  This paper proposes a new Linear Fractional Transformation (LFT) modeling
approach for uncertain Linear Parameter Varying (LPV) multibody systems with
parameter-dependent equilibrium. Traditional multibody approaches, which
consist in building the nonlinear model of the whole structure and linearizing
it around equilibrium after a numerical trimming, do not allow to isolate
parametric variations with the LFT form. Although additional techniques, such
as polynomial fitting or symbolic linearization, can provide an LFT model, they
may be time-consuming or miss worst-case configurations. The proposed approach
relies on the trimming and linearization of the equations at the substructure
level, before assembly of the multibody structure, which allows to only perform
operations that preserve the LFT form throughout the linearization process.
Since the physical origin of the parameters is retained, the linearized LFT-LPV
model of the structure exactly covers all plants, in a single parametric model,
without introducing conservatism or fitting errors. An application to the
LFT-LPV modeling of a robotic arm is proposed; in its nominal configuration,
the model obtained with the proposed approach matches the model provided by the
software Simscape Multibody, but it is enhanced with parametric variations with
the LFT form; a robust LPV synthesis is performed using Matlab robust control
toolbox to illustrate the capacity of the proposed approach for control design.
