This paper presents an observer-based inverse dynamics control strategy that results in small tip-position tracking errors while maintaining robust closed-loop performance for a class of multi-link structurally flexible manipulators. This is done by defining new outputs near the end points of the arms as well as by augmenting the control inputs by terms which ensure stable operation of the closed-loop system. As part of the control design, a nonlinear observer is introduced to estimate the rates of change of flexible modes. Experimental results are given for the case of a two-link manipulator with a flexible link that further confirm the theoretical and simulation results.