A partial differential equation for the lateral motion of a web conveyance system is derived by modeling the web as a viscoelastic beam under axial tension. This model treats the web position between rollers as a function of both time and space, assumes that there is no slip between the web material and the rollers, and incorporates the web material's viscoelastic damping property. A finite-difference approximation of the model is used to simulate a typical two-span web system. The finite-difference approximation is validated by comparing its frequency responses with those of an analytical frequency domain model. The analytical frequency domain model is used to design feedback compensation strategies that make the two-span web system less sensitive to upstream disturbances. The results show that, using a transverse vibration model incorporating viscoelasticity to design even simple classical controllers, it is possible to make the web system less sensitive to upstream disturbances at the sensor location.
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