Robust lyapunov-based feedback control of nonlinear web-winding systems

Abstract

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 timewith tension error also exponentially stable in the steady-state case. Simulations illustrate the performance of these schemes.

Decentralized control design using Integrator Backstepping for controlling web winding systems

“…Fuzzy logic [4] [5], neural network [6] [7], optimal control [8], nonlinear sliding mode [9], control active disturbance rejection control (ADRC) strategy [10] [11], and robust control approaches [12] are used. Robust Lyapunov-based feedback control [13] and multivariable H ∞ controller has been proposed for industrial web transport systems [14] [15].…”

Robust Rejection of Periodic and Almost Periodic Disturbances

“…T , with T (t) denoting the tape tension, V i (t) denoting the tangential velocity of the tape at each reel, and u i (t) denoting the current applied to each DC motor, i = 1, 2; the system matrices are too complicated to be stated here and are fully described in (Baumgart and Pao, 2003). The dominant frequency of the reel-eccentricity induced disturbance is the same as the rotating frequency of the corresponding reel, which varies with the change in pack radius because a control objective is to keep the tangential velocity of the tape at a constant value.…”

“…We implemented the above robust extension on the tape system model derived in (Baumgart and Pao, 2003). The model is nonlinear and time-varying, and is given byẋ…”

Control Methods in Data-Storage Systems

“…As the tape velocity increases, air entrainment increases the effective length of the tape path, thus lowering the spring constant of the tape and hence the resonance frequency of the transport system. Designs of closed-loop controllers for reel-to-reel systems taking into account air entrainment exist that are based on the gain-scheduling approach, with a 2-D grid to cover the desired range of tape velocity and tension [47], techniques [48], and guaranteed robustness properties [49]. Open-loop time-optimal control in the presence of air entrainment is addressed in [50].…”