Process optimization is used to improve the utility and the economic performance of industrial processes, and is as such central in most automation strategies. In this thesis, two feedback-based methods for online process optimization are considered: Extremum seeking control (ESC), a classic model-free method used for steady-state optimization which dates back to the early 1900's, and economic model predictive control (EMPC), a more recent method which utilizes a model to dynamically optimize the closed-loop process economics in real time. Part I of the thesis concerns ESC. Due to a well known result by Krsti\'c and Wang, it is known that the classic ESC-loop will possess a stable stationary solution in a neighborhood of the optimum when applied to dynamic plants. However, existence and stability of an optimal solution alone are not sufficient to guarantee that the ESC-loop will converge to the optimum; uniqueness also has to be considered. In this thesis, it is shown that the near-optimal solution is not necessarily unique, not even in cases where the objective, i.e., the steady-state input-output map, is convex. The stationary solutions to the loop are shown to be characterized by a condition on the local plant phase-lag, and for a biochemical reactor it is found that this condition can be satisfied not only locally at the optimum but also at arbitrary points away from the optimum. Bifurcation theory is used to show that the observed solution multiplicity may be explained by existence of fold bifurcation points, and conditions for existence of such points are given. The phase-lag condition for stationarity combined with the result by Krsti\'c and Wang suggest that the process phase-lag is connected to steady-state optimality. In this thesis, it is shown that the steady-state optimum corresponds to a bifurcation of the plant zero dynamics which is reflected in large local phase-lag variations. This explains why the classical ESC method will have a near-optimal stationary solution when applied to dynamic plants, and it also shows that a steady-state optimum may be located using only phase information. Finally, we introduce greedy ESC which is applicable to plants where the dynamics may be separated into different time-scales. By optimizing only the fast plant-dynamics, significant performance improvements may be achieved. Part II of this thesis concerns EMPC. The method is first evaluated for optimization of a paper-making process by means of simulations. These reveal several important properties of EMPC, e.g., that EMPC in the presence of excessive degrees of freedom automatically selects the inputs which are currently most efficient, and that EMPC effectively plans ahead which leads to significantly improved performance during grade changes. However, it is also observed that EMPC often operates with constraints active since economic objectives frequently are monotone, and this may lead to issues with robustness. To avoid active constraints, constraint margins are introduced to force the closed-loop to operate in the interior of the feasible set. The margins affect the economic performance significantly and the optimal choice is dependent on the uncertainty present in the problem. To avoid modeling of the uncertainty, it is suggested that the margins are adapted based on feedback from the realized closed-loop economic performance. / <p>QC 20180829</p>

Deregulation of electricity markets, increased usage of intermittent energy sources, and growing environmental concerns have created a volatile process manufacturing environment. Survival under this new paradigm requires chemical manufactures to shift from the traditional steady-state operation to a more dynamic and flexible operation mode. Under more frequent operating changes, the transition dynamics become increasingly relevant, rendering the traditional steady-state based scheduling decision-making suboptimal. This has motivated calls for the integration of scheduling and control. In an integrated scheduling and control framework, the scheduling decisions are based on a dynamic representation of the process. While various integration paradigms are proposed in the literature, our study concentrates on the closed-loop integration of scheduling and control. There are two main advantages to this approach: (i) seamless integration with the existing control system (i.e. it does not require a new control system infrastructure), (ii) the framework is aware of the control system dynamics, and hence has knowledge of the closed-loop process dynamics. The later aspect is particularly important as the control system plays a key role in determining the transition dynamics. The first part of our work is dedicated to developing an integrated scheduling and control framework that computes set-point trajectories, to be tracked by the lower-level linear model predictive control system, that are robust to demand uncertainty. We employ a piecewise linear representation of the nonlinear process model to obtain a mixed-integer linear programming (MILP) problem, thus alleviating the computational complexity compared to a mixed-integer nonlinear programming formulation. The value of the stochastic solution is used to confirm the superiority of the robust formulation against a nominal one that disregards uncertainty. In the second part of this study, we expand the framework to accommodate additional uncertainty types, including model and cost uncertainty. In the third part of this thesis, a deterministic integrated scheduling and control framework for processes controlled by distributed linear model predictive control is developed. The integrated problem is formulated as a MILP. To reduce the solution time, we introduce strategies to approximate the feedback control action. Through case studies, we demonstrate that knowledge of the control system enables the framework to effectively coordinate the MPC subsystems. The framework performs well even under conditions of plant-model mismatch conditions. In the final part of this study, we introduce an integrated scheduling and control formulation for processes controlled by nonlinear model predictive control (NMPC). Here, discrete scheduling decisions are represented using complementarity conditions. Additionally, we use the first-order Karush-Kuhn-Tucker conditions of the NMPC controller to compute the input values in the integrated problem. The resulting problem is a mathematical program with complementarity constraints that we solve using a regularization approach. For all case studies, the complementarity formulation effectively capture discrete scheduling decisions, and the KKT conditions always provides a local optimum of the associated NMPC problem. In summary, this study of the integration of scheduling and control addresses various control systems, uncertainty, and strategies for enhancing the solution time. Furthermore, we assess the performance of the proposed frameworks under conditions of plant-model mismatch, a common scenario in real-life applications. / Thesis / Doctor of Philosophy (PhD)

La industria química ha experimentado en las últimas décadas un aumento en la competencia por la cual las empresas se ven obligadas a adaptarse a un mercado cambiante y cada vez más exigente. Aunque la globalización ha abierto nuevos mercados, ha incrementado también el número de competidores, de tal manera que sólo las empresas que usen las plantas más integradas y eficientes podrán mantenerse en el negocio. En este contexto global, el principal propósito de esta tesis es desarrollar métodos que exploten la flexibilidad de los procesos, con el objetivo de aumentar la eficiencia de las plantas y asegurar los requerimientos de seguridad y calidad de los productos. Esta tesis contribuye a la optimización y a la gestión de la producción desde pequeñas plantas que usen procesos discontinuos hasta grandes plantas de procesado continuo.En primer lugar, esta tesis trata la gestión de los procesos continuos en los que suelen fabricar productos muy similares a gran escala. La gran ventaja de los procesos continuos es que pueden conseguir mayor consistencia en la calidad de los productos y que pueden aprovechar las economías de escala que reducen los costes y residuos. Sin embargo, la industria química para mantenerse competitiva necesita adaptar continuamente sus procesos a las condiciones del mercado y de operación. El sistema de control supervisor presentado en esta parte de la tesis disminuye el tiempo de reacción frente a incidentes en los procesos continuos y re-optimiza la producción en tiempo real, si existe posibilidad de mejora.A continuación, esta tesis trata la gestión de los procesos semicontinuos que permiten una operación más flexible y personalizada. Los procesos semicontinuos operan con puestas en marcha y paradas periódicas para acomodar las frecuentes transiciones entre diferentes productos. Esta tesis presenta un nuevo concepto de fabricación flexible que permite programar perfiles variables de velocidad de producción dentro de cada campaña de producción.La mayor parte del trabajo de investigación de esta tesis se dedica a la planificación de la producción en los procesos discontinuos por lotes, utilizados principalmente en la producción de productos químicos con alto valor añadido. Estos procesos ofrecen varias ventajas respecto a los procesos continuos y semicontinuos debido a la mayor flexibilidad para acomodar diversos productos, diferentes capacidades de producción, y la posibilidad de realizar operaciones completamente diferentes en los mismos equipos. Sin embargo, la obtención del plan de producción óptimo usando se complica al aumentar la complejidad de la planta y/o el número de lotes a planificar. La simplificación de considerar tiempos de transferencia despreciables es generalmente aceptada en la literatura para evitar la complejidad del manejo de las operaciones de transferencia. En cambio, esta tesis pretende resaltar el papel crítico que juegan las operaciones de transferencia en la sincronización de tareas, y en la consiguiente determinación de planes de producción factibles.Siguiendo con los procesos por lotes, esta tesis demuestra que el uso del concepto de recetas flexibles mejora la operación de los procesos en ambientes de producción con mucha incertidumbre. La flexibilidad de las receta se considera como una oportunidad adicional, tanto para la planificación de la producción reactiva como preactiva, reduciendo el riesgo de llegar a resultados económicamente desfavorables.Finalmente, esta tesis presenta las plantas discontinuas sin tuberías como una alternativas a las plantas por lotes clásicas. En la búsqueda de formas más competitivas y efectivas de producción, la flexibilidad para producir un elevado número de productos en plantas por lotes es limitada debido a la necesidad de equipos fijos conectados por tuberías y frecuentes tareas de limpieza. Las plantas sin tuberías presentan una mayor flexibilidad ya que el material se transfiere entre estaciones de procesamiento usando equipos que se mueven dentro de la planta. El trabajo presentado en esta parte de la tesis contribuye a la mejora en la gestión de este tipo de plantas proponiendo una formulación más eficiente a las encontradas en la literatura que resuelve el problema de la planificación de la producción.En resumen, esta tesis desarrolla nuevas estrategias de modelado y métodos de resolución encaminados al soporte de la toma de decisiones que explotan la flexibilidad intrínseca de los procesos químicos. Las principales ventajas de cada una de las contribuciones de esta tesis se demuestran mediante su aplicación a diferentes casos de estudio. / The chemical industry has become increasingly competitive over the past decades. Companies are required to adapt to changing market conditions and meet stricter product specifications. While globalization has opened new markets for the chemical industry, it has also increased the competitor pool, giving an advantage to companies with more efficient and highly integrated plants.In this context, the main aim of this thesis is to demonstrate new concepts and computational methods that exploit process flexibility to enhance plant profitability under transient operating conditions. These methods ensure that safety and product quality requirements are consistently met. This thesis makes contributions to the optimization and management of production in plants ranging from small batch plants to large capacity continuous processes.First, this thesis addresses the management of continuous processes, in which similar products are mass produced. Continuous processes can achieve the highest consistency and product quality by taking advantage of economies of scale and reduced manufacturing costs and waste. However, in order to remain competitive in the market, plants are required to dynamically adapt their processes to fit the continuously changing market and operating conditions. The supervisory control system presented in this part of the thesis decreases the system reaction time to incidences and re-optimizes the production in real time if the opportunity for improved performance exists.Next, this thesis addresses the management of semicontinuous processes, which allow more customized and flexible operation. Semicontinuous processes run with periodic start-ups and shutdowns to accommodate frequent product transitions. This thesis proposes an optimization model that creates improved production schedules by introducing a new concept of flexible manufacturing that allows production rate profiles to be programmed within each operation campaign.The major part of the research work of this thesis deals with the operational management of batch processes, which are mainly used for the production of high value-added chemicals. Batch processing offers the advantage of increased flexibility in product variety, production volume, and the assortment of operations that can be processed by a particular piece of equipment. However, the trade-off is that production scheduling is significantly complicated by the large number of batches involved with different production paths. In order to avoid the complexity of managing transfer operations, the assumption of negligible transfer times is generally accepted in batch scheduling. Conversely, this thesis highlights the critical role that transfer operations play in the synchronization of tasks and in determining the feasibility of production schedules.Continuing to focus on batch plant operation, this thesis demonstrates that the use of the concept of flexible recipes enhances the operation batch plants within an uncertain environment. Recipe flexibility is considered as an additional opportunity for reactive scheduling as well as a proactive way to reduce the risk of meeting unfavorable scenarios.Finally, this thesis examines pipeless plants as an alternative to batch plants. In the search for more competitive and effective ways of production, flexibility of batch plants for producing a large number of products is limited due to the need for equipment, piping and frequent cleaning tasks. Pipeless plants have enhanced flexibility over batch plants, because the material is moved along its production path through moveable vessels. This part of the thesis contributes to the optimization of the management of pipeless plants by proposing an alternative formulation for solving short-term scheduling problems.In summary, this thesis provides novel modeling approaches and solution methods aimed at supporting the decision-making process in plant production scheduling which exploit the existing flexibility in chemical processes. The main advantages of each contribution are highlighted through case studies.

This study develops a discrete search-based optimization method for path planning in a highly nonlinear dynamical system. The method enables real-time trajectory improvement and singular configuration avoidance in satellite rotation using Control Moment Gyroscopes. By streamlining a legacy optimization method and combining it with a local singularity management scheme, this optimization method reduces the computational burden and advances the capability of satellites to make autonomous look-ahead decisions in real-time. Current optimization methods plan offline before uploading to the satellite and experience high sensitivity to disturbances. Local methods confer autonomy to the satellite but use only blind decision-making to avoid singularities. This thesis' method seeks near-optimal trajectories which balance between the optimal trajectories found using computationally intensive offline solvers and the minimal computational burden of non-optimal local solvers. The new method enables autonomous guidance capability for satellites using discretization and stage division to minimize the computational burden of real-time optimization.

The actualization of real-time economically optimal process operation requires proper integration of real-time optimization (RTO) and dynamic control. This dissertation addresses the integration problem and provides a formal design technique that properly integrates RTO and model predictive control (MPC) under parametric uncertainties. The task is posed as an adaptive extremum-seeking control (ESC) problem in which the controller is required to steer the system to an unknown setpoint that optimizes a user-specified objective function. The integration task is first solved for linear uncertain systems. Then a method of determining appropriate excitation conditions for nonlinear systems with uncertain reference setpoint is provided. Since the identification of the true cost surface is paramount to the success of the integration scheme, novel parameter estimation techniques with better convergence properties are developed. The estimation routine allows exact reconstruction of the system's unknown parameters in finite-time. The applicability of the identifier to improve upon the performance of existing adaptive controllers is demonstrated. Adaptive nonlinear model predictive controllers are developed for a class of constrained uncertain nonlinear systems. Rather than relying on the inherent robustness of nominal MPC, robustness features are incorporated in the MPC framework to account for the effect of the model uncertainty. The numerical complexity and/or the conservatism of the resulting adaptive controller reduces as more information becomes available and a better uncertainty description is obtained. Finally, the finite-time identification procedure and the adaptive MPC are combined to achieve the integration task. The proposed design solves the economic optimization and control problem at the same frequency. This eliminates the ensuing interval of "no-feedback" that occurs between economic optimization interval, thereby improving disturbance attenuation. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2008-08-08 12:30:47.969

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Increasing environmental, economic, and political concerns regarding the consumption of fossil fuels have highlighted the need for more efficient and alternative energy solutions. Hybrid electric vehicles represent a near-term opportunity for reducing liquid fossil fuel consumption and green-house gas emissions in the transportation industry, and as a result, many automotive manufacturers have invested heavily in hybrid vehicle development. The increased complexity of hybrid electric vehicles over standard internal combustion engine-powered vehicles has subsequently placed significant emphasis on development of advanced control methods geared towards efficient energy management. Real-time optimization-based methods represent the current state-of-the-art in terms of hybrid vehicle control and energy management. This thesis summarizes the development of an optimization-based real-time control system – which determines the optimal instantaneous system operating point, including gear, traction split between front rear axles, and engine speed and torque – and its application to an all-wheel drive extended-range electric vehicle that uses a General Motor’s front-wheel drive 2-Mode electronic continuously variable transmission and an additional rear traction motor. The real-time control system was developed and validated using a plant model and preliminarily tested in the vehicle using a four-wheel drive chassis dynamometer. Results of simulation and in-vehicle testing demonstrate engine operation focused on high-efficiency operating regions and minimal use of the rear traction motor. Further testing revealed that a rule-based traction split system may be sufficient to replace the optimization-based traction split determination, and that the limited rear traction motor use was not a function of the motor itself, but rather an inherent result of the selected architecture. / Graduate

A otimização de processos vem se tornando uma ferramenta fundamental para o aumento da lucratividade das plantas químicas. Diversos métodos de otimização foram propostos ao longo dos anos, sendo que a otimização em tempo real (RTO) é a solução mais consolidada industrialmente, enquanto que o self-optimizing control (SOC) surge como uma alternativa simplificada, com um menor custo de implantação em relação a esse. Neste trabalho são estudados diversos aspectos da metodologia de SOC, iniciando pela análise do impacto do ponto de operação para o desenvolvimento de estruturas de controle auto-otimizáveis. São propostas modificações na formulação do problema de otimização de SOC de modo que as variáveis controladas sejam determinadas no mesmo problema de otimização em que é escolhido o ponto de operação, permitindo a redução da perda do processo. De forma a analisar a influência da dinâmica nos resultados obtidos, é realizado um estudo comparativo da perda gerada no processo ao longo da operação para as estruturas de otimização baseadas em RTO e em SOC. Com base nos resultados obtidos para uma unidade didática, mostra-se que o comportamento dinâmico do distúrbio possui grande influência na escolha da técnica de otimização, quebrando a ideia de que o RTO é um limite superior do SOC. A aplicação industrial das técnicas clássicas de SOC é validada em uma unidade de separação de propeno, baseada em uma unidade real em operação. A partir da modelagem do processo em simulador comercial, foram geradas as variáveis controladas que permitam uma perda aceitável para a unidade, comprovando a viabilidade de implantação da metodologia em unidades reais. / Process optimization has become a fundamental tool for increasing chemical plants profit. Several optimization methods have been proposed over the years, and real-time optimization (RTO) is the most consolidated solution industrially while self-optimizing control (SOC) appears as a simplified alternative with a lower implementation cost. In this work several aspects of SOC methodology are studied, starting from the analysis of the impact of operating point in the development of self-optimizing control structures. Improvements are proposed in SOC optimization problem formulation where controlled variables are determined in the same optimization problem that operating point, thus reducing significantly process loss. In order to analyze the influence of dynamics on the results, a comparative study is accomplished comparing the loss generated in the process throughout the operation for optimization structures based on RTO and SOC. With the results generated for a toy unit, it is shown that the disturbance dynamic behavior has a great influence on choosing the optimization technique, breaking the idea that RTO is an upper limit of SOC. The industrial application of classical SOC techniques is tested on a propylene separation unit, really operating nowadays. The process was modelled in a commercial simulator and with this model it was generated the best set of controlled variables, based on SOC, that achieve an acceptable loss for the unit, showing that the methodology can be applied in in real units.

A otimização de processos vem se tornando uma ferramenta fundamental para o aumento da lucratividade das plantas químicas. Diversos métodos de otimização foram propostos ao longo dos anos, sendo que a otimização em tempo real (RTO) é a solução mais consolidada industrialmente, enquanto que o self-optimizing control (SOC) surge como uma alternativa simplificada, com um menor custo de implantação em relação a esse. Neste trabalho são estudados diversos aspectos da metodologia de SOC, iniciando pela análise do impacto do ponto de operação para o desenvolvimento de estruturas de controle auto-otimizáveis. São propostas modificações na formulação do problema de otimização de SOC de modo que as variáveis controladas sejam determinadas no mesmo problema de otimização em que é escolhido o ponto de operação, permitindo a redução da perda do processo. De forma a analisar a influência da dinâmica nos resultados obtidos, é realizado um estudo comparativo da perda gerada no processo ao longo da operação para as estruturas de otimização baseadas em RTO e em SOC. Com base nos resultados obtidos para uma unidade didática, mostra-se que o comportamento dinâmico do distúrbio possui grande influência na escolha da técnica de otimização, quebrando a ideia de que o RTO é um limite superior do SOC. A aplicação industrial das técnicas clássicas de SOC é validada em uma unidade de separação de propeno, baseada em uma unidade real em operação. A partir da modelagem do processo em simulador comercial, foram geradas as variáveis controladas que permitam uma perda aceitável para a unidade, comprovando a viabilidade de implantação da metodologia em unidades reais. / Process optimization has become a fundamental tool for increasing chemical plants profit. Several optimization methods have been proposed over the years, and real-time optimization (RTO) is the most consolidated solution industrially while self-optimizing control (SOC) appears as a simplified alternative with a lower implementation cost. In this work several aspects of SOC methodology are studied, starting from the analysis of the impact of operating point in the development of self-optimizing control structures. Improvements are proposed in SOC optimization problem formulation where controlled variables are determined in the same optimization problem that operating point, thus reducing significantly process loss. In order to analyze the influence of dynamics on the results, a comparative study is accomplished comparing the loss generated in the process throughout the operation for optimization structures based on RTO and SOC. With the results generated for a toy unit, it is shown that the disturbance dynamic behavior has a great influence on choosing the optimization technique, breaking the idea that RTO is an upper limit of SOC. The industrial application of classical SOC techniques is tested on a propylene separation unit, really operating nowadays. The process was modelled in a commercial simulator and with this model it was generated the best set of controlled variables, based on SOC, that achieve an acceptable loss for the unit, showing that the methodology can be applied in in real units.

A otimização de processos vem se tornando uma ferramenta fundamental para o aumento da lucratividade das plantas químicas. Diversos métodos de otimização foram propostos ao longo dos anos, sendo que a otimização em tempo real (RTO) é a solução mais consolidada industrialmente, enquanto que o self-optimizing control (SOC) surge como uma alternativa simplificada, com um menor custo de implantação em relação a esse. Neste trabalho são estudados diversos aspectos da metodologia de SOC, iniciando pela análise do impacto do ponto de operação para o desenvolvimento de estruturas de controle auto-otimizáveis. São propostas modificações na formulação do problema de otimização de SOC de modo que as variáveis controladas sejam determinadas no mesmo problema de otimização em que é escolhido o ponto de operação, permitindo a redução da perda do processo. De forma a analisar a influência da dinâmica nos resultados obtidos, é realizado um estudo comparativo da perda gerada no processo ao longo da operação para as estruturas de otimização baseadas em RTO e em SOC. Com base nos resultados obtidos para uma unidade didática, mostra-se que o comportamento dinâmico do distúrbio possui grande influência na escolha da técnica de otimização, quebrando a ideia de que o RTO é um limite superior do SOC. A aplicação industrial das técnicas clássicas de SOC é validada em uma unidade de separação de propeno, baseada em uma unidade real em operação. A partir da modelagem do processo em simulador comercial, foram geradas as variáveis controladas que permitam uma perda aceitável para a unidade, comprovando a viabilidade de implantação da metodologia em unidades reais. / Process optimization has become a fundamental tool for increasing chemical plants profit. Several optimization methods have been proposed over the years, and real-time optimization (RTO) is the most consolidated solution industrially while self-optimizing control (SOC) appears as a simplified alternative with a lower implementation cost. In this work several aspects of SOC methodology are studied, starting from the analysis of the impact of operating point in the development of self-optimizing control structures. Improvements are proposed in SOC optimization problem formulation where controlled variables are determined in the same optimization problem that operating point, thus reducing significantly process loss. In order to analyze the influence of dynamics on the results, a comparative study is accomplished comparing the loss generated in the process throughout the operation for optimization structures based on RTO and SOC. With the results generated for a toy unit, it is shown that the disturbance dynamic behavior has a great influence on choosing the optimization technique, breaking the idea that RTO is an upper limit of SOC. The industrial application of classical SOC techniques is tested on a propylene separation unit, really operating nowadays. The process was modelled in a commercial simulator and with this model it was generated the best set of controlled variables, based on SOC, that achieve an acceptable loss for the unit, showing that the methodology can be applied in in real units.