Nanoforce estimation with Kalman filtering applied to a force sensor based on diamagnetic levitation

Abstract

Nano force sensors based on passive diamagnetic levitation with a macroscopic seismic mass are a possible alternative to classical Atomic Force Microscopes when the force bandwidth to be measured is limited to a few Hertz. When an external unknown force is applied to the levitating seismic mass, this one acts as a transducer that converts this unknown input into a displacement that is the measured output signal.Because the little damped and long transient response of this kind of macroscopic transducer can not be neglected, it is then necessary to deconvolve the output to correctly estimate the unknown input force. The deconvolution approach proposed in this article is based on a Kalman filter that use an uncertain a priori model to represent the unknown nanoforce to be estimated. The main advantage of this approach is that the end-user can directly control the unavoidable trade-off that exists between the wished resolution on the estimatedforce and the response time of the estimation.

Analysis of the trade-off between resolution and bandwidth for a nanoforce sensor based on diamagnetic levitation

“…An analysis of the trade-off between resolution and bandwidth is developped using a steady-state Kalman filter. Finally, some new experimental results different from whose present in [8] are presented.…”

“…It is aimed at the deflector located at the rear of the maglevtube (see Figure 3). The sensor is practically linear even for millimetric displacements of the maglevtube [8] [11] which makes a large range of force measurement possible. Coils located at the rear of the sensor are only used during the sensor calibration to generate a zero input response.…”

“…This approach only requires to adjust one parameter which seems directly related to a trade-off between the resolution and the bandwidth of the force sensor. This paper adds to [8] an analysis of this trade-off. Its goal is to provide some tools to the end-user to help him adjusting the parameter.…”

“…The DIO design proposed in [7] requires to set several parameters and the level of noise in the force estimation can't be directly adjusted. Another approach proposed in [8] is based on a Kalman filter using an uncertain a priori stochastic model to represented the unknown force. This approach only requires to adjust one parameter which seems directly related to a trade-off between the resolution and the bandwidth of the force sensor.…”

“…It is followed by a summary of the time-varying Kalman filter design presented in [8]. An analysis of the trade-off between resolution and bandwidth is developped using a steady-state Kalman filter.…”