This paper presents the modeling and position-sensorless vector control of a dual-airgap axial flux permanent magnet (AFPM) machine optimized for use in flywheel energy storage system (FESS) applications. The proposed AFPM machine has two sets of three-phase stator windings but requires only a single power converter to control both the electromagnetic torque and the axial levitation force. The proper controllability of the latter is crucial as it can be utilized to minimize the vertical bearing stress to improve the efficiency of the FESS. The method for controlling both the speed and axial displacement of the machine is discussed. An inherent speed sensorless observer is also proposed for speed estimation. The proposed observer eliminates the rotary encoder, which in turn reduces the overall weight and cost of the system while improving its reliability. The effectiveness of the proposed control scheme has been verified by simulations and experiments on a prototype machine.