Moving tumors, for example in the vicinity of the lungs, pose a challenging problem in radiotherapy, as healthy tissue should not be irradiated. Apart from gating approaches, one standard method is to irradiate the complete volume within which a tumor moves plus a safety margin containing a considerable volume of healthy tissue. This work deals with a system for tumor motion compensation using the HexaPOD® robotic treatment couch (Medical Intelligence GmbH, Schwabmünchen, Germany). The HexaPOD, carrying the patient during treatment, is instructed to perform translational movements such that the tumor motion, from the beams-eye view of the linear accelerator, is eliminated. The dynamics of the HexaPOD are characterized by time delays, saturations, and other non-linearities that make the design of control a challenging task. The focus of this work lies on two control methods for the HexaPOD that can be used for reference tracking. The first method uses a model predictive controller based on a model gained through system identification methods, and the second method uses a position control scheme useful for reference tracking. We compared the tracking performance of both methods in various experiments with real hardware using ideal reference trajectories, prerecorded patient trajectories, and human volunteers whose breathing motion was compensated by the system.