Identification of a Block-Structured Model with Localised Nonlinearity

Abstract

This paper considers the identification of a rather general nonlinear time-invariant system, consisting of a Multiple-Input Multiple-Output (MIMO) linear dynamic part and one static nonlinear part. It is sometimes referred to as Linear Fractional Transformation (LFT) or Linear Fractional Representation (LFR). The structure will be called nonlinear LFR and includes many standard block-structured models, such as Wiener, Hammerstein, Wiener-Hammerstein and nonlinear feedback. The identification does assume neither the states, nor the internal signals over the static nonlinearity to be measured. The static nonlinearity (SNL) is assumed to be polynomial. After estimation of a nonlinear state-space model with certain structural properties, the SNL can be separated from the MIMO linear part. Next, the linear system is represented by a combination of four linear dynamic blocks, yielding extra insight. The method is illustrated via an experimental-data example.