A Resonance Tracking Approach from Adaptive Control

Abstract

Resonance tracking is an approach to measuring concentrations, forces or viscosities. Such vibration-based measurements appear to be particularly well suited for applications at the micro- or even nano-scale. In order to monitor more than one parameter or parameter ratio simultaneously, a new kind of resonance tracking is developed with methods from adaptive control. It combines parameter estimation methods and state observers to adopt the resonant excitation to vibrating systems with time-varying parameters. At the same time, these parameters are measured. This approach is exemplified at two single-input-single-output (SISO) systems: a linear spring-mass-damper oscillator and a weakly nonlinear oscillator of Duffing-type.