Modeling and Control of Web Lateral Dynamics in Roll-to-Roll Manufacturing: New Governing Equations and Control Strategies
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© 2018 AACC. In this paper we derive spatially dependent transfer functions for web lateral dynamics which provide web lateral position and slope at any location within the web span. This is a significant improvement over existing lateral transfer functions which provide the web lateral response only on the rollers. Our approach relies on taking the Laplace transform with respect to the temporal variable of both the web span lateral governing equation and the normal entry boundary conditions on the rollers, and solving the resulting equations. A general web span lateral transfer function, which is an explicit function of the spatial position along the span, is obtained. The new governing equations provide mechanisms to analyze web lateral behavior within spans, study propagation of lateral disturbances, and aid in the development of closed loop lateral control systems in emerging applications that require precise lateral positioning of the web. Both web lateral position and slope must be controlled to minimize propagation of lateral web oscillations into downstream spans. We illustrate the use of the new governing equations by providing numerical simulations for some representative disturbance and span scenarios.
author list (cited authors)
Torres, E., & Pagilla, P. R.