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 vibration to propagate through the process due to the bending stiffness coupling between adjacent roller-supported spans. This paper introduces an active pivoting roller that adaptively decouples adjacent spans, thereby isolating a controlled span from bounded disturbances in an adjacent span. The system includes a partial diSerential equation for the two spans and an ordinary differential equation for the actuator. Exact model knowledge and adaptive isolation controllers, based on Lyapunov theory, regulate the controlled span from bounded disturbances in the adjacent, uncontrolled span. Assuming distributed damping in the uncontrolled span, the exact model knowledge and adaptive controllers exponentially and asymptotically drive the controlled span displacement to zero, respectively, while ensuring bounded uncontrolled span displacement and control force.