Recursive Identification of Wiener Type Nonlinear Systems

Abstract

This study is concerned with a problem of the recursive identification of a nonlinear dynamic system composed of a linear dynamic part followed by a known, pure time delay in series with a continuous static memoryless nonlinearity. The linear dynamic part is approximated by a transfer function model and the static nonlinearity by a piecewise-polynomial function model. The output signal from the linear part is not available for measurement. The combined model is nonlinear in its parameters and it is characterized by a larger number of parameters than the original Wiener model. The author proposes two identification methods: 1) the parameters of the linear and nonlinear parts are identified separately using an output error method, 2) the parameters of the combined model inverse are identified using an input error method. In a case of the second method a special stochastic generator was developed for generation a suitable excitation signal. The asymptotic properties in the presence of stochastic noises on the convergence properties of the proposed schemes are analysed. Then, the methods were applied for identification of a pH-process in a continuous flow reactor. The simulation and the experimental test results are presented.