Optimal Control for X-Ray Microscopes

In this article, a systematic framework for designing the control for fine positioning (scanning) stages of X-ray microscopes is presented. This framework facilitates designs that simultaneously achieve specifications on positioning resolution and tracking bandwidth while guaranteeing robustness of the closed loop device to unmodeled uncertainties. We use robust optimal control techniques for modeling, quantifying design objectives and system-specific challenges, and designing the control laws. The control designs were implemented on a three degree of freedom piezoactuated flexure stages dedicated for fine positioning of X-ray optics. Experimental results demonstrate significant improvements in positioning performance of 134%, 150%, and 132% in tracking bandwidths along the lateral ( X ), vertical ( Y ), and beam ( Z ) directions, respectively, when compared to proportional-integral-derivative controller designs. This was achieved while keeping similar or better positioning resolution and robustness measures. Fast scanning for X-ray imaging was demonstrated in both the step scan and flyscan modes, where bandwidth was improved by over 450 times with flyscan compared to the step scan.