This paper describes the application of linear parameter varying (LPV) control design to the positioning control of the first axis of an industrial manipulator. The manipulator is modeled as a single flexible joint robot. The parameter dependency of the manipulator dynamics results from movements of the other axes. They determine the inertia that has to be moved by the first axis. The controller is designed via a mixed sensitivity weighting scheme for LPV control. Structural properties of the weighting scheme allow the application of the separation principle. By splitting the synthesis problem into an observer and a state feedback problem, the complexity of the convex optimization problem which has to be solved is greatly reduced. A multistage parameter optimization is employed to tune the control system. Finally, the design is compared to an output feedback PID and an ad-hoc gain-scheduled observer based PI state feedback controller on a real-time testbed with a KUKA standard industrial manipulator.