Compensation of flexible vibrations in a two-link robot by piezoelectric actuation

This paper concerns the active control of flexural vibrations in a two-link robot consisting of two flexible arms with tip masses. Due to iner-tial forces of distributed and concentrated masses flexural vibrations occur. The robot is moving in a horizontal plane, such that gravity is not considered. In order to compensate the flexible vibrations, piezoelectric actuators are integrated in the arms. In the framework of linear beam theory, the solution of the shape control problem is derived, i.e. the necessary distribution of the piezoelectric actuation strains in order to completely compensate the inertial forces. Assuming that mass distribution, geometrical properties and the link angles are exactly known by appropriate measurements, the flexible vibrations can be fully suppressed. If some parameters are not known exactly, remaining vibrations may occur. Numerical simultions are performed in order to verify the solution of shape control and to study the sensitivity to uncertainties of the parameters