Linear Fractional Transformation modeling of multibody dynamics around parameter-dependent equilibrium

TL;DR

This paper introduces a novel LFT modeling method for uncertain LPV multibody systems with parameter-dependent equilibrium, enabling exact, conservative-free models that facilitate robust control design.

Contribution

The paper presents a new LFT modeling approach that linearizes multibody systems at the substructure level, preserving the LFT form and avoiding conservatism or fitting errors.

Findings

The proposed model matches Simscape Multibody in the nominal case.

It accurately captures parametric variations without conservatism.

Enables robust LPV control synthesis using MATLAB tools.

Abstract

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.