Adaptive vibration isolation for axially moving beams

Manufacture and use of metal bands, sheets, and cables often requires high- speed axial transport of the material Disturbance forces can cause vibratio n to propagate through the process due to the bending stiffness coupling be tween adjacent roller-supported spans. This paper introduces an active pivo ting roller that adaptively decouples adjacent spans, thereby isolating a c ontrolled span from bounded disturbances in an adjacent span. The system in cludes a partial differential equation for the two spans and an ordinary di fferential equation for the actuator, Exact model knowledge and adaptive is olation controllers, biased on Lyapunov theory, regulate the controlled spa n from bounded disturbances in the adjacent, uncontrolled span. Assuming di stributed damping in the uncontrolled span, the exact model knowledge and a daptive controllers exponentially and asymptotically drive the controlled s pan displacement to zero, respectively, while ensuring bounded uncontrolled span displacement and control force, Experiments demonstrate the effective ness of the proposed controller in damping and disturbance-isolating the co ntrolled span.