In this work an observer-based robust adaptive control approach for the axial force of friction stir welding (FSW) is used to overcome process disturbances and model error stemming from the simplistic dynamic models suitable for control. Good 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 adaptive robust control (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 (OAC). The combined ARC/ADDF technique is shown to dramatically reduce axial force variations in the presence of significant process disturbances.