High performance feedback for fast scanning atomic force microscopes

We identify the dynamics of an atomic force microscope (AFM) in order to design a feedback controller that enables faster image acquisition at reduced imaging error compared to the now generally employed proportional integral differential (PID) controllers. First, a force model for the tip–sample interaction in an AFM is used to show that the dynamic behavior of the cantilever working in contact mode can be neglected for control purposes due to the relatively small oscillation amplitude of the cantilever in response to a defined topography step. Consequently, the dynamic behavior of the AFM system can be reduced to the behavior of the piezoelectric scanner making the design of a model based controller for the AFM possible. Second, a black box identification of the scanner of a commercial AFM (Nanoscope IIIa, Digital Instruments) is performed using subspace methods. Identification yields a mathematical model of the scanner which allows us to design a new controller utilizing $H∞$ theory. Finally, this controller is implemented on an existing AFM and operated in contact mode. We demonstrate that such an $H∞$-controlled AFM system, while scanning at rates five times faster than conventional PID-controlled systems, operates with reduced measurement error and allows scanning at lower forces.