Robust and adaptive boundary control of a stretched string on a moving transporter

Suppression of vibration is an important engineering problem. In this note, control problem of a flexible system that includes a stretched string supported on a transporter is defined and solved. Such a system may be encountered in device manufacturing and process automation. Robust and adaptive control is designed to damp out transverse oscillation of the string via compensating for possible uncertainties in string dynamics and transporter motion. Standard robust control design based on a straightforward Lyapunov argument commonly seen in control design for rigid-body systems is extended to the flexible system. Asymptotically/exponentially and robustly stabilizing controls are found.