Hybrid-triggered backstepping control for a rotating flexible beam with a mobile actuator

This paper considers a rotating flexible beam equipped with a mobile actuator. The actuator leads to an extra translational degree of freedom and makes the spatial distribution of the control input vary with the actuator position. A coupled PDE-ODE model of the system is derived via Hamilton's principle. For the strongly coupled rigid-flexible dynamics, a continuous-time backstepping controller incorporating barrier Lyapunov functions is developed for attitude regulation and vibration suppression under output constraints. A hybrid-triggered control scheme is proposed to further balance control performance with control update frequency and mitigate mechanical wear of the actuator. Specifically, event-triggered control is applied to the rigid-body motions, while continuous-time control is maintained for the vibration suppression task. Numerical simulations verify the effectiveness of the proposed control scheme.