The problem of reel-to-reel web transport is considered, including a nonlinear complication called air entrainment. Air entrainment occurs when a thin layer of air is drawn between the layers of web media that wind onto the takeup reel, changing the amount of media that is free to vibrate and effectively making the spring and damping parameters of the system time-varying. First, system equations that include this phenomenon are formulated. Second, open-loop time-optimal controls are derived for this nonlinear system. Third, a feedback control is presented that is robust to air entrainment and motor torque and friction parameter uncertainties. No model is assumed for air entrainment; rather it is assumed that its effects are bounded in some sense. Finally, an observer-based feedback controller that does not require measurements of tension is presented. This controller is also robust to air entrainment and uncertainties in the motor friction parameters. Performance of the controllers is proven analytically and demonstrated in simulation. The settling time of the web velocity can be guaranteed, and it is ensured that tension remains in an acceptable range.
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