Parameter Optimization for an Accurate Swept-Sine Identification Procedure of Nonlinear Systems

Abstract

Modeling the nonlinearity of a system is of primary importance both for optimizing its design and for controlling the behavior of physical systems operating with a wide dynamic range of input values, for which the linearity hypothesis may not be sufficient. To become of practical use, the identification of nonlinear models must be accurate and computationally efficient. For these reasons, in recent years, among the numerous models of nonlinear systems that have been proposed in the technical literature, the Hammerstein model has been widely applied as a consequence of the proposal of a new pattern identification technique based on pulse compression, which makes the identification of the model very accurate in numerous applications for which it has been adopted. Hammerstein model identification of a nonlinear system requires characterization of the linear filters present on the different branches of the model. These linear filters, which constitute the parameters of the model to be identified, must be considered with respect to their trends over time or, equivalently, in their frequency trends, as amplitude and phase responses. The identification can be considered accurate if the trends obtained for each filter adequately characterize it for the entire frequency range to which that specific filter is subjected in the normal operation of the system to be identified. This work focuses on this aspect, i.e., on the adequacy of the frequency range for which the filter is identified and on how to obtain correct identification in the entire frequency range of interest. The identification procedure based on exponential swept-sine signals defines these filters in the time domain by making use of intermediate functions that are related to the impulse responses of the model filters through a linear transformation. In this paper, we analyze, in detail, the roles of the bandwidths of both the excitation signal and the matched filter, which are the basis of the procedure, we verify the assumptions made about the amplitudes of their frequency bands, and we propose criteria for defining the bandwidths in order to maximize accuracy in model identification. The experiment performed makes it possible to verify that the proposed procedure avoids possible limitations and significantly improves the quality of the identification results, both if the description is made in the time domain and in the frequency domain.