The trajectory-tracking control problem is considered for a one-link flexible arm described by a non-linear model. Two meaningful system outputs are chosen; namely, the joint angle and the angular position of a suitable point along the link. The common goal is to stiffen the behaviour of the flexible link with respect to the chosen output. Based on the input-output inversion algorithm, a state-feedback control law is designed that enables exact tracking of any smooth trajectory specified for the output. In the closed loop an unobservable dynamics naturally arises, related to the variables describing the arm's distributed flexibility. Joint-based design is shown to be always stable, whereas in the link-point design the closed-loop dynamics may become unstable depending on the location of the output along the link. Open- versus closed-loop strategies are developed and compared. Extensive simulation results are included.