Estrutura ANFIS modificada para identificação e controle de plantas com ampla faixa de operação e não linearidade acentuada

In this work a modification on ANFIS (Adaptive Network Based Fuzzy Inference System) structure is proposed to find a systematic method for nonlinear plants, with large operational range, identification and control, using linear local systems: models and controllers. This method is based on multiple model approach. This way, linear local models are obtained and then those models are combined by the proposed neurofuzzy structure. A metric that allows a satisfactory combination of those models is obtained after the structure training. It results on plant s global identification. A controller is projected for each local model. The global control is obtained by mixing local controllers signals. This is done by the modified ANFIS. The modification on ANFIS architecture allows the two neurofuzzy structures knowledge sharing. So the same metric obtained to combine models can be used to combine controllers. Two cases study are used to validate the new ANFIS structure. The knowledge sharing is evaluated in the second case study. It shows that just one modified ANFIS structure is necessary to combine linear models to identify, a nonlinear plant, and combine linear controllers to control this plant. The proposed method allows the usage of any identification and control techniques for local models and local controllers obtaining. It also reduces the complexity of ANFIS usage for identification and control. This work has prioritized simpler techniques for the identification and control systems to simplify the use of the method

Critério de correntropia no treinamento de redes fuzzy wavelet neural networks para identificação de sistemas dinâmicos não lineares

The great interest in nonlinear system identification is mainly due to the fact that a large amount of real systems are complex and need to have their nonlinearities considered so that their models can be successfully used in applications of control, prediction, inference, among others. This work evaluates the application of Fuzzy Wavelet Neural Networks (FWNN) to identify nonlinear dynamical systems subjected to noise and outliers. Generally, these elements cause negative effects on the identification procedure, resulting in erroneous interpretations regarding the dynamical behavior of the system. The FWNN combines in a single structure the ability to deal with uncertainties of fuzzy logic, the multiresolution characteristics of wavelet theory and learning and generalization abilities of the artificial neural networks. Usually, the learning procedure of these neural networks is realized by a gradient based method, which uses the mean squared error as its cost function. This work proposes the replacement of this traditional function by an Information Theoretic Learning similarity measure, called correntropy. With the use of this similarity measure, higher order statistics can be considered during the FWNN training process. For this reason, this measure is more suitable for non-Gaussian error distributions and makes the training less sensitive to the presence of outliers. In order to evaluate this replacement, FWNN models are obtained in two identification case studies: a real nonlinear system, consisting of a multisection tank, and a simulated system based on a model of the human knee joint. The results demonstrate that the application of correntropy as the error backpropagation algorithm cost function makes the identification procedure using FWNN models more robust to outliers. However, this is only achieved if the gaussian kernel width of correntropy is properly adjusted.

Algoritmo modificado de PSO matricial aplicado a identificação de sistemas com análise de convergência

Recentemente diversas técnicas de computação evolucionárias têm sido utilizadas em áreas como estimação de parâmetros de processos dinâmicos lineares e não lineares ou até sujeitos a incertezas. Isso motiva a utilização de algoritmos como o otimizador por nuvem de partículas (PSO) nas referidas áreas do conhecimento. Porém, pouco se sabe sobre a convergência desse algoritmo e, principalmente, as análises e estudos realizados têm se concentrado em resultados experimentais. Por isso, é objetivo deste trabalho propor uma nova estrutura para o PSO que permita analisar melhor a convergência do algoritmo de forma analítica. Para isso, o PSO é reestruturado para assumir uma forma matricial e reformulado como um sistema linear por partes. As partes serão analisadas de forma separada e será proposta a inserção de um fator de esquecimento que garante que a parte mais significativa deste sistema possua autovalores dentro do círculo de raio unitário. Também será realizada a análise da convergência do algoritmo como um todo, utilizando um critério de convergência quase certa, aplicável a sistemas chaveados. Na sequência, serão realizados testes experimentais de maneira a verificar o comportamento dos autovalores após a inserção do fator de esquecimento. Posteriormente, os algoritmos de identificação de parâmetros tradicionais serão combinados com o PSO matricial, de maneira a tornar os resultados da identificação tão bons ou melhores que a identificação apenas com o PSO ou, apenas com os algoritmos tradicionais. Os resultados mostram a convergência das partículas em uma região delimitada e que as funções obtidas após a combinação do algoritmo PSO matricial com os algoritmos convencionais, apresentam maior generalização para o sistema apresentado. As conclusões a que se chega é que a hibridização, apesar de limitar a busca por uma partícula mais apta do PSO, permite um desempenho mínimo para o algoritmo e ainda possibilita melhorar o resultado obtido com os algoritmos tradicionais, permitindo a representação do sistema aproximado em quantidades maiores de frequências.

Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

Identificação fuzzy-multimodelos para sistemas não lineares

This paper presents a new multi-model technique of dentification in ANFIS for nonlinear systems. In this technique, the structure used is of the fuzzy Takagi-Sugeno of which the consequences are local linear models that represent the system of different points of operation and the precursors are membership functions whose adjustments are realized by the learning phase of the neuro-fuzzy ANFIS technique. The models that represent the system at different points of the operation can be found with linearization techniques like, for example, the Least Squares method that is robust against sounds and of simple application. The fuzzy system is responsible for informing the proportion of each model that should be utilized, using the membership functions. The membership functions can be adjusted by ANFIS with the use of neural network algorithms, like the back propagation error type, in such a way that the models found for each area are correctly interpolated and define an action of each model for possible entries into the system. In multi-models, the definition of action of models is known as metrics and, since this paper is based on ANFIS, it shall be denominated in ANFIS metrics. This way, ANFIS metrics is utilized to interpolate various models, composing a system to be identified. Differing from the traditional ANFIS, the created technique necessarily represents the system in various well defined regions by unaltered models whose pondered activation as per the membership functions. The selection of regions for the application of the Least Squares method is realized manually from the graphic analysis of the system behavior or from the physical characteristics of the plant. This selection serves as a base to initiate the linear model defining technique and generating the initial configuration of the membership functions. The experiments are conducted in a teaching tank, with multiple sections, designed and created to show the characteristics of the technique. The results from this tank illustrate the performance reached by the technique in task of identifying, utilizing configurations of ANFIS, comparing the developed technique with various models of simple metrics and comparing with the NNARX technique, also adapted to identification

Identificação não linear usando uma rede fuzzy wavelet neural network modificada

In last decades, neural networks have been established as a major tool for the identification of nonlinear systems. Among the various types of networks used in identification, one that can be highlighted is the wavelet neural network (WNN). This network combines the characteristics of wavelet multiresolution theory with learning ability and generalization of neural networks usually, providing more accurate models than those ones obtained by traditional networks. An extension of WNN networks is to combine the neuro-fuzzy ANFIS (Adaptive Network Based Fuzzy Inference System) structure with wavelets, leading to generate the Fuzzy Wavelet Neural Network - FWNN structure. This network is very similar to ANFIS networks, with the difference that traditional polynomials present in consequent of this network are replaced by WNN networks. This paper proposes the identification of nonlinear dynamical systems from a network FWNN modified. In the proposed structure, functions only wavelets are used in the consequent. Thus, it is possible to obtain a simplification of the structure, reducing the number of adjustable parameters of the network. To evaluate the performance of network FWNN with this modification, an analysis of network performance is made, verifying advantages, disadvantages and cost effectiveness when compared to other existing FWNN structures in literature. The evaluations are carried out via the identification of two simulated systems traditionally found in the literature and a real nonlinear system, consisting of a nonlinear multi section tank. Finally, the network is used to infer values of temperature and humidity inside of a neonatal incubator. The execution of such analyzes is based on various criteria, like: mean squared error, number of training epochs, number of adjustable parameters, the variation of the mean square error, among others. The results found show the generalization ability of the modified structure, despite the simplification performed

Identificação e comparação entre controle preditivo com modelo não linear e PI sintonizados com PSO em sistema de separação gravitacional de águia-óleo

The separation methods are reduced applications as a result of the operational costs, the low output and the long time to separate the uids. But, these treatment methods are important because of the need for extraction of unwanted contaminants in the oil production. The water and the concentration of oil in water should be minimal (around 40 to 20 ppm) in order to take it to the sea. Because of the need of primary treatment, the objective of this project is to study and implement algorithms for identification of polynomial NARX (Nonlinear Auto-Regressive with Exogenous Input) models in closed loop, implement a structural identification, and compare strategies using PI control and updated on-line NARX predictive models on a combination of three-phase separator in series with three hydro cyclones batteries. The main goal of this project is to: obtain an optimized process of phase separation that will regulate the system, even in the presence of oil gushes; Show that it is possible to get optimized tunings for controllers analyzing the mesh as a whole, and evaluate and compare the strategies of PI and predictive control applied to the process. To accomplish these goals a simulator was used to represent the three phase separator and hydro cyclones. Algorithms were developed for system identification (NARX) using RLS(Recursive Least Square), along with methods for structure models detection. Predictive Control Algorithms were also implemented with NARX model updated on-line, and optimization algorithms using PSO (Particle Swarm Optimization). This project ends with a comparison of results obtained from the use of PI and predictive controllers (both with optimal state through the algorithm of cloud particles) in the simulated system. Thus, concluding that the performed optimizations make the system less sensitive to external perturbations and when optimized, the two controllers show similar results with the assessment of predictive control somewhat less sensitive to disturbances

Um ambiente computacional para modelagem simbólica de sistemas físicos lineares

Este trabalho propõe um ambiente computacional aplicado ao ensino de sistemas de controle, denominado de ModSym. O software implementa uma interface gráfica para a modelagem de sistemas físicos lineares e mostra, passo a passo, o processamento necessário à obtenção de modelos matemáticos para esses sistemas. Um sistema físico pode ser representado, no software, de três formas diferentes. O sistema pode ser representado por um diagrama gráfico a partir de elementos dos domínios elétrico, mecânico translacional, mecânico rotacional e hidráulico. Pode também ser representado a partir de grafos de ligação ou de diagramas de fluxo de sinal. Uma vez representado o sistema, o ModSym possibilita o cálculo de funções de transferência do sistema na forma simbólica, utilizando a regra de Mason. O software calcula também funções de transferência na forma numérica e funções de sensibilidade paramétrica. O trabalho propõe ainda um algoritmo para obter o diagrama de fluxo de sinal de um sistema físico baseado no seu grafo de ligação. Este algoritmo e a metodologia de análise de sistemas conhecida por Network Method permitiram a utilização da regra de Mason no cálculo de funções de transferência dos sistemas modelados no software

Identificação de uma planta de corrente de um motor de indução utilizando redes de base radial

The present work describes the use of a mathematical tool to solve problems arising from control theory, including the identification, analysis of the phase portrait and stability, as well as the temporal evolution of the plant s current induction motor. The system identification is an area of mathematical modeling that has as its objective the study of techniques which can determine a dynamic model in representing a real system. The tool used in the identification and analysis of nonlinear dynamical system is the Radial Basis Function (RBF). The process or plant that is used has a mathematical model unknown, but belongs to a particular class that contains an internal dynamics that can be modeled.Will be presented as contributions to the analysis of asymptotic stability of the RBF. The identification using radial basis function is demonstrated through computer simulations from a real data set obtained from the plant

Utilização da lógica difusa no controle inteligente de sistemas eletro-hidráulicos

Electro-hydraulic servo-systems are widely employed in industrial applications such as robotic manipulators, active suspensions, precision machine tools and aerospace systems. They provide many advantages over electric motors, including high force to weight ratio, fast response time and compact size. However, precise control of electro-hydraulic systems, due to their inherent nonlinear characteristics, cannot be easily obtained with conventional linear controllers. Most flow control valves can also exhibit some hard nonlinearities such as deadzone due to valve spool overlap on the passage´s orifice of the fluid. This work describes the development of a nonlinear controller based on the feedback linearization method and including a fuzzy compensation scheme for an electro-hydraulic actuated system with unknown dead-band. Numerical results are presented in order to demonstrate the control system performance

Controle por modos deslizantes com compensação difusa aplicado a sistemas com descontinuidade

The development of non-linear controllers gained space in the theoretical ambit and of practical applications on the moment that the arising of digital computers enabled the implementation of these methodologies. In comparison with the linear controllers more utilized, the non -linear controllers present the advantage of not requiring the linearity of the system to determine the parameters of control, which permits a more efficient control especially when the system presents a high level of non-linearity. Another additional advantage is the reduction of costs, since to obtain the efficient control through linear controllers it is necessary the utilization of sensors and more refined actuators than when it is utilized a non-linear controller. Among the non-linear theories of control, the method of control by gliding ways is detached for being a method that presents more robustness, before uncertainties. It is already confirmed that the adoption of compensation on the region of residual error permits to improve better the performance of these controllers. So, in this work it is described the development of a non-linear controller that looks for an association of strategy of control by gliding ways, with the fuzzy compensation technique. Through the implementation of some strategies of fuzzy compensation, it was searched the one which provided the biggest efficiency before a system with high level of nonlinearities and uncertainties. The electrohydraulic actuator was utilized as an example of research, and the results appoint to two configurations of compensation that permit a bigger reduction of the residual error

Identificação em tempo real de modelo dinâmico de robô móvel com acionamento diferencial e zona morta

Several mobile robots show non-linear behavior, mainly due friction phenomena between the mechanical parts of the robot or between the robot and the ground. Linear models are efficient in some cases, but it is necessary take the robot non-linearity in consideration when precise displacement and positioning are desired. In this work a parametric model identification procedure for a mobile robot with differential drive that considers the dead-zone in the robot actuators is proposed. The method consists in dividing the system into Hammerstein systems and then uses the key-term separation principle to present the input-output relations which shows the parameters from both linear and non-linear blocks. The parameters are then simultaneously estimated through a recursive least squares algorithm. The results shows that is possible to identify the dead-zone thresholds together with the linear parameters

Estudo e implementação de um controlador preditivo generalizado bilinear compensado adaptativo

The present work presents the study and implementation of an adaptive bilinear compensated generalized predictive controller. This work uses conventional techniques of predictive control and includes techniques of adaptive control for better results. In order to solve control problems frequently found in the chemical industry, bilinear models are considered to represent the dynamics of the studied systems. Bilinear models are simpler than general nonlinear model, however it can to represent the intrinsic not-linearities of industrial processes. The linearization of the model, by the approach to time step quasilinear , is used to allow the application of the equations of the generalized predictive controller (GPC). Such linearization, however, generates an error of prediction, which is minimized through a compensation term. The term in study is implemented in an adaptive form, due to the nonlinear relationship between the input signal and the prediction error.Simulation results show the efficiency of adaptive predictive bilinear controller in comparison with the conventional.

Identificação de modelos polinomiais narx utilizando algoritmos combinados de detecção de estrutura e estimação de parâmetros com aplicações práticas

A modelagem de processos industriais tem auxiliado na produção e minimização de custos, permitindo a previsão dos comportamentos futuros do sistema, supervisão de processos e projeto de controladores. Ao observar os benefícios proporcionados pela modelagem, objetiva-se primeiramente, nesta dissertação, apresentar uma metodologia de identificação de modelos não-lineares com estrutura NARX, a partir da implementação de algoritmos combinados de detecção de estrutura e estimação de parâmetros. Inicialmente, será ressaltada a importância da identificação de sistemas na otimização de processos industriais, especificamente a escolha do modelo para representar adequadamente as dinâmicas do sistema. Em seguida, será apresentada uma breve revisão das etapas que compõem a identificação de sistemas. Na sequência, serão apresentados os métodos fundamentais para detecção de estrutura (Modificado Gram- Schmidt) e estimação de parâmetros (Método dos Mínimos Quadrados e Método dos Mínimos Quadrados Estendido) de modelos. No trabalho será também realizada, através dos algoritmos implementados, a identificação de dois processos industriais distintos representados por uma planta de nível didática, que possibilita o controle de nível e vazão, e uma planta de processamento primário de petróleo simulada, que tem como objetivo representar um tratamento primário do petróleo que ocorre em plataformas petrolíferas. A dissertação é finalizada com uma avaliação dos desempenhos dos modelos obtidos, quando comparados com o sistema. A partir desta avaliação, será possível observar se os modelos identificados são capazes de representar as características estáticas e dinâmicas dos sistemas apresentados nesta dissertação

Desenvolvimento e avaliação de controladores preditivos baseados em modelos biliares

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