Robust H∞ control of a scanning tunneling microscope under parametric uncertainties

This paper is devoted to the control system design for high performance scanning tunneling microscope (STM). A common approach by scanning probe community is to use conventional proportional integral (PI) control design to control the vertical movement of STM tip (z-direction). In this article, a modern H_∞ control design is analyzed in order to obtain the dual purpose of ultrahigh positioning accuracy with high bandwidth. Uncertainty model, based on experimental analysis of tunneling characteristics and parametric description of the STM, and norm-bounded real perturbations are considered, and an H_∞ controller is designed by following the desired control objectives. A performance and robustness analysis is finally performed to test robust stability and performance of STM.