Linear Parameter Varying Representation of a class of MIMO Nonlinear Systems

TL;DR

This paper introduces a systematic method to convert MIMO nonlinear systems into LPV models using a factorization approach, simplifying model identification and control design.

Contribution

A novel LPV embedding technique from MIMO NLFR models that automates the conversion process and aids in scheduling variable selection.

Findings

Enables systematic LPV model extraction from nonlinear MIMO systems.

Facilitates the use of nonlinear identification tools for LPV models.

Demonstrated on a 2-DOF nonlinear mass-spring-damper system.

Abstract

Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying an LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, especially if a first principles based understanding of the system is unavailable. Converting a nonlinear model to an LPV form is also non-trivial and requires systematic methods to automate the process. Inspired by these challenges, a systematic LPV embedding approach starting from multiple-input multiple-output (MIMO) linear fractional representations with a nonlinear feedback block (NLFR) is proposed. This NLFR model class is embedded into the LPV model class by an automated factorization of the (possibly MIMO) static nonlinear block present in the model. As a result of the factorization, an LPV-LFR or an LPV state-space model with affine dependency on the scheduling is obtained. This approach facilitates the selection of the scheduling variable and the connected mapping of system variables. Such a conversion method enables to use nonlinear identification tools to estimate LPV models. The potential of the proposed approach is illustrated on a 2-DOF nonlinear mass-spring-damper example.