Robust H∞ control in fast atomic force microscopy

This paper presents the design of a robust H
^∞
controller for fast tracking of an Atomic Force Microscope (AFM). The controller design is based on a physical model of the AFM piezoelectric tube positioner. External capacitors are connected in series with the x and y contacts of the piezoelectric tube to provide measured voltages which are proportional to the charge on the actuator. The parameters for a nonlinear hysteresis model are obtained from measurements of the system frequency response and time domain response. Experimental results show that the robust H
^∞
controller can increase the scanning speed significantly.