Improved Embedding of Nonlinear Systems in Linear Parameter-Varying Models With Polynomial Dependence

Abstract

In this article, the problem of automated generation of linear parameter-varying (LPV) state-space models to embed the dynamic behavior of nonlinear (NL) systems is addressed. The LPV model depends polynomially on an introduced set of scheduling variables. This set comprises linear combinations of residuals, the differences between NL functions in the original model description with their polynomial approximations, in addition to some of the states. The salient feature of the proposed method (PM) is that the LPV model complexity, LPV model accuracy, and LPV model conservativeness are jointly considered through the embedding procedure. To quantitatively evaluate the LPV model accuracy and conservativeness, two cost functions are introduced based on which the model complexity can be adjusted. Numerical studies reveal that the presented method is capable to deliver more accurate and less conservative LPV models in comparison with the available approaches. The effectiveness of the PM is shown in an empirical case study where the dynamic behavior of a 3DOF gyroscope is embedded into an LPV model. Exploiting the obtained LPV model, a gain-scheduled state feedback controller is designed and validated on the gyroscope, clearly demonstrating the applicability of the presented method.