# Lehrstuhl Systemdynamik und Prozessfuehrung

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Item Process optimization under uncertainty(2023) Leo, Egidio; Engell, Sebastian; Grossmann, IgnacioShow more The ability of a production plant to be flexible by adjusting the operating conditions to changing demands, prices of the products and the raw materials is crucial to maintain a profitable operation. In this respect, the application of mathematical optimization techniques is unanimously recognized to be successful to improve the decision-making process. Typical examples are production planning, scheduling, real-time optimization and advanced process control. The more information are available to the optimization approach, the more "optimal" are the resulting decisions: the "optimal" production strategy cannot reduce the inventory costs if no supply-chain model is integrated into the production planning optimization. This thesis lies in the context of Enterprise-wide optimization with the goal of integrating decision layers and functions while accounting for uncertain information. A stochastic programming approach is adopted to integrate production scheduling with energy management and production planning with predictive maintenance. The approaches are analysed from a formulation perspective and from a computational point of view, which is necessary to deal with one of the challenges of the presented methods consisting in the size of the resulting optimization problems. To reduce the electricity cost that is generated by the uncertain peaks of the dayahead price, a two-stage risk-averse optimization is proposed to simultaneously define the optimal bidding curves for the day-ahead market and the optimal production schedule. The large-scale MILP problem is solved with a scenario-based decomposition technique, the progressive hedging algorithm. Heuristic procedures are applied to speed up the solution phase and to avoid the oscillatory behaviour due to the integer variables. Since large electricity consumers rely on Time-Of-Use power contracts to handle the volatility of the day-ahead price, the two-stage formulation is expanded into a multi-stage optimization to optimally purchase electricity from different sources and to generate electric power with a power plant. The unpractical size of the resulting problem is handled by approximating the multi-stage tree with a series of two-stage scenario-trees within a rolling horizon procedure. A mixed time grid handles the multi-scale nature of the problem by making short-term decisions with a detailed model and catching their effect on the long-term future with an aggregated model. While the electricity prices introduce exogenous uncertain information into the optimization problem, the predictive maintenance optimization carries endogenous uncertain sources into the production planning problem. Endogenous uncertainties, contrary to the exogenous ones, are uncertain information that can be modified (in the probability or in the timing of the realization) by the decision maker. The prognosis technique of the Cox model is embedded into a multi-stage stochastic program to consider an uncertain Remaining Useful Life of the equipment when the optimal operating conditions of the plant are defined. Two modelling approaches (based on superstructure-scenario trees and on conditional non-anticipativity constraints) are proposed to formulate the optimization problem with endogenous uncertainties. Two Benders-like decomposition techniques and several branching priority schemes are applied to handle the high complexity of the resulting optimization problems.Show more Item Modeling and energy efficiency analysis of the steelmaking process in an electric arc furnace(2022-09-16) Hernández, Jesús D.; Onofri, Luca; Engell, SebastianShow more This paper presents a comprehensive model of an industrial electric arc furnace (EAF) that is based upon several rigorous first-principles submodels of the heat exchange in the EAF and practical experience from an industrial melt shop. The model is suited for process simulation, optimization, and control applications. It assumes that the energy demand of the process is satisfied by six sources, the electric arc, the oxy-fuel burners, the oxygen lances, the combustion of coal, and the oxidation of metal in the liquid and in the solid phase. The energy exchange between the liquid and the solid phase due to liquid metal splashing is also considered. The different mechanisms of heat exchange are represented in the model as follows: (a) the radiative heat exchange from the arc to the other phases is computed using the DC circuit analogy, where the view factors are calculated using exact formulae and Monte-Carlo algorithms. (b) The energy input from the oxy-fuel burner is modeled using simplified geometries for which heat transfer relationships are known. (c) The amount of heat released by the oxidation of solid metal is described by the quadratic corrosion formula. (d) The energy exchange from the bath to the solid phase due to splashing is modeled using relationships and experimental data that are available in the literature. The model contains the melting rates and the efficiency of the oxygen lancing as free parameters; their values were computed by a least squares fit to process data of an industrial Ultra-High-Power EAF. In comparison with existing EAF models, the model presented here describes the dynamic behavior of the melting process more realistically. Based on the model, time-dependent energy efficiency curves for the various contributions and for the overall process are computed and discussed.Show more Item Supplement to Resource effiency indicator-based decision support for the operation of batch and mixed batch-continuous processing plants(2023-06-05) Kalliski, MarcShow more Item Resource effiency indicator-based decision support for the operation of batch and mixed batch-continuous processing plants(2022) Kalliski, Marc; Engell, Sebastian; Urbas, LeonShow more Steigende Konzentrationen von Treibhausgasen in der Atmosphäre sind der Grund für den globalen Klimawandel. Da die chemische Industrie wesentlich zu den Treibhausgasemissionen beiträgt, schaffen politische Entscheidungsträger Anreize und Gesetze, um die Industrie zu einer nachhaltigeren Produktion zu bewegen. In dieser Arbeit wird ein Rahmen zur Definition und Nutzung von Echtzeit-Ressourcene zienzindikatoren (REI) entwickelt, um die Ressourceneffizienz industrieller Produktionsprozesse kontinuierlich zu überwachen und zu optimieren. Die Ressourceneffizienz ist eine mehrdimensionale Größe, die in Relation zur Wirtschaftlichkeit bewertet werden kann. Der Fokus der Arbeit liegt dabei auf Batch-Prozessen und Prozessen, die diskontinuierliche und kontinuierliche Teilprozesse kombinieren. Diese stellen eine Herausforderung für die korrekte Erfassung relevanter Prozessgrößen und die anschlie ende Analyse dar. Das vorgeschlagene Propagationskonzept ermöglicht es, den Gesamtwirkungsgrad der Anlage auf Basis der Leistung ihrer Komponenten zu berechnen. Die daraus resultierenden REIs spiegeln die technische Leistung der Anlage wieder und werden zur Optimierung der gesamten Ressourceneffizienz eines Anwendungsbeispiels verwendet. Die Optimierung der Ressourceneeffizienz stellt ein mehrdimensionales Optimierungsproblem dar, bei dem die Pareto-optimalen Betriebspunkte die möglichen Kompromisse zwischen konkurrierenden Interessen angeben. Die Auswahl eines gewünschten Betriebspunktes aus der Paretomenge ist nicht trivial und kann sich ändernden Präferenzen folgen. Daher befasst sich der zweite Teil der Arbeit mit der Synthese eines effizienten und effektiven Entscheidungsunterstützungssystems (Decision Support System, DSS) zur Auswahl eines Betriebspunktes mit dem gewünschten Leistungsprofil. Die Methodik wird auf ein Beispiel angewendet und durch eine experimentelle Usability-Studie validiert. Damit leistet diese Arbeit einen Beitrag zur Optimierung der Ressourceneffizienz in der Prozessindustrie durch die Identifikation von ressourcenoptimalen Betriebszuständen. Die ganzheitliche Betrachtung der Ressourceneffizienz in Batchprozessen stellt eine wichtige Erweiterung der industriellen Praxis dar, die sich derzeit in der Regel auf eine Energieeffizienzanalyse nach ISO50001 beschränkt.Show more Item Numerical estimation of the geometry and temperature of an alternating current steelmaking electric arc(2020-10-09) Hernández, Jesús D.; Onofri, Luca; Engell, SebastianShow more A channel arc model (CAM) that predicts the temperature and the geometry of an electric arc from its voltage and impedance set-points is presented. The core of the model is a nonlinear programming (NLP) formulation that minimizes the entropy production of a plasma column, the physical and electrical properties of which satisfy the Elenbaas–Heller equation and Ohm's law. The radiative properties of the plasma are approximated utilizing the net emission coefficient (NEC), and the NLP is solved using a global numerical solver. The effects of the voltage and impedance set-points on the length of the electric arc are studied, and a linear formula that estimates the length of the arc in terms of its electrical set-points is deducted. The length of various electric arcs is measured in a fully operative electric arc furnace (EAF), and the results are used to validate the proposed models. The errors in the predictions of the models are 0.5 and 0.4 cm. In comparison, the existing empirical and Bowman formulae estimate the length of the experimental arcs with errors of 2.1 and 2.6 cm. A simplified formula to estimate the temperature of an electric arc in terms of its electrical set-points is also presented.Show more Item Tube-enhanced multi-stage model predictive control for flexible robust control of constrained linear systems with additive and parametric uncertainties(2021-03-24) Subramanian, Sankaranarayanan; Lucia, Sergio; Paulen, Radoslav; Engell, SebastianShow more The trade-off between optimality and complexity has been one of the most important challenges in the field of robust model predictive control (MPC). To address the challenge, we propose a flexible robust MPC scheme by synergizing the multi-stage and tube-based MPC approaches. The key idea is to exploit the nonconservatism of the multi-stage MPC and the simplicity of the tube-based MPC. The proposed scheme provides two options for the user to determine the trade-off depending on the application: the choice of the robust horizon and the classification of the uncertainties. Beyond the robust horizon, the branching of the scenario-tree employed in multi-stage MPC is avoided with the help of tubes. The growth of the problem size with respect to the number of uncertainties is reduced by handling small uncertainties via an invariant tube that can be computed offline. This results in linear growth of the problem size beyond the robust horizon and no growth of the problem size concerning small magnitude uncertainties. The proposed approach helps to achieve a desired trade-off between optimality and complexity compared to existing robust MPC approaches. We show that the proposed approach is robustly asymptotically stable. Its advantages are demonstrated for a CSTR example.Show more Item Surrogate modeling of thermodynamic equilibria: applications, sampling and optimization(2021-09-27) Winz, Joschka; Nentwich, Corina; Engell, SebastianShow more Models based on first principles are an effective way to model chemical processes. The quality of these depends critically on the accurate description of thermodynamic equilibria. This is provided by modern thermodynamic models, e.g., PC-SAFT, but they come with a high computational cost, which makes process optimization challenging. This can be addressed by using surrogate models to approximate the equilibrium calculations. A high accuracy of the surrogate model can be achieved by carefully choosing the points at which the original function is evaluated to create data for the training of the surrogate models, called sampling. Using a case study, different approaches to sampling are discussed and evaluated with a focus on new approaches to adaptive sampling.Show more Item Iterative process design with surrogate-assisted global flowsheet optimization(2021-11-03) Janus, Tim; Engell, SebastianShow more Flowsheet optimization is an important part of process design where commercial process simulators are widely used, due to their extensive library of models and ease of use. However, the application of a framework for global flowsheet optimization upon them is computationally expensive. Based on machine learning methods, we added mechanisms for rejection and generation of candidates to a framework for global flowsheet optimization. These extensions halve the amount of time needed for optimization such that the integration of the framework in a workflow for iterative process design becomes applicable.Show more Item Comparison of dual based optimization methods for distributed trajectory optimization of coupled semi-batch processes(2020-04-24) Maxeiner, Lukas Samuel; Engell, SebastianShow more The physical and virtual connectivity of systems via flows of energy, material, information, etc., steadily increases. This paper deals with systems of sub-systems that are connected by networks of shared resources that have to be balanced. For the optimal operation of the overall system, the couplings between the sub-systems must be taken into account, and the overall optimum will usually deviate from the local optima of the sub-systems. However, for reasons, such as problem size, confidentiality, resilience to breakdowns, or generally when dealing with autonomous systems, monolithic optimization is often infeasible. In this contribution, iterative distributed optimization methods based on dual decomposition where the values of the objective functions of the different sub-systems do not have to be shared are investigated. We consider connected dynamic systems that share resources. This situation arises for continuous processes in transient conditions between different steady states and in inherently discontinuous processes, such as batch production processes. This problem is challenging since small changes during the iterations towards the satisfaction of the overarching constraints can lead to significant changes in the arc structures of the optimal solutions for the sub-systems. Moreover, meeting endpoint constraints at free final times complicates the problem. We propose a solution strategy for coupled semi-batch processes and compare different numerical approaches, the sub-gradient method, ADMM, and ALADIN, and show that convexification of the sub-systems around feasible points increases the speed of convergence while using second-order information does not necessarily do so. Since sharing of resources has an influence on whether trajectory dependent terminal constraints can be satisfied, we propose a heuristic for the computation of free final times of the sub-systems that allows the dynamic sub-processes to meet the constraints. For the example of several semi-batch reactors which are coupled via a bound on the total feed flow rate, we demonstrate that the distributed methods converge to (local) optima and highlight the strengths and the weaknesses of the different distributed optimization methods.Show more Item Virtual splitting of shared resource networks for pricebased coordination with portfolio tariffs(2018) Wenzel, Simon; Maxeiner, Lukas Samuel; Engell, SebastianShow more In the process industries the optimal allocation of shared resources among physically coupled subsystems is key to an efficient operation of the overall system, e. g., an integrated production site. If the subsystems have a certain level of autonomy or it is desired to grant confidentiality to the constituent subsystems, price-based coordination can be employed, where an independent system operator (ISO) iteratively adjusts transfer prices for the shared resources until the demand and the supply match, i. e., the shared resource networks are balanced. In this contribution, a modified subgradient price update scheme is presented, which can be used for systems that are connected to external resources, such as pipelines, through which certain amounts of the resources can be exchanged at prices that are fixed in portfolio tariffs. The approach virtually splits the shared resource networks to account for the different price regimes in the available tariff. The principle is illustrated in a simulation study of a production site with three productions plants that are connected to an external distribution grid.Show more Item Price-based coordination of interconnected systems with access to external markets(2018) Maxeiner, Lukas; Wenzel, Simon; Engell, SebastianShow more Many industrial processes are coupled via multiple networks of energy and materials to achieve a resource and energy efficient production. In many cases however, setting up an integrated optimization problem for all units or plants that are directly connected to the networks is not possible, especially when not all information can be shared. In such cases, dual decomposition or price-based coordination can be used, where optimal transfer prices are iteratively determined at which the networks are balanced and the resources are allocated optimally between the participants. In this contribution, price-based coordination is extended to include the situation where limited resources can be bought or sold at predefined prices from external markets (e.g. via pipelines) and the resulting algorithms are demonstrated for a realistic example.Show more Item A model identification approach for the evaluation of plant efficiency(2019) Rahimi-Adli, Keivan; Schiermoch, Patrick D.; Beisheim, Benedikt; Wenzel, Simon; Engell, SebastianShow more Regulations and the public expectations on improving efficiency, reducing the carbon footprint and lowering the environmental impact drive the process industry towards improved operation and the development of new technologies. The efficiency of an existing production plant depends on a variety of factors like capacity utilisation, raw material quality, ambient temperature or operational performance. Identifying the influence of these factors on the performance of the plant helps to take suitable measures to drive it towards a more efficient operation. One approach to assess the resource efficiency potential of a plant is the comparison of the actual performance with the best possible operation under the given circumstances. This work presents a surrogate modelling approach for the identification of the best possible operation based on historical data. The surrogate model is compared to a more detailed rigorous model and advantages and possible shortcomings of the surrogate approach are discussed based on real production data at INEOS in K¨oln.Show more Item A study of explorative moves during modifier adaptation with quadratic approximation(2016-11-26) Gao, Weihua; Hernández, Reinaldo; Engell, SebastianShow more Modifier adaptation with quadratic approximation (in short MAWQA) can adapt the operating condition of a process to its economic optimum by combining the use of a theoretical process model and of the collected data during process operation. The efficiency of the MAWQA algorithm can be attributed to a well-designed mechanism which ensures the improvement of the economic performance by taking necessary explorative moves. This paper gives a detailed study of the mechanism of performing explorative moves during modifier adaptation with quadratic approximation. The necessity of the explorative moves is theoretically analyzed. Simulation results for the optimization of a hydroformylation process are used to illustrate the efficiency of the MAWQA algorithm over the finite difference based modifier adaptation algorithm.Show more Item Combined estimation and optimal control of batch membrane processes(2016-11-18) Jelemenský, Martin; Pakšiová, Daniela; Paulen, Radoslav; Latifi, Abderrazak; Fikar, MiroslavShow more In this paper, we deal with the model-based time-optimal operation of a batch diafiltration process in the presence of membrane fouling. Membrane fouling poses one of the major problems in the field of membrane processes. We model the fouling behavior and estimate its parameters using various methods. Least-squares, least-squares with a moving horizon, recursive least-squares methods and the extended Kalman filter are applied and discussed for the estimation of the fouling behavior on-line during the process run. Model-based optimal non-linear control coupled with parameter estimation is applied in a simulation case study to show the benefits of the proposed approach.Show more Item Application of Evolutionary Algorithms in Guaranteed Parameter Estimation(Institute of Electrical and Electronics Engineers (IEEE), 2016-11) Goerke, Thilo; Engell, SebastianShow more Model-based optimization and control is becoming more and more important in the process industries and in general. Modelling almost always involves the estimation of parameters from available data. The parameter estimation problem is usually posed as the minimization of the prediction error or the maximization of the likelihood function. If the uncertainty of the measurements taken from a real process is assumed to be an interval around the measured values, a set of parameter vectors exists that is able to describe the behavior of the systems within these uncertainties. Guaranteed parameter estimation deals with the problem of determining all parameter vectors that are compatible with uncertain observations. The solution of guaranteed parameter estimation problems for nonlinear dynamic models is computationally very demanding. In this contribution we present a memetic algorithm that determines the sets of feasible model parameters efficiently. It is applied to the estimation of kinetic parameters of a model that describes a copolymerization reaction. In the memetic algorithm, the fitness evaluation is based on the distance of the feasible solutions to each other, thus the presented approach is not restricted to a specific type of models.Show more Item Integrated electricity demand-side management and scheduling of energy-intensive plants(2015) Hadera, Hubert; Engell, Sebastian; Barbosa-Póvoa, AnaShow more Item Identifikation stückweise linearer Systeme aus Zeitreihen(2009-06-09T13:00:49Z) Wieland, Michael; Engell, S.; Bertram, T.Show more