Stabilizing a flexible beam handled by two manipulators via PD feedback

This paper proposes a simple PD feedback controller to regulate a flexible beam handled by two manipulators to a desired position and orientation while suppressing its vibration in the absence of the gravity force. The proposed controller uses no information about the vibration, but uses joint positions and velocities of the manipulators. The asymptotic stability is proved based on the vibration dynamics of the beam approximated by m assumed modes, in which m can be any large number. A hybrid controller is also developed to control the position of the beam and its interaction forces with the manipulators.