Optimal control of force microscope cantilevers. I. Controller design

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Abstract
In magnetic resonance force microscopy (MRFM) experiments, magnetic forces couple to the motion of microscale cantilever beams. Extension of MRFM to the detection of single electrons will require both unprecedented force sensitivity and motional stability of the cantilever. We describe the principles and performance of optimal cantilever motion control. The method accounts for inherent noise processes and practical application of control forces. We show that active feedback control improves cantilever motional stability, enabling instrument designs of much higher sensitivity and faster imaging than passive designs. Experimental results of implemented cantilever control systems are presented in Part II.