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This paper presents a model-based tracking control design for a mechanism dedicated to accurately reproduce the breathing-induced motion of a human lung tumour. A lung tumour mimic model should perform the same smooth motion as a real one in a human body during inhalation and exhalation. For this purpose, a 3-dimensional mechanism with three pneumatically driven axes has been developed and built up. The proposed control structure represents a cascaded flatness-based tracking control structure: In the fast inner loops, the chambers pressures of the pneumatic cylinders are controlled, whereas the outer loops are related to the position control of the cylinders. Furthermore, sliding mode observers are employed for each cylinder to estimate the corresponding states and a lumped disturbance force. The proposed overall control structure has been implemented and successfully validated on an innovative test rig.