An Iterative Method for Wiener–hammerstein Systems Parameter Identification

The class of nonlinear dynamic systems which can be represented by the block-oriented models, ie, by interconnection of linear dynamic and nonlinear static subsystems, has been studied by many authors. In the simplest case the models consist of a combination of two blocks giving the so-called Hammerstein (nonlinear-linear) and Wiener (linear-nonlinear) models and there are many methods for nonlinear system identification using these models (see [8] and [9] for a complete bibliography). The Wiener-Hammerstein model (also the general or sandwich model, see Fig. 1), defined as a linear system in cascade with a static nonlinear element followed by another linear system, represents a more complex case of block-oriented models. Nonlinear system identification using this model has been studied for many years. In the classical studies [2, 3, 6, 7], identification algorithms for the Wiener-Hammerstein model based on correlation analysis have been proposed. The identification problem has been decoupled into two distinct steps; identification of the linear dynamic subsystems and characterization of the static nonlinearity. Since then numerous contributions to the Wiener-Hammerstein systems identification have been published, eg, [1, 4, 5, 11, 12, 18], and this is still an active research area because many real systems are of this type (eg, sensor systems, electromechanical systems in robotics, mechatronics, biological and chemical systems). In this paper a new approach to the Wiener-Hammerstein model parameter estimation is presented. It is based on a new form of model description resulting from a decomposition technique [13] that is sequentially applied to the general model description. The model is linear in parameters and nonlinear in variables. As two unmeasurable internal variables are included into the model description, the estimation problem is solved iteratively as a pseudolinear one, where the parameters of the nonlinear and two linear blocks are estimated simultaneously using the input and output variables and the estimates of two internal variables.