Fuzzy predictive control based on relational matrix models

Abstract

The paper represents a new aproach to the predictive model-reference control. The prediction of the process output signal is made on the basis of fuzzy process model. Using the fuzzy model of the process the forecast of the process output over a certain horizont in the future is cMculated and can be used as a predictor in the long-range predictive control strategy. The concept is implemented on real industrial scale temperature plant. KEYWORDSpredictive control, fuzzy relational model, identification, nonlinear systems 1.INTRODUCTIONThe predictive control has become a very important area of research in recent years. The principal is based on the forecast of the output signal y at each sampling instant. The forecast is made implicitly or explicitly according to the model of the process to be controlled. In the next step the control is selected which brings the predicted process output signal back to the reference signal in way to minimize the area between the reference and the output signal. The fundamental methods which are essentially based on the principal of predictive control are Richalet's method (Richalet et al., 1976, Model Algorithmic Control), Cutler's method (Dynamic Matrix Control), De Keyser's method (Extended Prediction Self-Adaptive Control) and Ydstie's method (Extended Horizon Adaptive Control).According to the process model two main approaches have been developed in the area of predictive control. The first one is based on parametric model of the controlled process. The parametric model could be described in form of transfer-function or in state-space domain. An important disadvantage of using the parametric model is that it represents a linearized model of the process. The control of the strong nonlinear processes could be unsatisfactorilly. The second approach proposed in literature is based on nonparametric model. The advantage of this approach is that the model coefficient can be obtained directly from samples of the input and output responses without assuming the model structure. In our example a scheme of predictive control based on fuzzy relational matrix model is proposed, which represents a combination of nonparametric and parametric approach to the predictive control.Predictive control based on fuzzy relational matrix model is capable to control also very difficult processes, such as nonlinear processes, processes with long time delay and non-minimum phase. The controllers based on prediction strategy Mso exhibit remarkable robustness with respect to model mismatch and unmodeled dynamics.The first part of the paper deals with the concept of fuzzy relational matrix modelling. In the second part the concept of fuzzy predictive control is given. Finally, the implementation of fuzzy predictive control on the real temperature plant is presented.$931

Controle preditivo baseado em rede de modelos lineares locais aplicado a um reator de neutralização

“…Esforços iniciais para aplicação de abordagens locais em controladores MPC foram empregados por meio da simulação de modelos Takagi-Sugeno em paralelo ao processo controlado gerando coeficientes para o modelo de convolução do algoritmo DMC. O controlador DMC baseado nesse princípio foi apresentado primeiramente por Skrjanc et al (1996). A metodologia aplicada ao desenvolvimento do controlador consistia em utilizar o modelo fuzzy em uma camada superior, sendo responsável pelo cálculo dos coeficientes de resposta ao degrau requeridos no projeto do controlador.…”

“…No modelo preditivo linear, a matriz G é calculada na etapa de desenvolvimento do controlador e, portanto, fixa ao longo de todo o processo. Para o controlador DMC proposto por Skrjanc et al (1996), a matriz de coeficientes de resposta à perturbação degrau (G) é calculada em tempo real a cada iteração por meio da simulação do modelo identificado para a planta. Para esta estratégia a matriz é atualizada sempre que as características do processo são modificadas por distanciamento do ponto de operação.…”