Pinned-end vibration control of a flexible arm with tip payload

This paper addresses the vibration control problem for a flexible arm with the tip payload and pinned-end boundary input. The flexible arm is modeled by a partial differential equation combined with boundary conditions. The control objective is to steer the flexible arm to a specified angular position while simultaneously suppressing the vibration, with control force applied exclusively at the hub of the flexible arm. To achieve this objective, a pinned-end boundary controller is proposed that relies solely on pinned-end signals. Then, based on operator semigroup, Lyapunov technique, and LaSalle’s invariance principle, the well-posedness and asymptotic stability of the closed-loop system are guaranteed. Finally, the effectiveness and superiority of the designed boundary controller are verified through physical experiments. Compared with the proportional-derivative controller, the designed boundary controller reduces the vibration amplitude to approximately half.