Nonlinear Estimation of Fluid Properties using the Time Domain Response of a Vibrating Microcantilever

Abstract

A novel approach is presented for the modelling and analysis of the dynamic response of a microcantilever beam vibrating in a viscous fluid to determine the properties of the fluid. This new approach is based on modelling the time response of the deflection of the free end of the microcantilever, whereas other methods developed in the field of rheological measurements using vibrating microcantilevers are generally based on the analysis of the frequency response of the deflection of the cantilever. The proposed approach consists of spatially discretizing the beam along its length, approximately representing it with a finite-dimensional state-space model and determining the fluid properties using nonlinear state/parameter estimation techniques. In this work, the discrete-time extended Kalman filter is employed to find estimates of the fluid’s viscosity and density using temporal measurements of the deflection at the free end of the beam. Simulation studies illustrating the validity of the proposed approach are presented.