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Friction stir welding (FSW) is a relatively new and promising joining process that is the subject of much current research. When welding with constant parameters, the axial force can vary significantly due to changes in workpiece temperature and other process variations. These variations produce welds with inconsistent microstructure and tensile strength. Control of the axial weld force is desirable to improve the weld quality. In this paper, an observer-based adaptive robust control (ARC) approach for the axial force of FSW is presented to overcome process disturbances and model errors stemming from the simplistic dynamic models suitable for control. Some correlation is shown between spindle power and axial force, allowing readily available power measurements to be used for feedback. A model of the axial force is developed as a combination of a nonlinear static gain and linear dynamics. An axial force controller is constructed using the ARC approach and estimated state feedback from the adaptive divided difference filter (ADDF). Verification experiments are conducted on a vertical milling machine configured for FSW using an open architecture controller. The combined ARC/ADDF technique is shown to dramatically reduce axial force variations in the presence of significant process disturbances.