Optimally Designed Nonlinear Feedback Excitation for High-Sensitivity Sensing

Employing sensitivity vector field (SVF) analysis in active micro-sensors can increase both their sensitivity and their ability to differentiate between changes in multiple sensor parameters. However, since SVF analysis is based on quantifying attractor deformations in state space, maximizing its effectiveness depends on selecting a sensor excitation that generates an attractor having suitable deformation with respect to the parameter(s) of interest. This paper addresses issues surrounding such system excitation design for a simple, linear vibration-based sensor having a combination of harmonic and nonlinear feedback excitation. In order to reframe the search for an optimal excitation as a search for a set of optimal control parameters, the excitation is considered to be of a specified form with a set of adjustable control parameters. Determining how to adjust the excitation parameters so as to maximize the magnitude of the resulting sensitivity vectors is then the formal goal. Using a pattern search method that avoids difficulties caused by bifurcations, we show that improved excitation can be designed reliably and efficiently. We also show that for short trajectory evolution times (suitable for “large” sensor perturbations) limit cycle behavior generates the best SVFs while for longer evolution times (suitable for “small” sensor perturbations) chaotic behavior may be more useful. Other issues discussed include the relative importance of various controller terms and the significance of harmonic excitation phase when generating sensitivity vectors.