New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Projeto de reguladores fuzzy Takagi-Sugeno utilizando as condições iniciais da planta

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Realimentação derivativa e modelo fuzzy Takagi-Sugeno paracontrole da articulação do joelho de pacientes paraplégicos com o uso de acelerômetros

Feedback control systems have been used to move the muscles and joints of the limbs of paraplegic patients. The feedback signal, related to the knee joint angle, can be obtained by using an electrogoniometer. However, the use of accelerometers can help the measurements due the facility of adhering these devices to the skin. Accelerometers are also very suitable for these applications due their small dimensions and weight. In this paper a new method for designing a control system that can vary the knee joint angle using Functional Electrical Stimulation (FES) is presented, as well as a simulation with parameters values available in the literature. The nonlinear control system was represented by a Takagi-Sugeno fuzzy model and the feedback signals were obtained by using accelerometers. The design method considered all plant nonlinearities and was efficient and reliable to control the leg position of a paraplegic patient with the angle of the knee ranging from 0° to 30°, considering electric stimulation at the quadriceps muscle. The proposed method is viable and offers a new alternative for designing control systems of the knee joint angle using more comfortable sensors for the patients.

Modelagem e controle de sistemas fuzzy Takagi-Sugeno

Pós-graduação em Engenharia Elétrica - FEIS

Projeto de um controlador Fuzzy Takagi-Sugeno para uma estação de tratamento de esgoto por lodos ativados

Este trabalho propõe o projeto de um controlador Fuzzy do tipo Takagi-Sugeno em uma estação de tratamento de esgoto por lodos ativados. Este tipo de tratamento ocorre na presença de oxigênio, pois microorganismos aeróbios presentes no licor misto irão proporcionar a remoção tanto da matéria carbonácea quanto nutrientes formados por compostos à base de nitrogênio. O controlador atua via mecanismo de aeração e foi projetado para interpolar os ganhos proporcionais e integrativos de três controladores fixos locais que, por sua vez, foram projetados a partir da linearização de um modelo contínuo de balanço de massa de oxigênio. O controlador auxiliará manter a concentração de oxigênio dissolvido desejável na faixa de operação do processo para que ocorra a nitrificação, reação química de oxiredução que transforma amônio em nitrito, que é fundamental para o sucesso do processo, e poderá também economizar energia elétrica utilizada pelo mecanismo de aeração. Os ensaios foram realizados via simulação computacional em quatro cenários idealizados comparando o desempenho do controlador fuzzy e o desempenho de um controlador fixo projetado em um ponto de operação diferente do qual se utilizou como valor de referência na planta. Ao aplicar um degrau no valor de referência estabelecido no cenário de análise, observou-se o tempo de subida, o tempo de acomodação e o erro em regime. Após os ensaios, observou-se que o desempenho do controlador fuzzy nos quesitos tempo de subida e tempo de acomodação em relação ao controlador fixo foi melhor, enquanto nos quesitos sobressinal e erro em regime foi semelhante. Após as análises, concluiu-se que a estratégia de controle escolhida neste trabalho é viável, pois de acordo com o valor auferido de oxigênio dissolvido na entrada da planta, o controlador fuzzy irá interpolar os ganhos proporcionais e integrativos de um controlador fixo projetado na vizinhança deste valor e assim, atuar de forma bastante satisfatória.

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Seguimiento de trayectoria por esquema difuso Takagi-Sugeno : un enfoque de control óptimo inverso

Tesis (Maestro en Ciencias de la Ingeniería con Especialidad en Control) - Universidad Autónoma de Nuevo León, 2001

Controle ótimo H∞ de sistemas não-lineares com modelos fuzzy takagi-sugeno

Neste trabalho é proposta uma metodologia de rastreamento de sinais e rejeição de distúrbios aplicada a sistemas não-lineares. Para o projeto do sistema de rastreamento, projeta-se os controladores fuzzy M(a) e N(a) que minimizam o limitante superior da norma H∞ entre o sinal de referência r(t) e o sinal de erro de rastreamento e(t), sendo e(t) a diferença entre a entrada de referência e a saída do sistema z(t). No método de rejeição de distúrbio utiliza-se a realimentação dinâmica da saída através de um controlador fuzzy Kc(a) que minimiza o limitante superior da norma H∞ entre o sinal de entrada exógena w(t) e o sinal de saída z(t). O procedimento de projeto proposto considera as não-linearidades da planta através dos modelos fuzzy Takagi-Sugeno. Os métodos são equacionados utilizando-se inequações matriciais lineares (LMIs), que quando factíveis, podem ser facilmente solucionados por algoritmos de convergência polinomial. Por fim, um exemplo ilustra a viabilidade da metodologia proposta.

Design of a Takagi-Sugeno Fuzzy Regulator for a Set of Operation Points

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Design of a fuzzy Takagi-Sugeno controller to vary the joint knee angle of paraplegic patients

The papers shows, through theoretical studies and simulations, that using the description of the plant by Takagi-Sugeno (T-S), it is possible to design a nonlinear controller to control the position of the leg of a paraplegic patient. The control system was designed to change the angle of the joint knee of 60 degrees. This is the first study that describes the application of Takagi-Sugeno (T-S) models in this kind of problem.

Stability of nonlinear system using takagi-sugeno fuzzy models and hyper-rectangle of LMIs

This paper presents a theorem based on the hyper-rectangle defined by the closed set of the time derivatives of the membership functions of Takagi-Sugeno fuzzy systems. This result is also based on Linear Matrix Inequalities and allows the reduction of the conservatism of the stability analysis in the sense of Lyapunov. The theorem generalizes previous results available in the literature. © 2013 Brazilian Society for Automatics - SBA.

Projeto e implementação com chaveamento de reguladores fuzzy Takagi-Sugeno para um conjunto de pontos de operação

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análise da estabilidade de sistemas fuzzy Takagi-Sugeno utilizando as desigualdades de Lyapunov-Metzler

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)