Modelação e controlo de sistemas com incertezas baseados em lógica difusa de tipo-2

Doutoramento em Engenharia EletrotécnicaA última fronteira da Inteligência Artificial será o desenvolvimento de um sistema computacional autónomo capaz de "rivalizar" com a capacidade de aprendizagem e de entendimento humana. Ainda que tal objetivo não tenha sido até hoje atingido, da sua demanda resultam importantes contribuições para o estado-da-arte tecnológico atual. A Lógica Difusa é uma delas que, influenciada pelos princípios fundamentais da lógica proposicional do raciocínio humano, está na base de alguns dos sistemas computacionais "inteligentes" mais usados da atualidade. A teoria da Lógica Difusa é uma ferramenta fundamental na suplantação de algumas das limitações inerentes à representação de informação incerta em sistemas computacionais. No entanto esta apresenta ainda algumas lacunas, pelo que diversos melhoramentos à teoria original têm sido introduzidos ao longo dos anos, sendo a Lógica Difusa de Tipo-2 uma das mais recentes propostas. Os novos graus de liberdade introduzidos por esta teoria têm-se demonstrado vantajosos, particularmente em aplicações de modelação de sistemas não-lineares complexos. Uma das principais vantagens prende-se com o aumento da robustez dos modelos assim desenvolvidos comparativamente àqueles baseados nos princípios da Lógica Difusa de Tipo-1 sem implicar necessariamente um aumento da sua dimensão. Tal propriedade é particularmente vantajosa considerando que muitas vezes estes modelos são utilizados como suporte ao desenvolvimento de sistemas de controlo que deverão ser capazes de assegurar o comportamento ótimo de um processo em condições de operação variáveis. No entanto, o estado-da-arte da teoria de controlo de sistemas baseada em modelos não tem integrado todos os melhoramentos proporcionados pelo desenvolvimento de modelos baseados nos princípios da Lógica Difusa de Tipo-2. Por essa razão, a presente tese propõe-se a abordar este tópico desenvolvendo uma metodologia de síntese de Controladores Preditivos baseados em modelos Takagi-Sugeno seguindo os princípios da Lógica Difusa de Tipo-2. De modo a cumprir este objetivo, quatro linhas de investigação serão debatidas neste trabalho.Primeiramente proceder-se-á ao desenvolvimento de uma metodologia de treino de Modelos Difusos de Tipo-2 simplificada, focada em dois paradigmas: manter a clareza dos intervalos de incerteza introduzidos sobre um Modelo Difuso de Tipo-1; assegurar a validade dos diversos modelos localmente lineares que constituem a estrutura Takagi- Sugeno, de modo a torná-los adequados a métodos de síntese de controladores baseados em modelos. O modelo desenvolvido é tipicamente utilizado para extrapolar o comportamento do sistema numa janela temporal futura. No entanto, quando usados em aproximações de sistemas não lineares, os modelos do tipo Takagi-Sugeno estabelecem um compromisso entre exatidão e complexidade computacional. Assim, é proposta a utilização dos princípios da Lógica Difusa de Tipo-2 para reduzir a influência dos erros de modelação nas estimações obtidas através do ajuste dos intervalos de incerteza dos parâmetros do modelo. Com base na estrutura Takagi-Sugeno, um método de linearização local de modelos não-lineares será utilizado em cada ponto de funcionamento do sistema de modo a obter os parâmetros necessários para a síntese de um controlador otimizado numa janela temporal futura de acordo com os princípios da teoria de Controlo Preditivo Generalizado - um dos algoritmos de Controlo Preditivo mais utilizado na indústria. A qualidade da resposta do sistema em malha fechada e a sua robustez a perturbações serão então comparadas com implementações do mesmo algoritmo baseadas em métodos de modelação mais simples. Para concluir, o controlador proposto será implementado num System-on-Chip baseado no core ARM Cortex-M4. Com o propósito de facilitar a realização de testes de implementação de algoritmos de controlo em sistemas embutidos, será apresentada também uma plataforma baseada numa arquitetura Processor-In-the-Loop, que permitirá avaliar a execução do algoritmo proposto em sistemas computacionais com recursos limitados, aferindo a existência de possíveis limitações antes da sua aplicação em cenários reais. A validade do novo método proposto é avaliada em dois cenários de simulação comummente utilizados em testes de sistemas de controlo não-lineares: no Controlo da Temperatura de uma Cuba de Fermentação e no Controlo do Nível de Líquidos num Sistema de Tanques Acoplados. É demonstrado que o algoritmo de controlo desenvolvido permite uma melhoria da performance dos processos supramencionados, particularmente em casos de mudança rápida dos regimes de funcionamento e na presença de perturbações ao processo não medidas.The development of an autonomous system capable of matching human knowledge and learning capabilities embedded in a compact yet transparent way has been one of the most sought milestones of Artificial Intelligence since the invention of the first mechanical general purpose computers. Such accomplishment is yet to come but, in its pursuit, important contributions to the state-of-the-art of current technology have been made. Fuzzy Logic is one of such, supporting some of the most used frameworks for embedding human-like knowledge in computational systems. The theory of Fuzzy Logic overcame some of the difficulties that the inherent uncertainty in information representations poses to the development of computational systems. However, it does present some limitations so, aiming to further extend its capabilities, several improvements over its original formalization have been proposed over the years such as Type-2 Fuzzy Logic - one of its most recent advances. The additional degrees of freedom of Type-2 Fuzzy Logic are showing greater potential to supplant its original counterpart, especially in complex non-linear modeling tasks. One of its main outcomes is its capability of improving the developed model’s robustness without necessarily increasing its dimensionality comparatively to a Type-1 Fuzzy Model counterpart. Such feature is particularly advantageous if one considers these model as a support for developing control systems capable of maintaining a process’s optimal performance over changing operating conditions. However, state-of-the art model-based control theory does not seem to be taking full advantage of the improvements achieved with the development of Type-2 Fuzzy Logic based models. Therefore, this thesis proposes to address this problem by developing a Model Predictive Control system supported by Interval Type-2 Takagi- Sugeno Fuzzy Models. To accomplish this goal, four main research directions are covered in this work.Firstly, a simpler method for training a Type-2 Takagi-Sugeno Fuzzy Model focused on two main paradigms is proposed: maintaining a meaningful interpretation of the uncertainty intervals embedded over an estimated Type-1 Fuzzy Model; ensuring the validity of several locally linear models that constitute the Takagi-Sugeno structure in order to make them suitable for model-based control approaches. Based on the developed model, a multi-step ahead estimation of the process behavior is extrapolated. However, as Takagi-Sugeno Fuzzy Models establish a trade-off between accuracy and computational complexity when used as a non-linear process approximation, it is proposed to apply the principles of Type-2 Fuzzy Logic to reduce the influence of modeling uncertainties on the obtained estimations by adjusting the model parameters’ uncertainty intervals. Supported by the developed Type-2 Takagi-Sugeno Fuzzy Model, a locally linear approximation of each current operation point is used to obtain the optimal control law over a prediction horizon according to the principles of Generalized Predictive Control - one of the most used Model Predictive Control algorithms in Industry. The improvements in terms of closed loop tracking performance and robustness to unmodeled operation conditions are then assessed comparatively to Generalized Predictive Control implementations based on simpler modeling approaches. Ultimately, the proposed control system is implemented in a general purpose System-on-a-Chip based on a ARM Cortex-M4 core. A Processor-In-the-Loop testing framework, developed to support the implementation of control loops in embedded systems, is used to evaluate the algorithm’s turnaround time when executed in such computationally constrained platform, assessing its possible limitations before deployment in real application scenarios. The applicability of the new methods introduced in this thesis is illustrated in two simulated processes commonly used in non-linear control benchmarking: the Temperature Control of a Fermentation Reactor and the Liquid Level Control of a Coupled Tanks System. It is shown that the developed control system achieves an improved closed loop performance of the above mentioned processes, particularly in the cases of quick changes in the operation regime and in presence of unmeasured external disturbances

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Study of Intelligent Control Techniques Applied to a Stirring Tank with Heat Exchanger

This work presents a study and evaluation of intelligent control techniques applied to the problem of temperature control of a stirring tank with heat exchanger. This problem is represented by the example provided and documented by MathWorks in MATLAB/Simulink software, called Heatex. The intelligent techniques used are Fuzzy Logic Controller (FLC), Fuzzy Cognitive Maps (FCM), Artificial Neural Networks (ANN) and the combination of these. The proportional-integral (PI) controller provided in the Heatex example is considered as a reference basis during the evaluation of the intelligent control techniques in different test scenarios. The metrics Integral of Absolute Error (IAE) and Integral Time-weighted Absolute Error (ITAE), as well as the parameters overshoot percentage and settling time are the criteria used to evaluate the control techniques performance

The Application of Fuzzy Logic in Determining Linguistic Rules and Associative Membership Functions for the Control of a Manufacturing Process

Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory. Its methodology aims to provide a definitive solution from information that may be construed as ambiguous, imprecise or noisy. Classical set theory studies the properties of sets, while fuzzy set theory investigates the degree to which an element can be related to a set. The aim of this project is to develop a control strategy for a specific technical challenge relating to the food processing sector based on the deployment of fuzzy logic control concepts. Specifically, in this paper the author is concerned with the ability to control the density input of a variable feed product stream by automatically adjusting the „thermo pressure‟ & „feed flow‟ within desired limits. For the purpose of this study, the expert knowledge of both senior automation engineers and process operators was procured in order to develop an understanding of the dynamics and the limitations of the manufacturing process. The focus of this study is the development of a fuzzy logic control system for the production of “Whey Permeate Concentrate” in the production facilities of Glanbia plc. in Ballyragget, County Kilkenny

A review of dynamic models and stability analysis for a hydro-turbine governing system

Industrial Ecolog

Effect of control horizon in model predictive control for steam/water loop in large-scale ships

This paper presents an extensive analysis of the properties of different control horizon sets in an Extended Prediction Self-Adaptive Control (EPSAC) model predictive control framework. Analysis is performed on the linear multivariable model of the steam/water loop in large-scale watercraft/ships. The results indicate that larger control horizon values lead to better loop performance, at the cost of computational complexity. Hence, it is necessary to find a good trade-off between the performance of the system and allocated or available computational complexity. In this original work, this problem is explicitly treated as an optimization task, leading to the optimal control horizon sets for the steam/water loop example. Based on simulation results, it is concluded that specific tuning of control horizons outperforms the case when only a single valued control horizon is used for all the loops

Control predictivo basado en modelos fuzzy de sistemas complejos. Aplicación al control y supervisión de procesos de depuración de aguas

Tesis por compendio de publicaciones[ES] El Control Predictivo basado en Modelos (MPC) es un caso particular de estrategia de control automático de procesos que abarca un conjunto de procedimientos cuyo denominador común es la utilización de un modelo de predicciones para determinar una ley de control óptima. El tipo de modelo elegido, los criterios de optimización y el procedimiento de deducción de la ley de control caracterizan cada una de las múltiples alternativas de MPC que existen. El control predictivo es una consolidada y, al mismo tiempo, prometedora estrategia de control con múltiples aplicaciones en el ámbito industrial y con numerosas líneas de investigación 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 está enmarcado en el subcampo del Control Predictivo No Lineal (NLMPC/NMPC) y al mismo tiempo pertenece también, parcialmente al menos, al campo del Control Inteligente (IC), debido a que utiliza una de las herramientas características de la inteligencia artificial, como es la lógica borrosa. En la Tesis Doctoral que aquí se presenta se considera una estrategia FMBPC cuyo modelo base es un modelo borroso, o Fuzzy Model (FM) en la literatura en inglés, de tipo Takagi-Sugeno (TS), obtenido mediante identificación a partir de series de datos numéricos de entrada-salida (que pueden ser datos estrictamente experimentales o adaptaciones de estos, generados en simulación). Esta característica dota a nuestra estrategia FMBPC de una interesante cualidad que aporta valor añadido dentro del campo del control NMPC, consistente en la útil información cualitativa implícita en el modelo borroso, consecuencia de la capacidad que tiene la identificación borrosa de capturar fielmente la dinámica de un sistema a partir de datos numéricos. Esta propiedad repercute directamente de forma positiva en la validez de las predicciones y supone, en última instancia, un incremento significativo del rendimiento o desempeño del algoritmo de control predictivo, en el caso de tratar con sistemas fuertemente no lineales, complejos o desconocidos. Esta es la razón por la que en esta tesis se propone la estrategia FMBPC como la idónea para abordar el control de un cierto tipo de procesos conocidos como Procesos de Fangos Activados (ASP), muy habituales como mecanismo de depuración biológica en Estaciones Depuradoras de Aguas Residuales (EDAR) (también conocidas en la literatura en inglés como Wastewater Treatment Plants (WWTP)). El interés de la propuesta es doble: por un lado, contribuir a ampliar las líneas de investigación en el campo del control predictivo no lineal y por otro, aportar una estrategia y una metodología que puedan ser útiles en la mejora de los procesos de depuración de aguas, cuya importancia en la salud pública y en el cuidado del medio ambiente es creciente, cono así se refleja en las legislaciones medioambientales, cada vez más exigentes. Una parte importante del esfuerzo investigador desarrollado en la presente tesis ha sido enfocado a la aplicación de la estrategia FMBPC propuesta al paradigmático caso de estudio elegido (procesos biológicos ASP en plantas depuradoras de aguas residuales). Dadas las características de estos procesos, principalmente su alta no linealidad, su complejidad intrínseca y su carácter multivariable, derivadas de su naturaleza biológica, las investigaciones realizadas pueden trascender más allá del mero ámbito del propio proceso. La implementación practica se ha llevado a cabo mediante simulación y ello ha supuesto un importante reto, principalmente en dos aspectos: por un lado, el desarrollo del software necesario y por otro, la implementación de los cálculos matemáticos apropiados. La investigación realizada puede descomponerse, de una manera esquemática, en las siguientes cuatro fases o etapas: a) identificación borrosa del proceso ASP a partir de datos numéricos de entrada-salida y conversión del modelo borroso obtenido en un modelo equivalente en el espacio de estados, discreto, lineal y variante en el tiempo (DLTV); b) determinación de una ley de control predictivo de tipo FMBPC, analítica y explícita, siguiendo los principios del denominado Control Predictivo Funcional (PFC); c) análisis de estabilidad local en lazo cerrado de la estrategia FMBPC propuesta; d) integración de esta estrategia dentro de la configuración de control predictivo conocida como Paradigma de Lazo Cerrado (CLP), también llamada control predictivo en lazo cerrado, con el objetivo de imponer restricciones de manera automática en la acción de control. Los resultados obtenidos son satisfactorios, principalmente en lo que se refiere a la demostración de la utilidad de la estrategia FMBPC propuesta como una alternativa válida en el campo del control predictivo no lineal, para sistemas complejos o desconocidos, con dos ventajas destacables en relación con otras estrategias, a saber: por un lado, la útil información contenida en el modelo base de las predicciones, capturada durante el proceso de identificación borrosa previo a la aplicación de la estrategia y, por otro, la forma analítica y explicita de la ley de control deducida, que facilita tanto la implementación del algoritmo de control como las tareas de análisis (entre ellas, las de análisis 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

Experimental investigation and control of a hot-air tunnel with improved performance and energy saving

The paper is focused on the identification, control design, and experimental verification of a two-input two-output hot-air laboratory apparatus representing a small-scale version of appliances widely used in the industry. A decentralized multivariable controller design is proposed, satisfying control-loop decoupling and measurable disturbance rejection. The proposed inverted or equivalent noninverted decoupling controllers serve for the rejection of cross-interactions in controlled loops, whereas open-loop antidisturbance members satisfy the absolute invariance to the disturbances. Explicit controller-structure design formulae are derived, and their equivalence to other decoupling schemes is proven. Three tuning rules are used to set primary controller parameters, which are further discretized. All the control responses are simulated in the Matlab/Simulink environment. In the experimental part, two data-acquisition, communication, and control interfaces are set up. Namely, a programmable logic controller and a computer equipped with the peripheral component interconnect card commonly used in industrial practice are implemented. A simple supervisory control and data acquisition human-machine interface via the Control Web environment is developed. The laboratory experiments prove better temperature control performance measured by integral criteria by 35.3%, less energy consumption by up to 6%, and control effort of mechanical actuator parts by up to 17.1% for our method compared to the coupled or disturbance-ignoring design in practice. It was also observed that the use of a programmable logic controller gives better performance measures for both temperature and air-flow control.Tomas Bata University in Zlin [RVO/CEBIA/2020/001]RVO/CEBIA/2020/001; Univerzita Tomáše Bati ve Zlín