9813080 Devasia This research project addresses the vibrational problem that limits the band-width of piezo-based ultra-high resolution positioning stages like Inchworms and Flexural-frames - the problem of transient errors which are caused by induced structural-vibrations during high-speed positioning maneuvers. The goal is to improve speed and thereby to increase throughput by developing the theoretical and experimental expertise needed for high-speed positioning stages. The proposed paradigm uses nonlinear-inversion of piezo-positioning-stage dynamics for finding inputs that compensate for structural vibrations. This approach will lead to precision tracking of the desired maneuvers. The key techniques to be used include: (i) modeling of the nonlinear dynamics of the piezo-based positioning-stages via the Finite Element Methods; Balanced-Realization-based model order reduction; incorporating nonlinear hysteresis effects; and online parameter estimation; (ii) development of nonlinear inverse of the piezo-dynamics; and (iii) an experimental evaluation using an Inchworm piezo-stage and a Flexural piezo-stage. Piezo-based high-resolution positioners are key enabling tools with applications in advanced-technology areas like opto-electronics, semiconductors, and smart-structures. By achieving high speeds in piezo-based positioning-systems, the research aims to increase throughputs of systems which employ these positioners. This work also impacts other high-tech industries from transportation to medical technology by making rapid progress based on the ever-increasing cost effectiveness of micro-electronics technologies. ***