H∞ controller design for high-performance scanning tunneling microscope

Ultrahigh positioning accuracy with high bandwidths are the great challenges in the field of nano-positioning and scanning systems. This article talks about the controller design for a closed-loop scanning tunneling microscope to deal with such challenges, considering fast continuous variations in sample surface with the presence of noise in the loop. The desired performances in vertical Z-direction of the scanner are imposed on the closed-loop sensitivity functions using appropriate weighting functions and then a mixed-sensitivity H_∞ controller is designed. The results are compared with the conventional proportional-integral control design commonly used by the scanning probe community, underlining the improvements obtained in terms of high precision with high bandwidth.