Heterodyne digital control and frequency estimation in magnetic resonance force microscopy

This dissertation presents heterodyne control as a technique for computationally efficient digital feedback control of a high-frequency, narrowband micromechanical oscillator. In this technique, isolated and synchronized hardware downconversion and upconversion components are used in conjunction with digital signal processing (DSP) to control the oscillator. Heterodyne control offers several advantages over conventional control for high-frequency systems including reduced computational effort, reduction of noise outside the passband, and generation of lock-in amplifier signals useful for online diagnostics, system identification and adaptive control. I present two generally applicable techniques for the design of a heterodyne estimator and controller for a magnetic resonance force microscopy (MRFM) cantilever. Combined heterodyne regulators designed using these techniques have performance characteristics comparable to conventional optimal controllers. This dissertation presents design criteria for heterodyne control of a narrowband system as determined by closed-loop time delays, phase considerations and carrier/natural frequency mismatch; simulation and analytical results provide the basis for discussion. As the last point in the presentation of heterodyne control, I discuss implementation of the optimal heterodyne controller on physical digital signal processing (DSP) hardware and present experimental results of heterodyne control applied to an emulated radio-frequency microcantilever system.; The MRFM experiment requires frequency estimation both for adaptive control and the interrupted OScillating Cantilever-driven Adiabatic Reversal (iOSCAR) spin manipulation protocol. This dissertation also discusses the selection and characterization of a frequency estimation technique known as frequency modulation (FM) discrimination; FM discrimination is unbiased, computationally efficient, and useful for noise-driven resonant systems. Through statistical characterization, we introduce the mean and variance of the FM discriminator as applied to a noise-driven resonant system; experimental results validate the theoretical predictions for the open-loop system and quantify deviations from theory under closed-loop control.; Finally, this dissertation presents heterodyne gain-controlled oscillation (GCO), which also uses isolated and synchronized hardware downconversion and upconversion processes to sustain oscillation of a narrowband micromechanical oscillator at a given amplitude. FM discrimination is employed together with heterodyne GCO in the context of an MRFM iOSCAR experiment.