In this paper, an inversion-based control of the end effector of a two-link flexible robot arm is investigated. The challenge in solving this problem consists in the instability of the inverse system. Arbitrary initialization of the inverse system leads to unbounded elastic vibrations, even if along the desired trajectory the inertial forces associated with the rigid motion are bounded. We show that bounded solutions of the inverse system exist and we provide procedures for computing such solutions in the case of periodic velocities of the end effector. In particular, we consider the case of tracking an unbounded trajectory, e.g., an end point ramp. A technique for the stabilization of the trajectories to be tracked is also proposed and some numerical simulations illustrate the performance of the controlled system.

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