Automated Linear Parameter-Varying Modeling of Nonlinear Systems: A Global Embedding Approach

TL;DR

This paper introduces an automated method for converting nonlinear systems into Linear Parameter-Varying models using a global embedding technique that leverages calculus, demonstrated on mechanical systems and implemented in MATLAB.

Contribution

It presents a novel, approximation-free approach for global LPV embedding of nonlinear systems, with software tools and practical examples included.

Findings

Effective LPV embedding of nonlinear systems demonstrated

Software implementation available for practical use

Successful control design based on LPV models

Abstract

In this paper, an automated Linear Parameter-Varying (LPV) model conversion approach is proposed for nonlinear dynamical systems. The proposed method achieves global embedding of the original nonlinear behavior of the system by leveraging the second fundamental theorem of calculus to factorize matrix function expressions without any approximation. The implementation of the proposed method in the LPVcore toolbox for Matlab is discussed, and its performance is showcased on a comprehensive example of automated LPV model conversion of an unbalanced disk system, which is then used to design an LPV controller that is deployed on the original nonlinear system. In addition, the conversion capabilities are further demonstrated by obtaining an LPV embedding of a three-degree-of-freedom control moment gyroscope. All software implementations are available at www.lpvcore.net.