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The control of a flexible arm is the focus of this work. The dynamic model is obtained via an assumed mode method, and a singularly perturbed model of the system is then derived. The new feature of this model is that multiple boundary layers are considered, one for each assumed mode. A composite control strategy is then pursued. First a slow control is designed for the rigid system, then a number of fast controls (one for each layer) make the fast dynamics in the layers suitably damped. A case study is finally worked out and simulation results are presented.