Energy-based control of axially translating beams: varying tension, varying speed, and disturbance adaptation

In this brief, the investigational results for a robust adaptive vibration control of a translating tensioned beam with a varying traveling speed are presented. The dynamics of beam and actuator is modeled via the extended Hamilton´s principle, in which the tension applied to the beam is given as a nonlinear spatiotemporally varying function. The moving beam is divided into two parts, a controlled span and an uncontrolled span, by a hydraulic touch-roll actuator that is located in the middle section of the beam. The transverse vibration of the controlled span is suppressed by the touch-roll actuator, whereas the vibration of the uncontrolled span is treated as a disturbance, and the magnitude of unknown disturbance is estimated. In a proper mathematical manner, the Lyapunov method is employed to design robust adaptive boundary control laws for ensuring the vibration reduction of the nonlinear time-varying system, and also to ensure the stability of the closed-loop system. The effectiveness of the proposed controller is demonstrated via numerical simulations.