure CS(1), the economics-oriented tracking controller is able to track the purity references while slightly maintaining the economics of the process. The economics optimizing controller, on the other hand, manages
Conclusion and future work
By economics optimizing nonlinear control, the plant economics can be enhanced without sacrificing product specifications. The economics optimizing and the economics-oriented tracking controllers were applied successfully to two different control structures for a simulated complex model of a catalytic distillation column with plant-model mismatch. The economics oriented tracking controller can improve the plant economics when more degrees of freedom than controlled variables are present,
Acknowledgements
The authors gratefully acknowledge the financial support of the International University of Africa (IUA), Khartoum, Sudan. Fruitful discussions with Christian Sonntag and the other members of the Process Dynamics and Operations Group (DYN) contributed to the results presented here. The research leading to these results has received funding from the European Union Seventh Frame-work Programe FP7/2007-2013 under grant agreement number FP7-ICT-2009-4248940 (EMBOCON).
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