In this paper, a model-based tracking control is proposed for a mechanism dedicated to accurately reproduce the breathing-induced motion of a human lung tumour. In former work, a 3-dimensional mechanism equipped with three pneumatically driven axes has been developed and constructed for this purpose. The overall control structure consists of decentralised axis controller for each pneumatic cylinder with a cascaded structure: A fast inner control loop governs the pressure induced drive force using backstepping techniques, whereas the outer control loop is related to an optimal, robust position control of the cylinder. Additionally, discrete-time iterative learning controllers are utilised to compensate lumped disturbance forces and model uncertainties. The suggested overall control structure has been implemented on the innovative test rig and successfully validated in a clinical framework. The given work represents the basis for future improvements of algorithms regarding PET/CT-imaging as well as radiotherapy.