Optimal control of ultrasoft cantilevers for force microscopy

The goals of optimal control in force microscopy are: (1) to obtain favorable cantilever dynamic properties and (2) to control the cantilever to a desired amplitude, while (3) exerting as little control force as possible, and (4) preserving the force signal-to-noise ratio of the uncontrolled cantilever. This article describes the experimental implementation of an optimal controller that achieves these goals. The application of this controller to an ultrasoft cantilever with spring constant of 110 μN/m at 10 K reduced the resonant quality from 15 000 to 220, reduced the Brownian amplitude from 11.2 Å to 1.4 Å, used less than 7×10−17 N of control effort, left the force sensitivity unaltered at 9.8×10−18 N/ Hz, and demonstrated feedback control can force cantilever motion to track a reference input.