Iterative fuzzy model inversion

Nowadays model based techniques play very important role in solving measurement and control problems. Recently for representing nonlinear systems fuzzy models became very popular. For evaluating measurement data and for controller design also the inverse models are of considerable interest. In this paper a technique to perform fuzzy model inversion is introduced. The method is based on solving a nonlinear equation derived from the multiple-input single-output (MISO) forward fuzzy model simple by interchanging the role of the output and one of the inputs. The utilization of the inverse model can be either a direct compensation of some measurement nonlinearities or a controller mechanism for nonlinear plants. For discrete-time inputs the proposed technique provides good performance if the iterative inversion is fast enough compared to system variations, i.e. the iteration is convergent within the sampling period applied. The proposed method can be considered also as a simple nonlinear state observer, which reconstructs the selected input of the forward fuzzy model from its output using an appropriate strategy and a copy of the fuzzy model itself. It is also shown that using this observer concept completely inverted models can also be derived.