Adaptive Vibration Control of an Axially Moving String

In this paper, the displacement of an axially moving string is regulated using a control force and a control torque applied to the string via a mechanical 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, respectively. The proposed control laws are based on measurements of the string displacement, velocity, slope, and slope rate at the mechanical guide. While the model-based controller requires exact knowledge of the actuator/string parameters (e.g., actuator mass and string tension), the adaptive controller estimates the parameters online. Dynamic simulation results demonstrate the vibration damping provided by the control strategies.

Vibration Control of a Distributed Axially Moving String Using Two Actuators

In this paper, we consider the problem of regulating the displacement of an axial moving string using a control force and a control torque applied to the string via a mechanical guide. Given the hybrid model of the web system (i.e., distributed parameter field equation coupled to a discrete actuator equation), a Lyapunov-type analysis is utilized to design exact model knowledge and adaptive control laws that exponentially and asymptotically stabilize the string displacement, respectively. Dynamic simulation results demonstrate the vibration damping provided by the control strategy.