Lynn Würth

Economic Dynamic Real-Time Optimization and Nonlinear Model-Predictive Control on Infinite Horizons

Abstract Abstract This paper investigates the formulation of nonlinear model-predictive control problems with economic objectives on an infinite horizon. The proposed formulation guarantees nominal stability for closed-loop operation. Furthermore, a novel solution method of the infinite horizon method through a transformation of the independent time variable is employed. The closed-loop optimization with infinite horizon is compared to a finite-horizon formulation. A small case study is presented for illustration purposes.

Infinite-Horizon Continuous-Time NMPC via Time Transformation

In this note, a solution method is presented for nonlinear model-predictive control of open-loop stable systems on an infinite horizon. The proposed method first reformulates the infinite-horizon continuous-time problem by a time-coordinate transformation as a finite horizon problem and computes the solution after discretization of the control variables. This method aims to ensure stability without imposing a terminal constraint set. The adaptive discretization algorithm allows an efficient and accurate solution of the infinite-horizon problem with a moderate number of discrete decision variables. The time transformation function is adapted such that the important dynamics of the system can be captured and the control variables can be discretized appropriately. An illustrative case study is presented.

Model-based investment planning model for stepwise capacity expansions of chemical plants

Abstract In this contribution a novel investment planning model for the development of stepwise capacity expansion strategies for chemical plants is proposed. This method is implemented in a decision support tool that can be, used during the early stage of plant engineering — a phase which is concerned with the conversion of a chemical process into a highly profitable plant. Based on a previous work by Oldenburg et al. [1], who proposed a method for a quick economic comparison of possible stepwise plant expansion scenarios versus building a full capacity plant, the approach presented in this paper is capable of identifying the optimal process-specific investment strategy on the level of unit operations. A mixed-integer linear programming model dedicated for stepwise capacity expansion strategies for chemical process plants forms the core of the tool.

Strategien zur Echtzeitoptimierung transient betriebener Prozesse (Strategies for Real-Time Optimization of Transient Processes)

Dieser Beitrag gibt eine Übersicht über neue Entwicklungen der Echtzeitoptimierung transienter Prozesse. Die Entwicklungen basieren auf einer Zerlegung des Prozessführungsproblems auf zwei durch unterschiedliche Zeitskalen gekennzeichnete Ebenen, die den wirtschaftlichen und den regelungstechnischen Zielen entsprechen. Zwei modellgestützte Strategien wurden entwickelt, welche die beiden Ebenen enger integrieren und auch bei Unsicherheiten eine nahezu wirtschaftlich optimale Prozessführung ermöglichen. Die Anwendung auf simulierte industrielle Prozesse mit verschiedenen betrieblichen Szenarien zeigen, dass mit diesen Strategien erhebliche wirtschaftliche Vorteile erreicht werden können. This paper gives an overview of recent developments and applications of dynamic real-time optimization. The developments are based on a decomposition strategy, which separates the economical and control objectives by formulating two sub-problems in closed-loop. Two approaches (model-based and model-free at the implementation level) are developed to provide tight integration of dynamic optimization of plant economics and control, and to handle uncertainty. Simulated industrial applications involving different dynamic operational scenarios demonstrate significant economical benefits to plant operation.

An Efficient Strategy for Real-Time Dynamic Optimization based on Parametric Sensitivities

Abstract The optimal operation of chemical processes is challenged by frequent transitions and by the influence of process or model uncertainties. Under uncertainties, it is necessary to quickly update the optimal trajectories in order to avoid the violation of constraints and the deterioration of the economic performance of the process. Although an economically optimal operation can be ensured by online dynamic optimization, the high computational load of dynamic optimization associated with nonlinear and complex models is often prohibitive in real-time applications. To reduce the computational time required for online computation of the optimal trajectories in the neighborhood of the optimal solution under uncertainty, different strategies have been explored recently. If the operation is affected by small perturbations, efficient techniques for updating the nominal trajectories based on parametric sensitivities are applied, which do not require the solution of the rigorous optimization problem. However for larger perturbations, the linear updates obtained by the neighboring extremal solutions are not sufficiently accurate, and the solution of the nonlinear optimization problem requires further iterations with updated sensitivities to give a feasible and optimal solution. In this work, the sensitivity-based approach of Kadam and Marquardt (2004) is extended with a fast computational method for second-order derivatives based on composite adjoints. The application of the method to a simulated semi-batch reactor demonstrates that fast and optimal trajectory updates can be obtained.