Fuzzy Modeling Applying Interpolation Mechanism

In system control theory, system modeling has the most basic importance. However, in fuzzy control system, we can't get the mathematics model of controlled object usually; it is hard to go on studying the theory on fuzzy control. In this paper, a new method called modeling method based on fuzzy inference (MMFI) to make up for the problem, which transfers a group of fuzzy inference rules into a nonlinear differential equation with variable coefficients. It overcomes the obstacle existing in studying the fuzzy control theory deeply. At first, it applies modeling method based on fuzzy inference (MMFI) to fisrt order system and finishes the modeling and simulating on fisrt order system. The correctness of the model is testified by many examples. Then second order system is modeled and simulated by the same method. The state space model of a fuzzy control system is established as well. We analysing the results of the experiments, the reasons that cause the errors are obtained. Then a conclusion is drawn about the fuzzy modeling, that is, the model obtained by MMFI has a good precision in contrast with the real model. For the models by MMFI is a nonlinear differential equation with variable coefficients and the 'nonlinearity' brings discommodiousness to analyse the nature and quantification of a control system, it applies brim linearization method to better MMFI. By transforming 'triangle wave' membership functions of the base elements into 'rectangle wave' membership functions, we get three models which represent different aspect respectively. By simulating second order system and analysing the errors of the results, a conclusion is drawn, that is, the model obtained by brim linearization method has a good precision in contrast with the real model.