Affine Linear Parameter-Varying Embedding of Nonlinear Models with Improved Accuracy and Minimal Overbounding

TL;DR

This paper presents a method for generating affine LPV models of nonlinear systems that balances accuracy and complexity, demonstrated on a gyroscope control case.

Contribution

The paper introduces an automated approach for affine LPV embedding of nonlinear models, reducing conservativeness and complexity compared to existing methods.

Findings

Effective LPV embedding of a 3-DOF gyroscope model

Low scheduling complexity achieved with improved accuracy

Successful gain-scheduled control implementation

Abstract

In this paper, automated generation of linear parameter-varying (LPV) state-space models to embed the dynamical behavior of nonlinear systems is considered, focusing on the trade-off between scheduling complexity and model accuracy and on the minimization of the conservativeness of the resulting embedding. The LPV state-space model is synthesized with affine scheduling dependency, while the scheduling variables themselves are nonlinear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the nonlinear system model and also it can be used to minimize complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first-principle motion model of a 3-DOF control moment gyroscope is converted by the proposed method to LPV model with low scheduling complexity. Using the resulting model, a gain-scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach.