Active vibration control of axially moving continua

Velocity feedback based actin vibration control of axially moving continua, which include mechanical systems such as high-speed magnetic and paper tapes and band saws, is presented in this paper. Lyapunov direct method is used to prove the asymptotic stability of the closed-loop system under the proposed control law. The stability analysis is performed directly on the system's partial differential equation so that no approximation is involved. Thus the 'spillover' problem, which is caused by using finite dimensional (truncated) models to approximate the infinite dimensional models of distributed parameter systems, is eliminated. The proposed control law can be implemented in either distributed or discrete forms. The sufficient condition for stabilizing the system using non-collocated sensors and actuators is also given. A numerical example of an axially moving string is presented for illustration.