An improved linear fractional model for robustness analysis of a winding system

Web winding systems exhibit nonlinear dynamics and their behaviors vary with respect to several quantities such as elasticity modulus and end roll radii. Being able to guarantee that the system remains stable during the whole winding process when parameters vary appears to be crucial. μ-analysis is a classical technique for evaluating robustness of parameter-dependent systems and is used herein. It requires the model to be under the ad hoc form of a linear fractional representation. Following the physics equations, the different steps are detailed until to come to the ad hoc model including parameters with independent variations. Notably, the nonlinear dependence between the winder and unwinder radii is considered. Numerical results are given in the case where the system is driven by a H∞ controller.