CONTROL OF A TWO-LINK RIGID–FLEXIBLE MANIPULATOR WITH A MOVING PAYLOAD MASS

Control of a two-link rigid–flexible manipulator carrying a moving payload mass is considered. The stability of the system when the payload mass is moving along the flexible link during the time of maneuver is investigated. A candidate Lyapunov function is constructed and its time rate of change is examined. It is shown that the use of an independent PD-type controller yields a convergence of residual vibration to zero, an attainment of the rigid-body rotations to their prespecified desired angles of maneuver, and an axial guidance of the payload mass. It is shown that allowing the relative motion of the payload mass, as it moves along the flexible link, leads to a considerable reduction of its residual vibrations as compared with the case when it is fixed to the link tip during the time of maneuver. The performance of the proposed controller is also verified in case the links and the payload mass are required to track prespecified reference trajectories.