Robust H∞ Control in Fast Atomic Force Microscopy.

This paper develops a robust H^∞ method for fast tracking position control problems arising in an atomic force microscope ( AFM). A commercial type NT- MDT AFM is used to generate 3D images of scanned material surfaces at high speeds and accuracies. A major component of this AFM is a piezoelectric tube actuator used for position control in three directions. Due to the nature of the piezoelectric actuator, there is nonlinear hysteresis present which affects the AFM scanning qualities. The original commercial AFM uses traditional proportional-integral-derivative position control and can only obtain good quality images for scanning rates under about 20 Hz in both the x and y directions. In this paper, a robust H^∞ controller is designed based on a physical model of the AFM piezoelectric tube positioner in the x and y directions. On the electrical side of the positioning system, 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 model are obtained from measurements of the system frequency response and time domain response. This model also takes into account the time delay resulting from the sensor electronics. This nonlinear model is represented as a linear uncertain system model with norm bounded uncertainty. The uncertain system model is used to design a robust H^∞ tracking controller for the AFM scanning system. Experimental results show that the robust H^∞ controller can improve the AFM scanning quality and increase the scanning speed significantly. The controller performs well in tracking a given reference scanning signal with frequencies up to 125 Hz. [ABSTRACT FROM AUTHOR]