Title: Linear Parameter Varying Representation of a class of MIMO Nonlinear Systems,
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.