Moving tumors, especially in the vicinity of lungs, pose a challenging problem in radiotherapy as healthy tissue should not be irradiated. We developed a system to compensate tumor motion with the robotic treatment couch HexaPOD to improve treatment quality. The HexaPOD, carrying the patient, counteracts the tumor motion so that it is eliminated in the beams-eye-view of the linear accelerator. The focus of this work is on two control methods for the HexaPOD in order to realize reference tracking. The first method is a simple position control scheme to enable reference tracking. It is reformulated as second method to be adopted by a model predictive controller to better account for patient comfort and to maintain tracking accuracy. The performance of both methods is compared in experiments with real hardware using prerecorded patient trajectories and human volunteers whose breathing motion was compensated.