Economic model predictive control based on a periodicity constraint

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper addresses a novel economic model predictive control (MPC) formulation based on a periodicity constraint to achieve an optimal periodic operation for discrete-time linear systems. The proposed control strategy does not rely on forcing the terminal state by means of a terminal equality constraint and hence it does not require a priori knowledge of a periodic steady trajectory. Instead, at each sampling time step the economic cost function is optimized based on a periodicity constraint over all the periodic trajectories that include the current state. The recursive feasibility and the closed-loop convergence to a periodic steady trajectory are discussed. Moreover, an optimality certificate of this steady trajectory is provided based on the Karush–Kuhn–Tucker (KKT) optimality conditions. Finally, an application to a well-known water distribution network benchmark is presented to demonstrate the proposed economic MPC in which the closed-loop simulation results obtained with a linear model and a virtual–reality simulator are both provided.Peer ReviewedPostprint (author's final draft

Advances in state estimation, diagnosis and control of complex systems

This dissertation intends to provide theoretical and practical contributions on estimation, diagnosis and control of complex systems, especially in the mathematical form of descriptor systems. The research is motivated by real applications, such as water networks and power systems, which require a control system to provide a proper management able to take into account their specific features and operating limits in presence of uncertainties related to their operation and failures from component malfunctions. Such a control system is expected to provide an optimal operation to obtain efficient and reliable performance. State estimation is an essential tool, which can be used not only for fault diagnosis but also for the controller design. To achieve a satisfactory robust performance, set theory is chosen to build a general framework for descriptor systems subject to uncertainties. Under certain assumptions, these uncertainties are propagated and bounded by deterministic sets that can be explicitly characterized at each iteration step. Moreover, set-invariance characterizations for descriptor systems are also of interest to describe the steady performance, which can also be used for active mode detection. For the controller design for complex systems, new developments of economic model predictive control (EMPC) are studied taking into account the case of underlying periodic behaviors. The EMPC controller is designed to be recursively feasible even with sudden changes in the economic cost function and the closed-loop convergence is guaranteed. Besides, a robust technique is plugged into the EMPC controller design to maintain these closed-loop properties in presence of uncertainties. Engineering applications modeled as descriptor systems are presented to illustrate these control strategies. From the real applications, some additional difficulties are solved, such as using a two-layer control strategy to avoid binary variables in real-time optimizations and using nonlinear constraint relaxation to deal with nonlinear algebraic equations in the descriptor model. Furthermore, the fault-tolerant capability is also included in the controller design for descriptor systems by means of the designed virtual actuator and virtual sensor together with an observer-based delayed controller.Esta tesis propone contribuciones de carácter teórico y aplicado para la estimación del estado, el diagnóstico y el control óptimo de sistemas dinámicos complejos en particular, para los sistemas descriptores, incluyendo la capacidad de tolerancia a fallos. La motivación de la tesis proviene de aplicaciones reales, como redes de agua y sistemas de energía, cuya naturaleza crítica requiere necesariamente un sistema de control para una gestión capaz de tener en cuenta sus características específicas y límites operativos en presencia de incertidumbres relacionadas con su funcionamiento, así como fallos de funcionamiento de los componentes. El objetivo es conseguir controladores que mejoren tanto la eficiencia como la fiabilidad de dichos sistemas. La estimación del estado es una herramienta esencial que puede usarse no solo para el diagnóstico de fallos sino también para el diseño del control. Con este fin, se ha decidido utilizar metodologías intervalares, o basadas en conjuntos, para construir un marco general para los sistemas de descriptores sujetos a incertidumbres desconocidas pero acotadas. Estas incertidumbres se propagan y delimitan mediante conjuntos que se pueden caracterizar explícitamente en cada instante. Por otra parte, también se proponen caracterizaciones basadas en conjuntos invariantes para sistemas de descriptores que permiten describir comportamientos estacionarios y resultan útiles para la detección de modos activos. Se estudian también nuevos desarrollos del control predictivo económico basado en modelos (EMPC) para tener en cuenta posibles comportamientos periódicos en la variación de parámetros o en las perturbaciones que afectan a estos sistemas. Además, se demuestra que el control EMPC propuesto garantiza la factibilidad recursiva, incluso frente a cambios repentinos en la función de coste económico y se garantiza la convergencia en lazo cerrado. Por otra parte, se utilizan técnicas de control robusto pata garantizar que las estrategias de control predictivo económico mantengan las prestaciones en lazo cerrado, incluso en presencia de incertidumbre. Los desarrollos de la tesis se ilustran con casos de estudio realistas. Para algunas de aplicaciones reales, se resuelven dificultades adicionales, como el uso de una estrategia de control de dos niveles para evitar incluir variables binarias en la optimización y el uso de la relajación de restricciones no lineales para tratar las ecuaciones algebraicas no lineales en el modelo descriptor en las redes de agua. Finalmente, se incluye también una contribución al diseño de estrategias de control con tolerancia a fallos para sistemas descriptores

Optimization of refinery preheat trains undergoing fouling: control, cleaning scheduling, retrofit and their integration

Crude refining is one of the most energy intensive industrial operations. The large amounts of crude processed, various sources of inefficiencies and tight profit margins promote improving energy recovery. The preheat train, a large heat exchanger network, partially recovers the energy of distillation products to heat the crude, but it suffers of the deposition of material over time – fouling – deteriorating its performance. This increases the operating cost, fuel consumption, carbon emissions and may reduce the production rate of the refinery. Fouling mitigation in the preheat train is essential for a profitable long term operation of the refinery. It aims to increase energy savings, and to reduce operating costs and carbon emissions. Current alternatives to mitigate fouling are based on heuristic approaches that oversimplify the representation of the phenomena and ignore many important interactions in the system, hence they fail to fully achieve the potential energy savings. On the other hand, predictive first principle models and mathematical programming offer a comprehensive way to mitigate fouling and optimize the performance of preheat trains overcoming previous limitations. In this thesis, a novel modelling and optimization framework for heat exchanger networks under fouling is proposed, and it is based on fundamental principles. The models developed were validated against plant data and other benchmark models, and they can predict with confidence the main effect of operating variables on the hydraulic and thermal performance of the exchangers and those of the network. The optimization of the preheat train, an MINLP problem, aims to minimize the operating cost by: 1) dynamic flow distribution control, 2) cleaning scheduling and 3) network retrofit. The framework developed allows considering these decisions individually or simultaneously, although it is demonstrated that an integrated approach exploits the synergies among decision levels and can reduce further the operating cost. An efficient formulation of the model disjunctions and time representation are developed for this optimization problem, as well as efficient solution strategies. To handle the combinatorial nature of the problem and the many binary decisions, a reformulation using complementarity constraints is proposed. Various realistic case studies are used to demonstrate the general applicability and benefits of the modelling and optimization framework. This is the first time that first principle predictive models are used to optimize various types of decisions simultaneously in industrial size heat exchanger networks. The optimization framework developed is taken further to an online application in a feedback loop. A multi-loop NMPC approach is designed to optimize the flow distribution and cleaning scheduling of preheat trains over two different time scales. Within this approach, dynamic parameter estimation problems are solved at frequent intervals to update the model parameters and cope with variability and uncertainty, while predictive first principle models are used to optimize the performance of the network over a future horizon. Applying this multi-loop optimization approach to a case study of a real refinery demonstrates the importance of considering process variability on deciding about optimal fouling mitigation approaches. Uncertainty and variability have been ignored in all previous model based fouling mitigation strategies, and this novel multi-loop NMPC approach offers a solution to it so that the economic savings are enhanced. In conclusion, the models and optimization algorithms developed in this thesis have the potential to reduce the operating cost and carbon emission of refining operations by mitigating fouling. They are based on accurate models and deterministic optimization that overcome the limitations of previous applications such as poor predictability, ignoring variability and dynamics, ignoring interactions in the system, and using inappropriate tools for decision making.Open Acces