A new identification method for Wiener and Hammerstein Systems

System identification is very important to technical and nontechnical areas. All physical systems are nonlinear to some extent and it is natural better to use nonlinear model to describe a real system. The Wiener and Hammerstein systems are proved to be good descriptions of nonlinear dynamic systems in which the nonlinear static subsystems and linear dynamic subsystems are separated in different order. Descriptions of different nonlinear systems need different Wiener and Hammerstein model structures. The aim of this doctoral dissertation is to develop an unified new recursive identification method in the prediction error method and model scheme for Wiener and Hammerstein systems; to derive the identification algorithms for a class of Wiener and Hammerstein model structures with continuous and discontinuous nonlinearities and to implement and test the algorithms with simulation examples in a MATLAB/Simulink environment. With the definition and extraction of intermediate variables by using the key term separation principle, a Wiener and Hammerstein system can be described by a nonlinear pseudo-regression model. If some suitable submodel structures are selected, such a nonlinear pseudo-regression model could be pseudo-linear and can be approximately transformed into a pseudo-linear MISO system. The intermediate variables can be estimated recursively. The errors in estimated parameters and in intermediate variables affect strongly the identification procedure and results. Therefore, the estimated parameters or rather the intermediate variables should be smoothed by using smoothing techniques. Under some common assumptions and by using the adaptive recursive pseudo-linear regressions (RPLR), satisfied parameter estimates of the Wiener and Hammerstein system can be obtained in the presence of a white or a coloured measurement noise without parameter redundancy. The new method gives good results for all considered Wiener and Hammerstein systems and for some comparable examples, the results are also better. The major advantage of the new method is its unity and efficiency. It can be easily extended to identify other block-oriented nonlinear dynamic systems.

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