Velocity tracking control of an axially accelerating string and actuator system

In this paper, we present a control strategy for an axially moving string system that achieves vibration regulation along the string and ensures that the string tracks a desired axial velocity trajectory. The control strategy is implemented by utilizing the roller torque inputs applied at the entry and exit points of the string and a pair of control forces applied to the string via an interstitial mechanical guide. Given the hybrid model of the string system (i.e., the distributed parameter field equation coupled to discrete actuator equations), Lyapunov-type arguments are utilized to design a model-based control law that exponentially regulates the axial velocity tracking error and the string displacement along the entire span. The proposed control law is based on measurements of the string displacement, velocity, slope, and slope rate at the mechanical guide.