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G. Schitter, P. Menold, H. Knapp, F. Allgöwer, A. Stemmer:
"High performance feedback for fast scanning atomic force microscopes";
Review of Scientific Instruments, 72 (2001), 8; 3320 - 3327.

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.