Robots that enable safe human-robot collaboration can be realized by using compliant drive units. In previous works, different mechanical designs of compliant pneumatic rotary drive units with similar characteristics have been presented. In this paper, we present the overall control approach that we use to operate one of these compliant pneumatic rotary drive units. We explain the mechanical design and derive the differential equation that describes the dynamics of the system. In order to successfully operate a pneumatic drive unit with three or more working chambers, the torque specified by the controller has to be split up onto the working chambers. We transfer the well-known field-oriented control approach from electric motors to the investigated pneumatic drive unit to create such a torque mapping. Moreover, we develop optimized torque mappings that are tailored to work with this type of drive unit. Furthermore, we introduce and compare two control algorithms based on different implementations of state feedback to realize position control. Finally, we present the step responses that we achieve when we implement either one of the control algorithms in combination with the different torque mappings.