Identificação e controle de processos via desenvolvimentos em séries ortonormais. Parte A: identificação

In this paper, an overview about the identification of dynamic systems using orthonormal basis function models, such as those based on Laguerre and Kautz functions, is presented. The mathematical foundations of these models as well as their advantages and limitations are discussed within the contexts of linear, robust, and nonlinear identification. The discussions comprise a broad bibliographical survey on the subject and a comparative analysis involving some specific model realizations, namely, linear, Volterra, fuzzy, and neural models within the orthonormal basis function framework. Theoretical and practical issues regarding the identification of these models are also presented and illustrated by means of two case studies related to a polymerization process.O presente artigo apresenta uma visão geral do estado da arte na área de identificação de sistemas utilizando modelos dinâmicos com estrutura desenvolvida através de bases de funções ortonormais, como as funções de Laguerre, Kautz ou funções ortonormais generalizadas. Discute-se as vantagens e possíveis limitações desse tipo de estrutura bem como os fundamentos matemáticos dos modelos correspondentes nos contextos de identificação linear, linear com incertezas paramétricas (identificação robusta) e não linear, incluindo uma revisão bibliográfica abrangente sobre o tema. Diferentes realizações de modelos com funções de base ortonormal, a saber, modelos lineares, de Volterra, fuzzy e neurais, são detalhadas e discutidas comparativamente em termos de capacidade de representação, parcimônia, complexidade de projeto e interpretabilidade. Aspectos práticos da identificação desses modelos são também apresentados e ilustrados através de dois casos de estudo envolvendo um processo simulado de polimerização isotérmica.301321Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Advanced Mathematics and Computational Applications in Control Systems Engineering

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering

Nonlinear sytems modeling based on ladder-strutured generalized orthonormal basis functions

Orientadores: Wagner Caradori do Amaral, Ricardo Jose Grabrielli Barreto CampelloTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho enfoca a modelagem e identificação de sistemas dinâmicos não-lineares estáveis através de modelos fuzzy Takagi-Sugeno (TS) e/ou Volterra, ambos com estruturas formadas por bases de funções ortonormais (BFO), principalmente as bases de funções ortonormais generalizadas (GOBF - Generalized Orthonormal Basis Functions) com funções internas. As GOBF¿s com funções internas modelam sistemas dinâmicos com múltiplos modos através de uma parametrização que utiliza somente valores reais, sejam os polos do sistema reais e/ou complexos. Uma das principais contribuições desta tese concentra-se na proposta da otimização e ajuste fino dos parâmetros destes modelos não-lineares. Realiza-se a identificação dos modelos fuzzy TS-BFO utilizando-se de medidas dos sinais de entrada e saída do sistema a ser modelado. Os modelos fuzzy TS-BFO são inicialmente determinados utilizando-se uma técnica de agrupamento fuzzy (fuzzy clustering) e simplificados por algoritmos que eliminam eventuais redundâncias. Em sequência desenvolve-se o cálculo analítico dos gradientes da saída do modelo TS-BFO em relação aos parâmetros do modelo (polos da BFO, coeficientes da expansão da BFO e parâmetros das funções de pertinência). Utilizando-se técnicas de otimização não-linear e o valor dos gradientes, realiza-se a sintonia fina dos parâmetros dos modelos inicialmente obtidos. Para os modelos de Volterra-GOBF desenvolve-se uma nova abordagem utilizando-se GOBF com funções internas nos kernels dos modelos. São calculados os gradientes analíticos da saída do modelo de Volterra-GOBF, seja com kernels simétricos ou não simétricos, com relação aos parâmetros a serem determinados. Estes valores são utilizados em algoritmos de otimização que possibilitam a obtenção de modelos mais precisos do sistema sem nenhum conhecimento a priori de suas características. Além da identificação de sistemas não-lineares por modelos BFO, abordou-se também, nesta tese, uma nova metodologia para a otimização de modelos lineares BFO no domínio da frequência. Neste contexto, destaca-se como principal contribuição o desenvolvimento, no domínio da frequência, do cálculo analítico dos gradientes da resposta em frequência das funções de Kautz e Laguerre, com relação aos seus parâmetros de projeto. Os valores dos gradientes fornecem a direção de busca dos parâmetros dos modelos em processos de otimização não-linear. Também foram otimizados os modelos GOBF com funções internas, com o cálculo numérico dos seus gradientes, pois, ainda não foi possível estabelecer uma fórmula genérica para o cálculo analítico dos gradientes dos modelos GOBF, de qualquer ordem, em relação aos parâmetros a serem determinados. Exemplos ilustram a aplicação e eficiência dos métodos de identificação e otimização propostos na modelagem de sistemas lineares (domínio do tempo e da frequência) e não-lineares utilizando BFO¿s.Abstract: This work is concerned with the modeling and identification of stable nonlinear dynamic systems using Takagi-Sugeno fuzzy and Volterra models within the framework of orthonormal basis functions (OBF), mainly ladder-structured generalized orthonormal basis functions (GOBF). The ladderstructured GOBFs allows to model dynamic systems with multiple modes, real and/or complex poles, through a parameterization, which uses only real values. The main contribution of this thesis is the optimization and fine tuning of the parameters of OBF nonlinear models. The GOBF models identification are performed using only input and output measurements. The initial GOBF-TS fuzzy model is obtained using a fuzzy clustering technique and simplified by algorithms that eliminate any redundancies. Next, the analytical calculation of the gradients of GOBF-TS model concerning model parameters (GOBF poles, OBF expansion coefficients and the parameters of membership functions) is developed. A fine tuning of the model parameters is obtained by using a nonlinear optimization technique and the calculated gradients. For Volterra-GOBF models a new approach using kernels with ladder-structured GOBF is also proposed. Furthermore, Volterra-GOBF model optimization, with symmetrical or asymmetrical kernels, using an analytical gradients calculation of the output model regarding their parameters is presented. Following, a new approach for linear OBF models optimization, in frequency domain, is also addressed. In this context, the analytical calculation of the gradients of the Laguerre and Kautz frequency response concerning its parameters is presented The ladder-structured GOBF models optimization, in the frequency domain, is performed using only numerical calculation of its gradients, as it has not yet been possible to derive a generic analytical gradients. Examples illustrate the performance and effectiveness of identification methods proposed here in the modeling and optimization of linear (time domain and frequency) and non-linear systems.DoutoradoAutomaçãoDoutor em Engenharia Elétric

Health-aware predictive control schemes based on industrial processes

Aplicat embargament des de la data de defensa fins el dia 30 de desembre de 2021The research is motivated by real applications, such as pasteurization plant, water networks and autonomous system, which each of them require a specific control system to provide proper management able to take into account their particular features and operating limits in presence of uncertainties related to their operation and failures from component breakdowns. According to that most of the real systems have nonlinear behaviors, it can be approximated them by polytopic linear uncertain models such as Linear Parameter Varying (LPV) and Takagi-Sugeno (TS) models. Therefore, a new economic Model Predictive Control (MPC) approach based on LPV/TS models is proposed and the stability of the proposed approach is certified by using a region constraint on the terminal state. Besides, the MPC-LPV strategy is extended based on the system with varying delays affecting states and inputs. The control approach allows the controller to accommodate the scheduling parameters and delay change. By computing the prediction of the state variables and delay along a prediction time horizon, the system model can be modified according to the evaluation of the estimated state and delay at each time instant. To increase the system reliability, anticipate the appearance of faults and reduce the operational costs, actuator health monitoring should be considered. Regarding several types of system failures, different strategies are studied for obtaining system failures. First, the damage is assessed with the rainflow-counting algorithm that allows estimating the component’s fatigue and control objective is modified by adding an extra criterion that takes into account the accumulated damage. Besides, two different health-aware economic predictive control strategies that aim to minimize the damage of components are presented. Then, economic health-aware MPC controller is developed to compute the components and system reliability in the MPC model using an LPV modeling approach and maximizes the availability of the system by estimating system reliability. Additionally, another improvement considers chance-constraint programming to compute an optimal list replenishment policy based on a desired risk acceptability level, managing to dynamically designate safety stocks in flowbased networks to satisfy non-stationary flow demands. Finally, an innovative health-aware control approach for autonomous racing vehicles to simultaneously control it to the driving limits and to follow the desired path based on maximization of the battery RUL. The proposed approach is formulated as an optimal on-line robust LMI based MPC driven from Lyapunov stability and controller gain synthesis solved by LPV-LQR problem in LMI formulation with integral action for tracking the trajectory.Esta tesis pretende proporcionar contribuciones teóricas y prácticas sobre seguridad y control de sistemas industriales, especialmente en la forma maten ática de sistemas inciertos. La investigación está motivada por aplicaciones reales, como la planta de pasteurización, las redes de agua y el sistema autónomo, cada uno de los cuales requiere un sistema de control específico para proporcionar una gestión adecuada capaz de tener en cuenta sus características particulares y limites o de operación en presencia de incertidumbres relacionadas con su operación y fallas de averías de componentes. De acuerdo con que la mayoría de los sistemas reales tienen comportamientos no lineales, puede aproximarse a ellos mediante modelos inciertos lineales politopicos como los modelos de Lineal Variación de Parámetros (LPV) y Takagi-Sugeno (TS). Por lo tanto, se propone un nuevo enfoque de Control Predictivo del Modelo (MPC) económico basado en modelos LPV/TS y la estabilidad del enfoque propuesto se certifica mediante el uso de una restricción de región en el estado terminal. Además, la estrategia MPC-LPV se extiende en función del sistema con diferentes demoras que afectan los estados y las entradas. El enfoque de control permite al controlador acomodar los parámetros de programación y retrasar el cambio. Al calcular la predicción de las variables de estado y el retraso a lo largo de un horizonte de tiempo de predicción, el modelo del sistema se puede modificar de acuerdo con la evaluación del estado estimado y el retraso en cada instante de tiempo. Para aumentar la confiabilidad del sistema, anticipar la aparición de fallas y reducir los costos operativos, se debe considerar el monitoreo del estado del actuador. Con respecto a varios tipos de fallas del sistema, se estudian diferentes estrategias para obtener fallas del sistema. Primero, el daño se evalúa con el algoritmo de conteo de flujo de lluvia que permite estimar la fatiga del componente y el objetivo de control se modifica agregando un criterio adicional que tiene en cuenta el daño acumulado. Además, se presentan dos estrategias diferentes de control predictivo económico que tienen en cuenta la salud y tienen como objetivo minimizar el daño de los componentes. Luego, se desarrolla un controlador MPC económico con conciencia de salud para calcular los componentes y la confiabilidad del sistema en el modelo MPC utilizando un enfoque de modelado LPV y maximiza la disponibilidad del sistema mediante la estimación de la confiabilidad del sistema. Además, otra mejora considera la programación de restricción de posibilidades para calcular una política ´optima de reposición de listas basada en un nivel de aceptabilidad de riesgo deseado, logrando designar dinámicamente existencias de seguridad en redes basadas en flujo para satisfacer demandas de flujo no estacionarias. Finalmente, un enfoque innovador de control consciente de la salud para vehículos de carreras autónomos para controlarlo simultáneamente hasta los límites de conducción y seguir el camino deseado basado en la maximización de la bacteria RUL. El diseño del control se divide en dos capas con diferentes escalas de tiempo, planificador de ruta y controlador. El enfoque propuesto está formulado como un MPC robusto en línea optimo basado en LMI impulsado por la estabilidad de Lyapunov y la síntesis de ganancia del controlador resuelta por el problema LPV-LQR en la formulación de LMI con acción integral para el seguimiento de la trayectoria.Postprint (published version

Neuronale Netze mit externen Laguerre-Filtern zur automatischen numerischen Vereinfachung von Getriebemodellen

Detailed physical models properties of automatic transmissionswith complex numerical are need to simulate the shift dynamics. This work considers the automatic numerical simplification of those models to use them in other simulation task of vehicle development. Therefore a method is presented which uses neural networks in combination with laguerre-filters

Neuronale Netze mit externen Laguerre-Filtern zur automatischen numerischen Vereinfachung von Getriebemodellen

Zur Simulation der Schaltdynamik von Stufenautomaten werden detaillierte physikalische Modelle mit komplexen numerischen Eigenschaften benötigt. Die Arbeit beschäftigt sich mit der automatischen numerischen Vereinfachung dieser Getriebemodelle, um diese dann in weiteren Simulationsfragestellungen in der PKW-Entwicklung zu verwenden. Dazu wird eine Methode vorgestellt, bei der neuronale Netze mit externen Laguerre-FIltern verwendet werden

A non-linear approach to modelling and control of electrically stimulated skeletal muscle

This thesis is concerned with the development and analysis of a non-linear approach to modelling and control of the contraction of electrically stimulated skeletal muscle. For muscle which has lost nervous control, artificial electrical stimulation can be used as a technique aimed at providing muscular contraction and producing a functionally useful movement. This is generally referred to as Functional Electrical Stimulation (FES) and is used in different application areas such as the rehabilitation of paralysed patient and in cardiac assistance where skeletal muscle can be used to support a failing heart. For both these FES applications a model of the muscle is essential to develop algorithms for the controlled stimulation. For the identification of muscle models, real data are available from experiments with rabbit muscle. Data for contraction with constant muscle length were collected from two muscle with very different characteristics. An empirical modelling approach is developed which is suitable for both muscles. The approach is based on a decomposition of the operating space into smaller sub-regions which are then described by local models of simple, possibly linear structure. The local models are blended together by a scheduler, and the resulting non-linear model is called a Local Model Network (LMN). It is shown how a priori knowledge about the system can be used directly when identifying Local Model Networks. Aspects of the structure selection are discussed and algorithms for the identification of the model parameters are presented. Tools of the analysis of Local Model Networks have been developed and are used to validate the models. The problem of designing a controller based on the LMN structure is discussed. The structure of Local Controller Networks is introduced. These can be derived directly from Local Model Networks. Design techniques for input-output and for state feedback controllers, based on pole placement, are presented. Aspects of the generation of optimal stimulation patterns (which are defined as stimulation patterns which deliver the smallest number of pulses to obtain a desired contraction) are discussed, and various techniques to generate them are presented. In particular, it is shown how a control structure can be used to generate optimal stimulation patterns. A Local Controller Network is used as the controller with a design based on a non-linear LMN model of muscle. Experimental data from a non-linear heat transfer process have been collected and are used to demonstrate the basic modelling and control principles throughout the first part of the thesis

Ship steering control using feedforward neural networks

One significant problem in the design of ship steering control systems is that the dynamics of the vessel change with operating conditions such as the forward speed of the vessel, the depth of the water and loading conditions etc. Approaches considered in the past to overcome these difficulties include the use of self adaptive control systems which adjust the control characteristics on a continuous basis to suit the current operating conditions. Artificial neural networks have been receiving considerable attention in recent years and have been considered for a variety of applications where the characteristics of the controlled system change significantly with operating conditions or with time. Such networks have a configuration which remains fixed once the training phase is complete. The resulting controlled systems thus have more predictable characteristics than those which are found in many forms of traditional self-adaptive control systems. In particular, stability bounds can be investigated through simulation studies as with any other form of controller having fixed characteristics. Feedforward neural networks have enjoyed many successful applications in the field of systems and control. These networks include two major categories: multilayer perceptrons and radial basis function networks. In this thesis, we explore the applicability of both of these artificial neural network architectures for automatic steering of ships in a course changing mode of operation. The approach that has been adopted involves the training of a single artificial neural network to represent a series of conventional controllers for different operating conditions. The resulting network thus captures, in a nonlinear fashion, the essential characteristics of all of the conventional controllers. Most of the artificial neural network controllers developed in this thesis are trained with the data generated through simulation studies. However, experience is also gained of developing a neuro controller on the basis of real data gathered from an actual scale model of a supply ship. Another important aspect of this work is the applicability of local model networks for modelling the dynamics of a ship. Local model networks can be regarded as a generalized form of radial basis function networks and have already proved their worth in a number of applications involving the modelling of systems in which the dynamic characteristics can vary significantly with the system operating conditions. The work presented in this thesis indicates that these networks are highly suitable for modelling the dynamics of a ship