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In this paper, we present a control strategy for an axially moving web system that regulates transverse vibration and ensures that the web speed tracks a desired trajectory. The control strategy is implemented using roller torque inputs applied at the boundary and a pair of control forces applied to the web via a mechanical guide. Given the hybrid model of the web system (i.e. the distributed parameter field equation coupled to discrete actuator equations), Lyapunov-type arguments are utilised to design a model-based control law that exponentially regulates the axial speed tracking error and the web displacement. The proposed control law is based on measurements of the web speed and displacement, slope, and slope rate at the mechanical guide. Experimental results demonstrate the speed tracking and vibration damping provided by the control strategy.

This paper introduces boundary controllers for a general class of non-linear string–actuator systems. The non-linear distributed-parameter model accounts for large amplitude displacement and the associated varying tension according to a general class of non-linear stress–strain relationships. A non-linear, model-based controller asymptotically drives the system energy to zero. Redesign of the controller using adaptation laws allows compensation for parametric uncertainty while asymptotically driving the system energy to zero. Experimental results verify the feasibility of implementing the proposed controllers and compare the performance with damper and linear controllers.