A new structure for non-linear black-box system identification using the extended Kalman filter

Abstract

A new tool for black-box non-linear system identification of multi-input multi-output systems is presented in this paper. The new structure extends the conventional linear state-space model into a non-linear framework, where each parameter is a non-linear function of the inputs or the states. The method works iteratively in the time domain using an extended Kalman filter. The model retains a state-space structure in modal canonical form, which ensures that a minimal number of parameters need to be identified and also produces additional information in terms of the system eigenvalues and the dominant modes. This structure is a completely black-box system, which requires no physical understanding of the process for successful identification, and it is possible to expand easily the order and the complexity of non-linearities, while ensuring good parameter conditioning. A simple non-linear example illustrates the method, and identification of a highly non-linear brake model is also presented. These examples show that the method can be applied as a mechanism for model order reduction; it is equally very suitable as a tool for non-linear plant system identification. In both capacities this new method is valuable, particularly as the generation of simplified models for the whole vehicle and its subsystems is an increasingly important aspect of modern vehicle design.