A finite dimensional algorithm is presented which by trial searches for a control law is able to move a two-link flexible arm between two given equilibrium configurations in a finite time interval. Using a singular perturbation analysis, the possibility of considering the system as a linear perturbed one is shown, allowing the use of a linear learning algorithm which is able to reject all the nonlinear disturbances. The effectiveness of this algorithm is proven by theoretical arguments and experimental results. Robustness with respect to unmodeled high frequency dynamics is also addressed.