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    Integration of the FMBPC strategy in a Closed-Loop Predictive Control structure. Application to the control of activated sludge

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    [ES] En este trabajo se aborda la integraci贸n de dos m茅todos o estrategias de Control Predictivo basado en Modelos, a saber: Control Predictivo basado en Modelos Borrosos (FMBPC) y Control Predictivo en Lazo Cerrado (CLP MPC). La primera de estas estrategias utiliza principios de Control Predictivo Funcional (PFC) y est谩 enmarcada, al mismo tiempo, en el 谩mbito del Control Inteligente (IC). La integraci贸n tiene como principal objetivo proporcionar a la estrategia de control no lineal FMBPC un procedimiento de optimizaci贸n que permita el manejo autom谩tico de restricciones en la variable de control. La soluci贸n propuesta consiste en hacer uso de una estructura complementaria de tipo CLP MPC para determinar mediante optimizaci贸n, en cada instante de muestreo, los valores 贸ptimos de un cierto t茅rmino aditivo, a sumar a la ley de control FMBPC, de tal modo que se satisfagan las restricciones. El modelo de predicciones y la ley de control base necesarios para realizar los c谩lculos en la estructura CLP MPC son proporcionados por la estrategia FMBPC. La estrategia mixta FMBPC/CLP propuesta ha sido validada, en simulaci贸n, aplic谩ndola al control de fangos activados en plantas de tratamiento de aguas residuales (EDAR), poniendo el foco en la imposici贸n de restricciones a la acci贸n de control. Los resultados obtenidos son satisfactorios, observando un buen rendimiento del algoritmo de control dise帽ado, al tiempo que se garantiza tanto la satisfacci贸n de las restricciones, que era el principal objetivo, como la estabilidad del sistema en lazo cerrado.[EN] This work addresses the integration of two methods or strategies of Model-Based Predictive Control, namely: Fuzzy Model-Based Predictive Control (FMBPC) and Closed-Loop Predictive Control (CLP-MPC). The first of these strategies uses principles of Predictive Functional Control (PFC) and is framed, at the same time, in the field of Intelligent Control (IC). The main objective of the integration is to provide to the FMBPC nonlinear control strategy an optimization procedure that allows the automatic handling of constraints in the control variable. The proposed solution consists of making use of a complementary structure of the CLP-MPC type to determine by optimization, at each sampling instant, the optimal values of a certain additive term, to be added to the FMBPC control law, in such a way that they are satisfied the constraints. The prediction model and base control law necessary to perform the calculations on the CLP-MPC structure are provided by the FMBPC strategy. The proposed FMBPC/CLP mixed strategy has been validated, in simulation, applying it to the control of activated sludge processes in wastewater treatment plants (WWTP), focusing on the imposition of constraints on the control action. The results obtained are satisfactory, observing a good performance of the designed control algorithm, while guaranteeing both the satisfaction of the constraints, which was the main objective, and the stability of the closed-loop system.Este trabajo cont贸 con el apoyo econ贸mico del Gobierno de Espa帽a a trav茅s del proyecto MICINN PID2019-105434RB-C31 y de la Fundaci贸n Samuel Sol贸rzano a trav茅s del proyecto FS / 20-2019.Vallejo, PM.; Vega, P. (2021). Integraci贸n de la estrategia FMBPC en una estructura de control predictivo en lazo cerrado. Aplicaci贸n al control de fangos activados. Revista Iberoamericana de Autom谩tica e Inform谩tica industrial. 19(1):13-26. https://doi.org/10.4995/riai.2021.15793OJS1326191Adetola, V., & Guay, M., 2010. 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    Control predictivo basado en modelos fuzzy de sistemas complejos. Aplicaci贸n al control y supervisi贸n de procesos de depuraci贸n de aguas

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    Tesis por compendio de publicaciones[ES] El Control Predictivo basado en Modelos (MPC) es un caso particular de estrategia de control autom谩tico de procesos que abarca un conjunto de procedimientos cuyo denominador com煤n es la utilizaci贸n de un modelo de predicciones para determinar una ley de control 贸ptima. El tipo de modelo elegido, los criterios de optimizaci贸n y el procedimiento de deducci贸n de la ley de control caracterizan cada una de las m煤ltiples alternativas de MPC que existen. El control predictivo es una consolidada y, al mismo tiempo, prometedora estrategia de control con m煤ltiples aplicaciones en el 谩mbito industrial y con numerosas l铆neas de investigaci贸n abiertas. Una de las modalidades de este tipo de control es el denominado Control Predictivo basado en Modelos Borrosos (FMBPC), que utiliza modelos cualitativos basados en reglas, globalmente no lineales, para representar el proceso a controlar. El control FMBPC est谩 enmarcado en el subcampo del Control Predictivo No Lineal (NLMPC/NMPC) y al mismo tiempo pertenece tambi茅n, parcialmente al menos, al campo del Control Inteligente (IC), debido a que utiliza una de las herramientas caracter铆sticas de la inteligencia artificial, como es la l贸gica borrosa. En la Tesis Doctoral que aqu铆 se presenta se considera una estrategia FMBPC cuyo modelo base es un modelo borroso, o Fuzzy Model (FM) en la literatura en ingl茅s, de tipo Takagi-Sugeno (TS), obtenido mediante identificaci贸n a partir de series de datos num茅ricos de entrada-salida (que pueden ser datos estrictamente experimentales o adaptaciones de estos, generados en simulaci贸n). Esta caracter铆stica dota a nuestra estrategia FMBPC de una interesante cualidad que aporta valor a帽adido dentro del campo del control NMPC, consistente en la 煤til informaci贸n cualitativa impl铆cita en el modelo borroso, consecuencia de la capacidad que tiene la identificaci贸n borrosa de capturar fielmente la din谩mica de un sistema a partir de datos num茅ricos. Esta propiedad repercute directamente de forma positiva en la validez de las predicciones y supone, en 煤ltima instancia, un incremento significativo del rendimiento o desempe帽o del algoritmo de control predictivo, en el caso de tratar con sistemas fuertemente no lineales, complejos o desconocidos. Esta es la raz贸n por la que en esta tesis se propone la estrategia FMBPC como la id贸nea para abordar el control de un cierto tipo de procesos conocidos como Procesos de Fangos Activados (ASP), muy habituales como mecanismo de depuraci贸n biol贸gica en Estaciones Depuradoras de Aguas Residuales (EDAR) (tambi茅n conocidas en la literatura en ingl茅s como Wastewater Treatment Plants (WWTP)). El inter茅s de la propuesta es doble: por un lado, contribuir a ampliar las l铆neas de investigaci贸n en el campo del control predictivo no lineal y por otro, aportar una estrategia y una metodolog铆a que puedan ser 煤tiles en la mejora de los procesos de depuraci贸n de aguas, cuya importancia en la salud p煤blica y en el cuidado del medio ambiente es creciente, cono as铆 se refleja en las legislaciones medioambientales, cada vez m谩s exigentes. Una parte importante del esfuerzo investigador desarrollado en la presente tesis ha sido enfocado a la aplicaci贸n de la estrategia FMBPC propuesta al paradigm谩tico caso de estudio elegido (procesos biol贸gicos ASP en plantas depuradoras de aguas residuales). Dadas las caracter铆sticas de estos procesos, principalmente su alta no linealidad, su complejidad intr铆nseca y su car谩cter multivariable, derivadas de su naturaleza biol贸gica, las investigaciones realizadas pueden trascender m谩s all谩 del mero 谩mbito del propio proceso. La implementaci贸n practica se ha llevado a cabo mediante simulaci贸n y ello ha supuesto un importante reto, principalmente en dos aspectos: por un lado, el desarrollo del software necesario y por otro, la implementaci贸n de los c谩lculos matem谩ticos apropiados. La investigaci贸n realizada puede descomponerse, de una manera esquem谩tica, en las siguientes cuatro fases o etapas: a) identificaci贸n borrosa del proceso ASP a partir de datos num茅ricos de entrada-salida y conversi贸n del modelo borroso obtenido en un modelo equivalente en el espacio de estados, discreto, lineal y variante en el tiempo (DLTV); b) determinaci贸n de una ley de control predictivo de tipo FMBPC, anal铆tica y expl铆cita, siguiendo los principios del denominado Control Predictivo Funcional (PFC); c) an谩lisis de estabilidad local en lazo cerrado de la estrategia FMBPC propuesta; d) integraci贸n de esta estrategia dentro de la configuraci贸n de control predictivo conocida como Paradigma de Lazo Cerrado (CLP), tambi茅n llamada control predictivo en lazo cerrado, con el objetivo de imponer restricciones de manera autom谩tica en la acci贸n de control. Los resultados obtenidos son satisfactorios, principalmente en lo que se refiere a la demostraci贸n de la utilidad de la estrategia FMBPC propuesta como una alternativa v谩lida en el campo del control predictivo no lineal, para sistemas complejos o desconocidos, con dos ventajas destacables en relaci贸n con otras estrategias, a saber: por un lado, la 煤til informaci贸n contenida en el modelo base de las predicciones, capturada durante el proceso de identificaci贸n borrosa previo a la aplicaci贸n de la estrategia y, por otro, la forma anal铆tica y explicita de la ley de control deducida, que facilita tanto la implementaci贸n del algoritmo de control como las tareas de an谩lisis (entre ellas, las de an谩lisis estabilidad). [EN] Model Predictive Control (MPC) is a particular case of automatic process control strategy that encompasses a set of procedures whose common denominator is the use of a prediction model to determine an optimal control law. The type of model chosen, the optimization criteria and the control law deduction procedure characterize each one of the multiple MPC alternatives that exist. Predictive control is a consolidated and, at the same time, promises a control strategy with multiple applications in the industrial field and with many open lines of research. One of the modalities of this type of control is the so-called Fuzzy Model-Based Predictive Control (FMBPC), which uses qualitative models based on rules, globally non-linear, to represent the process to be controlled. The FMBPC control is framed in the subfield of Non-Linear Predictive Control (NLMPC/NMPC) and at the same time it also belongs, partially at least, to the field of Intelligent Control (IC), because it uses one of the characteristic tools of intelligence artificial, as is fuzzy logic. In the Doctoral Thesis presented here, a FMBPC strategy is considered whose base model is a fuzzy model, or Fuzzy Model (FM) in the English literature, of the Takagi-Sugeno (TS) type, obtained through identification from series of input-output numerical data (which can be strictly experimental data or adaptations of these, generated in simulation). This feature provides our FMBPC strategy with an interesting quality that provides added value within the field of NMPC control, consisting of the useful qualitative information indicated in the fuzzy model, a consequence of the fuzzy identification's ability to faithfully capture the dynamics of a system from numerical data. This property has a direct positive impact on the validity of the predictions and, ultimately, a significant increase in the performance of the predictive control algorithm, in the case of dealing with expensive non-linear, complex or unknown systems. This is the reason why in this thesis the FMBPC strategy is proposed as the ideal one to address the control of a certain type of processes known as Activated Sludge Processes (ASP), very common as a biological purification mechanism in Water Treatment Plants. Waste (WWTP) (also known in English literature as Wastewater Treatment Plants (WWTP)). The interest of the proposal is twofold: on the one hand, to contribute to expanding the lines of research in the field of nonlinear predictive control and, on the other, to provide a strategy and methodology that can be useful in improving the debugging processes of waters, whose importance in public health and in caring for the environment is growing, as reflected in the increasingly demanding environmental legislation. An important part of the research effort developed in this thesis has been focused on the application of the FMBPC strategy to the chosen paradigmatic case study (ASP biological processes in wastewater treatment plants). Given the characteristics of these processes, mainly their high non-linearity, their intrinsic complexity and their multivariable character, derived from their biological nature, the investigations carried out can transcend beyond the mere scope of the process itself. The practical implementation has been carried out through simulation and this has been an important challenge, mainly in two aspects: on the one hand, the development of the necessary software and, on the other, the implementation of the appropriate mathematical calculations. The research carried out can be broken down, schematically, into the following four phases or stages: a) fuzzy identification of the ASP process from numerical input-output data and conversion of the fuzzy model obtained into an equivalent model in the space of states , discrete, linear and variant in time (DLTV); b) determine a predictive control law of the FMBPC type, analytical and clean, following the principles of the so-called Predictive Functional Control (PFC); c) closed-loop local stability analysis of the proposed FMBPC strategy; d) integration of this strategy within the predictive control configuration known as Closed Loop Paradigm (CLP), also called closed loop predictive control, with the aim of automatically imposing restrictions on the control action. The results obtained are satisfactory, mainly in what refers to the demonstration of the utility of the FMBPC strategy as a valid alternative in the field of nonlinear predictive control, for complex or unknown systems, with two advantage
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