Graded concrete is a novel technology in the construction industry, allowing for up to 50% mass savings in the fabrication of concrete elements. This is achieved by casting around hollow bodies and thus producing cavities in the interior, which are placed and sized in such way that the load-bearing capacity is not inhibited. For a prototypical on-site fabrication system, a conventional concrete piston pump is employed, which is in focus of this paper.For this pump, a detailed model is derived. From this model, it is seen that the concrete volume flow is directly linked to the hydraulic volume flow conveyed by an axial piston pump. The swash angle of the pump is controlled by a setting pressure, set through a pressure reducing valve. As the valve is of low quality, it is subject to heavy hysteresis. While the qualitative behaviour of the valve can be reproduced by physical modeling, a data-driven approach with a NARX model is shown to be superior. The NARX model is used as a simulation model for designing a linear inner loop controller for the setting pressure, which is validated by experiments. The volume flow control is then achieved by a subsequent outer loop, which is based on the identified dynamics of the swash plate.