Adaptive vibration control of an axially moving string

In this paper, the displacement of an axially moving string is regulated us ing a control force and a control torque applied to the string via a mechan ical guide. Given the hybrid model of the string system (i.e., distributed parameter field equation coupled to discrete actuator equations), Lyapunov- type arguments are utilized to design model-based and adaptive control laws that exponentially and asymptotically stabilize the string displacement, r espectively. The proposed control laws are based on measurements of the str ing displacement, velocity, slope, and slope rate at the mechanical guide. While the model-based controller requires exact knowledge of the actuator/s tring parameters (e.g., actuator mass and string tension), the adaptive con troller estimates the parameters online. Dynamic simulation results demonst rate the vibration damping provided by the control strategies.