Robust Lyapunov-Based Feedback Control of Nonlinear Web-Winding Systems

Abstract— Web-winding systems such as tape drives are often modeled as linear and time-invariant (LTI), but at least two nonlinearities are common in these systems. First, the reel radii and moments of inertia change as web media spools from one reel to another. Second, friction can draw a thin layer of air between the layers of web media wrapped on the takeup reel, making the system’s spring and damping characteristics nonlinear by allowing a greater length of media to vibrate freely. Little has been published regarding the dynamic behavior of this “air entrainment” phenomenon. This paper first describes a model for web-winding systems that includes these nonlinearities. No particular model is taken for air entrainment; it is only assumed that its effects are bounded in a certain sense. It is further assumed that the motor parameters are not known exactly. Feedback linearization, state feedback, and changes of variables are then used to transform the system into decoupled and intuitively meaningful tension and velocity loops. Lyapunov redesign techniques are then used to develop control laws that are robust with respect to the motor parameters. Under these laws, velocity error is exponentially stable and tension error satisfies a desired bound for all time— with tension error also exponentially stable in the steady-state case. Simulations illustrate the performance of these schemes.