Structure Discrimination in Block-Oriented Models Using Linear Approximations: A Theoretic Framework

TL;DR

This paper presents a theoretical framework for identifying the structure of complex block-oriented nonlinear systems by analyzing pole-zero movements in linear approximations around different setpoints.

Contribution

It introduces a method to determine system structure using pole-zero dynamics from linearized models, applicable to various block-oriented and closed-loop systems.

Findings

Pole-zero movements reveal system structure information.

Applicable to Wiener, Hammerstein, Wiener-Hammerstein, and more complex models.

Framework extends to closed-loop and multi-branch systems.

Abstract

In this paper we show that it is possible to retrieve structural information about complex block-oriented nonlinear systems, starting from linear approximations of the nonlinear system around different setpoints.The key idea is to monitor the movements of the poles and zeros of the linearized models and to reduce the number of candidate models on the basis of these observations. Besides the well known open loop single branch Wiener-, Hammerstein-, and Wiener-Hammerstein systems, we also cover a number of more general structures like parallel (multi branch) Wiener-Hammerstein models, and closed loop block oriented models, including linear fractional representation (LFR) models.