A desire to improve the positioning accuracy of ball screws prompted an investigation into the dynamics of nanometer motion. Characterization of the ball screw indicated that nanometer motion is possible prior to friction breakaway via elastic deformation of the frictional contacts while macroscopic motion involves slipping across the friction interfaces. The observed dynamics are nonlinear, and consequently result in inconsistent and unpredictable closed-loop response while under PI position control. The ball-screw can be modeled in two stages: The microdynamic stage includes “elastic” friction while the macrodynamic stage incorporates kinetic (sliding) friction. A two-stage model reference adaptive control (MRAC) strategy is adopted and a Lyapunov design technique is applied to derive the adaptive laws. Experimental results obtained via a DSP implementation of the adaptive controller indicate that the each stage of the adaptive control performs well within the respective dynamic regions, but performance deteriorates as either controller is operated near the boundary of the regions.

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