Identification of systems with localised nonlinearity: From state-space to block-structured models

Abstract

This paper presents a method that generates initial estimates for a rather general block-structured model, starting from the (more general) polynomial nonlinear state-space model. The considered block-structure, sometimes referred to as Linear Fractional Transformation (LFT) or Linear Fractional Representation (LFR), encompasses several simpler structures. It can e.g. describe Wiener, Hammerstein, Wiener–Hammerstein and nonlinear feedback structures. In fact, the chosen block-structure is the most general representation of a system with one Single-Input Single-Output (SISO) static nonlinearity. As is quite common in block-structure identification, the states and internal signals are assumed to be unknown. The method gradually imposes the structure of the LFR system, and at the same time finds an estimate of the Multiple-Input Multiple-Output (MIMO) linear dynamic part and the static nonlinearity (SNL). The method is illustrated via an experimental-data example.