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This paper addresses modeling a HexaPOD treatment couch used in robot assisted radiotherapy for motion compensation of lung tumors. The HexaPOD, on which the patient is lying, is supposed to move the patient to counteract the tumor motion. For the purpose of modeling the dynamic behavior of the HexaPOD, linear ARX models are used. It was found that these models work when no velocity saturation occurs. However, from real patient data acquired by our clinical system it is shown in this work that, during some phases, the HexaPOD needs to operate at its maximum velocity. This imposes nonlinearities on the ARX model which cause their performance to degrade. To overcome this drawback, the models are enhanced with a nonlinear extension which can be applied in a generic way to a wide variety of models. It is proved by experimental data that the extended model is capable of exhibiting linear behavior from the underlying ARX model where it is necessary while it can simultaneously deal with velocity saturation. Emphasis is laid on system identification as this is a crucial topic to achieve good model performance.