This paper outlines a complete methodology for designing a control system that reshapes the dynamic response of the flexible structure to robustly match the dynamics of a given adaptable reference model. The procedure was experimentally verified on a setup developed at the European Space Agency, consisting of a cantilevered flexible plate actuated by two shakers. Angular displacements at the free tip of the plate were measured with sub-microradian resolution using a laser autocollimator. Following a comprehensive system identification phase, mathematical models of the uncertain plant were extracted. The models reliably fit the experimental data and were used to synthesize a low order and high bandwidth structured Linear Parameter Varying controller. The controller was designed by taking into account the limits of achievable performance and the closed loop effectively constrained the flexible structure to behave like it was made out of an adaptable material. The robust stability and worst case performances were assessed by means of a structured singular value analysis and excellent agreement between theoretical predictions and experimental results was observed.