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Tilt rotor is a thrust force vectoring actuation strategy, mainly employed on aircraft to increase the control degrees of freedom. On multi-rotors, this strategy can be profitable for control purposes in terms of stability and maneuverability. Therefore, the present paper presents the design, model, and control of a 3 DOF tilt-rotor bi-copter test bench. The resulting apparatus is composed of a tilt-rotor bi-copter attached to an articulated arm that enables the vehicle to shift its position vertically, laterally, and rotate about its axis. Therefore, different control strategies for vehicles with tilting capability can be evaluated, ensuring safety and repeatability. In particular, the considered control task consists of tracking position references with proper enforcement of input constraints. For this purpose, a dual-mode control strategy, composed of a linear quadratic regulator and a model predictive controller, is adopted. Experimental results are compared to numerical simulations to corroborate the effectiveness and robustness of the proposed control system in the presence of model uncertainties and external disturbances.