Time-optimal control of web-winding systems with air entrainment

Models of web-winding systems such as tape drives often ignore the phenomenon of air entrainment, in which friction can draw a thin layer of air many layers deep into the web media wrapped on the takeup reel. Air entrainment allows a greater length of the media to vibrate freely and thus changes the spring and damping characteristics of the system and results in nonlinearities. This paper first explores the structure of nonlinear models for air entrainment and proposes one such model for tape systems. Without specifying a particular air entrainment model, time-optimal inputs for transient maneuvers are explored for the cases of constant- and varying-tension trajectories. These inputs are useful for determining the effect of air entrainment (and the utility of modeling it) on a given system and for establishing bounds on performance for a given system. Simulations illustrate these results on an example tape system.