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In this paper, we propose a generic model and a controller design for a class of underactuated aerial vehicles, namely for unmanned aerial vehicles whose primary support against gravity is thrust. The approach followed is based on energetic consideration and uses the formalisms of port-Hamiltonian systems and bond graphs. The controller is designed for both stabilization during hovering and for trajectory tracking tasks. The competency of the model and the performance of the controller are validated in simulation.