REDUCTION OF RESIDUAL VIBRATIONS IN A ROTATING FLEXIBLE BEAM WITH A MOVING PAYLOAD MASS

The reduction of residual vibrations for the position control of a fle xible rotating beam carrying a payload mass is investigated. The commo n practice used to find the position control of a flexible multi-link arm is to assign a torque actuator to each joint while the payload mas s is kept fixed relative to the end-link during the time of manoeuvre. This paper examines the stability of the system if either the payload is freed accidentally to move along the beam during the time of manoe uvre or is allowed to span the beam in a desired path for control purp oses. A candidate Lyapunov function is constructed and its time rate o f change is examined. It is shown that the use of a PD (proportional p lus derivative) torque control yields a convergence of residual vibrat ion to zero, an attainment of the rigid-body rotation to a prespecifie d desired angle of manoeuvre and a constant velocity of the payload ma ss as it moves relative to the beam. For manipulation purposes, an add itional control force is added to the moving actuator in order to regu late its axial motion. It is shown that allowing the axial motion of t he payload mass in a prescribed manner leads to a considerable reducti on of its residual vibrations as compared to the case where the payloa d mass is fixed to the beam tip during the time of manoeuvre. Stabilit y is also verified through simulations of rigid-body rotation and payl oad axial motion track prespecified reference trajectories.