Digital feedback controller for force microscope cantilevers

Abstract

We present a fast, digital signal processor (DSP)-based feedback controller that allows active motion damping of low- k, high- Q cantilevers in magnetic resonance force microscopy. A setup using a piezoelement attached to the cantilever base for actuation and a beam deflection sensor for tip motion detection is employed for controller demonstration. Controller parameters, derived according to stochastic optimal control theory, are formulated in a simple form readily implemented on a DSP, and extensions to other detection and actuation schemes are indicated. The controller is combined with an automated calibration scheme allowing for adaptive parameter adjustment. With the digital device operating at a sampling rate of 625 kHz and 16 bits of dynamic range, we were able to obtain closed-loop quality factors Qcl <5 for cantilevers with Q≈10 000 and resonance frequencies up to 15 kHz. This corresponds to an increase in bandwidth of > 103 at undiminished signal to noise, and reduces response time and vibration amplitude by the same factor. © 2006 American Institute of Physics.